How do we measure the gravitational constant?

Daniel and Jorge talk about the number that controls the strength of gravity and why it's so hard to measure.

See omnystudio.com/listener for privacy information.

Episode Transcript

Speaker 1 (00:08):
Quor, Hey, have you found your first gray hair yet?

Speaker 2 (00:11):
I have. I have quite a few of them. Yeah,
although I like to think of them as silver not gray.

Speaker 1 (00:17):
Oh that sounds like a good plan. Really lean into
the dignity of aging.

Speaker 2 (00:22):
I don't have a lot of dignity, but I am
definitely aging. How about you? How's your transition going to
full Einstein hairstyle mode?

Speaker 1 (00:32):
I still have no silver hair. In fact, I'm thinking
about dying my.

Speaker 2 (00:35):
Temples, dyeing them, like bleaching them to get gray hairs.

Speaker 1 (00:40):
Yeah. So people take me a little bit more seriously.

Speaker 2 (00:42):
Oh, I see, you want to look like one of
those senior established physicists gray hairs exactly.

Speaker 1 (00:48):
I want to increase my gravitass not just my personal gravity.

Speaker 2 (00:53):
Yeah, I may. Your problem is you're increasing in with
and not with them.

Speaker 1 (00:58):
That was a weighty burn. H.

Speaker 2 (01:14):
I am Poor hammy cartoonist and the creator of PhD comics.

Speaker 3 (01:17):
Hi.

Speaker 1 (01:18):
I'm Daniel. I'm a particle physicist and a professor at
UC Irvine. And I was once accidentally c seed on
an email where I was described as young ish.

Speaker 2 (01:27):
Oh all right, yeah, that's good. But how long ago
was this? Was this like twenty years ago, in which
case it was true back then.

Speaker 1 (01:34):
Yeah, long enough that I shouldn't be telling that story anymore.

Speaker 2 (01:39):
Right, You're like I was in my thirties and people
were calling me youngish. That's a better adjective than many
other adjectives people can call you.

Speaker 1 (01:48):
Absolutely, I'd rather be youngish than oldish or stinkish.

Speaker 2 (01:51):
But anyways, welcome to our podcast, Daniel and Jorge Explain
the Universe, a production of iHeartRadio.

Speaker 1 (01:56):
In which we dig into the mysteries of this oldish
universe and our youngish attempts to understand it. We think
that the universe should make sense to humans. We should
be able to go out there and measure things about it,
to figure it out, to unravel its mysteries, and to
explain it to each other. And that's our job on
this podcast to unravel as many of those mysteries as

(02:17):
possible and to explain them to you.

Speaker 2 (02:19):
That's right, It's our job to increase the gravity of
your brain. Hopefully all of this amazing knowledge about the
universe is maybe making more connections in the neurons in
your brain and making your brain grow a little bit,
and also increasing the wisdom in there. Because I guess
knowing about the universe sort of increases your wisdom, right,
if you know how the world works, that's sort of
the definition of wisdom.

Speaker 1 (02:39):
Yeah, what other kind of wisdom is there other than
knowing how the world works? If you lump like people
and animals and society and all that kind of stuff
into the world. And that's exactly what we're trying to do.
We're trying to describe the world. And the way we
do it is by telling these mathematical stories. We say
there are relationships between these things. We notice if you
push on this thing a certain way, goes a certain speed,

(03:01):
or they don't move if you don't push on them.
All these things are mathematical stories that we use to
describe the universe that's out there. We hope to boil
it down to a bunch of equations, which in the end,
they're just describing what we see out there in the universe.

Speaker 2 (03:15):
It's right, we're trying to find what the wise crack
of the universe is. That kind of what the job
of a physicist is.

Speaker 1 (03:24):
I hope there will be some humor in these stories.
You know, every good story has some comic relief in it,
even mathematical.

Speaker 2 (03:29):
Stories, but I guess it's wisden the same as common sense.
Do you think the universe has common sense?

Speaker 1 (03:34):
Absolutely not. Intuitive ideas about the universe what makes sense
to us from our limited experience here on Earth are
not always reflective of what's really happening in the universe.
You know, it made sense to Aristotle that things fell down,
but that doesn't mean that everything always falls down, or
that down't even means something when you're out in space
far away from any gravity.

Speaker 2 (03:55):
Yeah, it is a pretty perplexing universe, and sometimes it
sort of seems like it does think that that don't
make sense, And in fact, you can sort of ask
the question whether humans will ever make full sense of
the universe or if there are just some things about
it that are sort of random, right, or arbitrary.

Speaker 1 (04:10):
Yeah, there's lots of layers. There are humans smart enough
to describe the workings of the universe in terms of
our mathematics. Is our mathematics actually the language of the
universe itself or just our description of what we see?
And philosophically, we aren't even sure if there is a
single mathematical prescription that describes everything that happens out there

(04:30):
in the universe. A whole group of philosophers believe in
disunity that there might not be a single holistic description
of the universe. So it's pretty complicated, but we do
our best. We find these mathematical stories, which are equations.
They relate things like force and acceleration, or force and mass,
all sorts of things. But they're not just equations. The
equations also have numbers in them, constants that describe the

(04:54):
way the universe works.

Speaker 2 (04:55):
Yeah, the universe seems to have lots of consonants, lots
of numbers in them, like pi, and I guess the
expansion of the universe is also defined by a number.

Speaker 1 (05:04):
Yeah, that's right, the speed of light, All sorts of
things seem to control the way that the universe works.
And in lots of cases, we don't know why they
have this value and not some other value. Why is
the universe expanding at this rate? Why is the speed
of light not faster or slower? Why are some of
the forces strong and some of them are powerful. It
seems like there's a control panel somewhere on the universe,
and all these things are just parameters. They're just like

(05:26):
knobs on the control panel, and you could have twirled
them one way or another way and still gotten a
universe one very different from ours. But we don't know
if there's a reason why the parameters have the values
they do.

Speaker 2 (05:37):
I feel like every time you say that the universe
has a control panel, I always imagine, for some reason,
the Simpsons, you know, the opening scene with Homer sitting
in front of like the control panel floor for the
nuclear plant that he works at. I always always imagine
that when you say the control panel of the universe, Like,
is there a Homer Simpson about to spill some coffee
or donuts onto the fabric of our universe?

Speaker 1 (06:00):
That would explain maybe why the universe seems so crazy
and bonkers sometimes because maybe there's an idiot in charge.

Speaker 2 (06:06):
Because it was designed by bad groaning exactly, or because
Homer symptom isn't charge.

Speaker 1 (06:11):
Yeah, either because there's a cartoonist who's the designer of
the universe and we all know they can't be trusted.

Speaker 2 (06:18):
Are you saying God is the ultimate cartoonists or cartoonists
are the ultimate gods?

Speaker 1 (06:22):
I'm saying if either of those are true, then we're screwed.

Speaker 2 (06:26):
No, wouldn't you want to live in a cartoon, Like
if the universe was controlled by cartoon physics, I mean,
wouldn't that be more fun? Wouldn't your job be more fun?

Speaker 1 (06:36):
My job would be impossible because there is no physics
in cartoons. There don't seem to be any laws that
anybody follows. It's just like make it all up as
you go. So science is basically out the window.

Speaker 2 (06:47):
Is that your goal, well, to put you out of
a job. meEach episode, I'm trying to embarrass us to
the point where we don't know what he gots anymore.

Speaker 1 (06:58):
But it does seem like there are the laws that
describe what's out there. And sometimes in these laws there
are just numbers, like if you look at Maxwell's equations
or how electromagnetic radiation propagates to the universe, there are
a couple constants in there, the permittivity of free space,
for example. All those things determine the speed of light.
But these are just numbers that we measure in the universe.
We don't have like a theoretical reason to say why

(07:20):
should be this number or the other number. It's just
like an unknown parameter in the equations that we have
to go out and do experiments to discover.

Speaker 2 (07:28):
Yeah, like you were saying, like the speed of light,
it is three hundred thousand meters per second, but it
could also be something else. And that's what you mean
by a control not like somehow when the universe was created,
somebody said that not to three hundred thousand meters per second,
but it could have been something else.

Speaker 1 (07:42):
Yea, actually I think it is something else. It's three
hundred million meters per second.

Speaker 2 (07:45):
Oh three, that's what I said.

Speaker 1 (07:47):
You go, somebody fell asleep on the control panel and
the speed of light is slower over there in Pasadena
than it is down here, apparently.

Speaker 2 (07:53):
Well there you go. Don't put me in charge of
the knob because obviously we've set it to a thousand
times the wrong aunt.

Speaker 1 (08:01):
All right, Homer. But these constants are fascinating, and physicists
look at them and they go, why this number, why
not some other number? Especially when the numbers are weird.
The numbers are like one or two, people are like, yeah, cool,
that makes sense. But if the numbers are like seventy
four bajillion or ten to the negative thirty two, people
are like, that's really strange. It's got to be a story.

Speaker 2 (08:21):
There, right, Because I guess if it's one, then that
means that something canceled out sort of right.

Speaker 1 (08:26):
This is a really controversial way of thinking in theoretical
physics to say that like numbers like one are natural,
that they make sense. That you know, two things are
related by a factor or close to one, that means
that it's a natural relationship. And if the factor is
really really big, then you got to ask why what's
going on? So why didn't things cancel out? Why are
these things not in balance? It's really kind of esthetics.

(08:48):
It's not really driven by any deep principle in theoretical physics.
It's just like wondering why numbers are not close to one,
just preferring numbers close to one. There isn't even really
a great argument that I could take for why you
would prefer numbers close to one.

Speaker 2 (09:03):
Well, they say one is the loneliest numbers, So maybe
you're an introvert. That sounds like the best number.

Speaker 1 (09:09):
Maybe the secrets to the universe are actually hidden in
the names of eighties pop.

Speaker 2 (09:13):
Songs, Yeah, there you go, or in the lyrics, right,
maybe eighties pop stars are the gods of the universe.

Speaker 1 (09:20):
Yeah, maybe it's all just about ice. Ice baby.

Speaker 2 (09:23):
Yeah, there wasn't there a group called Genesis back in
the eighties. There you go. Well, so there are all
these amazing numbers that seem to sort of control how
the universe behaves and what it does and what the
particles in it all do. But we don't understand some
of these constants, and in some cases we don't even
know exactly what they are, right.

Speaker 1 (09:41):
That's right. Sometimes we can do experiments to measure them
very very precisely, but some of these are a little slippery.
Some of them are very difficult to actually nail down,
especially one of the most fundamental constants in the universe.

Speaker 2 (09:55):
Yeah. So today own the program, we'll be asking the question,
how do we measure the gravitational constant G upper case G,
that's how you call it.

Speaker 1 (10:07):
In physics, we call it big G, or the universal
gravitational constant, because we want to distinguish it from little G,
which is the acceleration due to gravity here on Earth
nine point eight meters per second squared, which everybody uses
in their freshman physics class, and big G is the
number that appears in like Newton's equation for gravity.

Speaker 2 (10:26):
Mmm, do you think G has anyone asked, gieve it
minds being called big G.

Speaker 1 (10:33):
I'm glad that you're always thinking about these things from
the point of view of the subject. You know, in
physics we tend not to anthropomorphize everything. But I'm glad
that somebody out there is looking out for the little
g's and the big g's of the world.

Speaker 2 (10:45):
Well, that's what cartoonists are here for, to anthrop forum
orphize everything, even physics, I guess, But I guess it's
big G, like like you said, to distinguish it from
the little G that I think most people are familiar
with from like high school physics. Right, little G is
the one that tells you the exceleration of gravity here
on Earth, Like if you drop a ball, it's going
to accelerate at nine point eight meters per second square.

(11:05):
That's little G. Uppercase G is the more general gravitational constant.

Speaker 1 (11:10):
That's right. Little G is only relevant on the surface
of the Earth. If you go up in an airplane
and you go deep down into the Earth, you're going
to feel a different acceleration due to gravity because you're
going to have a different amount of mass of the Earth,
or be a different distance from the Earth. And on
other planets or in other solar systems. Little g's are
totally irrelevant number. I mean, there's like a medium G
and a smallish G. There's a G junior and a

(11:33):
G the third and all sorts of gs. Men is
the OG you know, a G whiz. But big G
is universal. It's supposed to reflect something about the universe
itself and be independent of anything that happens on Earth
or the size of the Earth, or your distance from
the Earth. It's something about the universe, not something about

(11:53):
our neighborhood.

Speaker 2 (11:55):
Right, So this is like the G that relates to
the actual force of gravity exactly.

Speaker 1 (11:59):
It's the numbers that controls really the strength of gravity
in the universe.

Speaker 2 (12:03):
Well, as usually, we were wondering how many people out
there had thought about the uppercase G of the universe
and how we might measure it.

Speaker 1 (12:11):
So thank you very much to everybody who answers these
questions for this fun segment of the podcast. We love
hearing your thoughts, and if you would like to share
your thoughts for a future segment, please write to me
too questions at Danielandjorge dot com. Everyone wants to hear
your voice.

Speaker 2 (12:27):
So think about it. For a second, how do you
think the universal gravitational constant G is measured? Here's what
people have to say.

Speaker 4 (12:34):
I assume gravitational constant G is unique to planet Earth,
which exerts gravity upon us. To calculate that constant, I
would try to figure out how much force is necessary
for us to go against the gravitational force of Earth,
and then we know what the gravitational force itself is.

Speaker 2 (12:51):
I think we measure the gravitational constant by measuring how
quickly galaxies and moving away from us and stretching the
space in between.

Speaker 1 (13:00):
This is an easy one for me to answer, because
I don't know what the gravitational constant G is, but
I'm looking forward to hearing and finding out.

Speaker 5 (13:07):
I guess it's true. The observation of planets, stars and
other celes your bodies, and coming to a number that
adjusts that motion to our other units of measuring.

Speaker 3 (13:19):
Probably something to do at the moon. See we can
estimate its mass, estimate the Earth's mass, then see what's
going on there, and we can probably find a G.

Speaker 2 (13:29):
All right, Well, somebody here confusedly with little G. You
know they do look alike.

Speaker 1 (13:33):
I guess do theyre?

Speaker 3 (13:34):
Though?

Speaker 1 (13:35):
Big capital G and little G look pretty different. I
sent this an email, so I wrote explicitly big G. Hmmmm,
I'm not giving a lot of partial credit on that one.

Speaker 2 (13:44):
Oh boy, there's pointage involved here. Do you get a grade?

Speaker 1 (13:48):
I'm handing out degrees over here.

Speaker 2 (13:50):
And I don't think that's going to encourage people to
call it.

Speaker 1 (13:53):
Well, look, if you want to get your PhD in
podcast science, then you know you got to take it
for credit.

Speaker 2 (13:57):
None of this past fial stuff I see. But everyone
gets an A though, right.

Speaker 1 (14:02):
Yeah, I'm a softy. I'm not going to give you
a lot of.

Speaker 2 (14:05):
A little A or a capital A.

Speaker 1 (14:08):
I give everyone a big A plus. I'm a softy
in the end. All right.

Speaker 2 (14:11):
But some interesting answers here, Like some people are saying
you can measure the gravitational constant by looking at planets
and stars and how things move around in space.

Speaker 1 (14:18):
Yeah, those are interesting ideas, but fundamentally they don't work
because they don't let you establish what G is because
you don't know what the masses of those planets are,
and so there's too many unknowns in that equation.

Speaker 2 (14:30):
And somebody said it has something to do with the moon,
like maybe you can measure G using the moon.

Speaker 1 (14:34):
Yeah, and again, you could measure G using the Moon
and the Earth if you knew very very precisely the
mass of the Earth and the mass of the Moon.
But if you don't, then you can't use that to
measure G.

Speaker 2 (14:46):
All right, let's dig into it. Lets first of all
define for our audience, what is the gravitational constant G.

Speaker 1 (14:52):
So the gravitational constant G is the number that defines
the strength of gravity, and it appears in Newtonian gravity
in his equation for the force between two objects that
have mass. So Newtonian gravity says that the force is
big G times one mass times the other mass divided
by the distance squared, So gmm over R squared, and

(15:15):
that number G is the one that controls it. If
G was bigger, you would have a larger force between objects,
and if G was smaller, you would have a smaller
force between objects of the same mass and at the
same distance. So it's really just this like tunable parameter.

Speaker 2 (15:29):
And it's kind of what determines how strong the gravity
is between two things. Basically, right, Like, what's the basic
Newtonian formula for gravity?

Speaker 1 (15:36):
Exactly? The Newtonian formula for gravity has big G in it.
It's just gmm over R squared. And it's a similar
structure to other forces, right, Like the electrostatic repulsion between
two objects like two electrons or whatever, has the same structure,
and it also has a constant in front of it.
It's a different constant. So each of the forces you
can write using this kind of equation, and each one

(15:57):
has a constant in front of it that tells you
how powerful the force is.

Speaker 2 (16:01):
So like, if you had two things floating out there
in space, a mass one and a mass two, you
can compute the force that attracts them together. We're using
this formula, right. You take the mass of one thing,
and then take the mass of the other thing. You
multiply together. You divide by the square of the distance
between them, and then you take the number and that's
what you multiply by G to get the force of

(16:22):
gravity between them exactly.

Speaker 1 (16:24):
And if we lived in a universe where G was
twice as big, or if the cartoonist at the control
panel fell asleep on the knob and doubled big G,
then all the forces of gravity would be twice as big.
And if you divided G by a factor of two.
If you made it twice as small, then the force
of gravity would be twice as small.

Speaker 2 (16:42):
Yeah, And so that's why it's called the universal gravitational constant,
because it's supposed to be the same all over the universe, right, Like,
if you measured the gravity between two things here or
in another planet or in another part of the galaxy,
you should be able to use the same constant G
to calculate that force exactly.

Speaker 1 (16:58):
And what if Newton's great achievement was using this to
describe gravity here on Earth between fairly small masses and
small distances, and gravity between planets and stars and moons,
to show that it works in lots of different settings
over huge differences and masses and huge differences in distances.
So you sort of unified the heavens and the Earth
in that sense. So yeah, it's supposed to be universal.

Speaker 2 (17:21):
Yeah, And it's pretty amazing that the formula is so
simple if you think about it, right, it's like one multiplication,
one division, and one squared and boom, you can like
decipher the workings of the universe, you know, Like it's
not like the one point seventh square root of the
distance between them nuts, it's like the square of the
distance between them. And it's just like mass one times

(17:41):
mass too. It's not like mass one plus seventeen divided
by five point two. You know.

Speaker 1 (17:47):
Yeah, it is kind of cool, and the structure sort
of makes sense. Like, first of all, it has to
be symmetric. It can't be like mass one times mass
two squared, right, because it needs to be the same
force between mass one and mass two. At mass two
and mass one, right, it shouldn't matter which one you
call mass one or mass two, So it has to
be symmetric. It also makes sense that it's one over
the distance squared because as things get further and further apart,

(18:11):
the force gets diluted over a larger and larger area,
and the surface area of that sphere grows with the
distance squared, so the same way like if you have
a light source like a star, and you're twice as
far away from it, then the same number of photons
are now distributed over a larger sphere. That sphere has
four times the area, and so one of our distance square.
It really makes sense, and I think that's why it

(18:32):
appears in all of the force laws, not just the
one for gravity, the one for electromagnetism also has a
one over distance squared.

Speaker 2 (18:40):
Right, it makes sense. But it didn't have to be
that way, right, it could have been r to the
one point seventy two or something like that.

Speaker 1 (18:46):
Right, Yeah, it could have been. And there are actually
theories of gravity that do change that that suggest that
gravity changes at very small distances maybe or at different accelerations.
So it's not one over are squared, but one of
our squared is also the simpler. But you're right, the
universe didn't have to make sense, and it doesn't have
to be simple. It could be crazy complicated.

Speaker 2 (19:05):
All right, Well, that's the universal gravitational constant uppercase G,
which tells you the strength of the force of gravity
in the universe. But as we know, gravity is not
quite a force, and also maybe this constant can change,
so let's dig into that. But first let's take a
quick break. All right, we're talking about the universal gravitational

(19:34):
constant uppercase G. It basically kind of tells you the
general strength of the force of gravity in the universe. Right, Like,
if G was much bigger, then the gravity would be
much stronger in the universe. If it was smaller, gravity
would be much weaker.

Speaker 1 (19:48):
Exactly, and we don't know why it has this value.
There's nothing in physics that says it should be this number.
There's no set of equations you can use to like
derive it or predict this value. It's just something we
have to go out and measure and discover in the universe.

Speaker 2 (20:02):
Right. So the origin of this constant is that it
came from Newtont's right, Newtent's laws about the force of
gravity between like planets and the sun and things like that.
But nowadays we think of gravity more like a bending
of space. Does the gravitational constant G still come into play?

Speaker 1 (20:19):
Then it actually does. The same constant G also appears
in Einstein's equation. So we've replaced Newtonian physics that says
that there's a force between masses and that pulls them
together by saying, actually, there's no force there. It just
looks like a force. What's really happening is that masses
are bending space, and when they move through that bent space,

(20:42):
it looks like there's a force on them. And Einstein
gives us equations that describe how that space is bent
when mass is around, and those equations the Einstein field
equations also have constants in them, and one of those
constants is big G, the same exact number, And that
shouldn't be a surprise because einstein field equations also reproduce
all the predictions of Newtonian physics, like Einstein and Newton

(21:06):
agree about the force on the Earth from the sun,
for example, because you know, Newtonian physics got a lot
of stuff right, So it wouldn't make sense if they
had totally different constants.

Speaker 2 (21:14):
Now that Einstein sort of derived this constant independently, or
did he like start with Newton's equations and kept it in.

Speaker 1 (21:20):
You can't derive this constant, right. If we didn't have
Newton and we just started with Einstein, he would have
come up with his field equations and said, okay, but
there's a number in it, and I don't know what
that number is. Let's go out and measure it. In
the same way that when we first got Newton's equations.
There's a constant in there, and we have to go
out and measure it. And Newton actually suggested some ways
to go and measure this. So Einstein just sort of

(21:42):
inherited this constant from Newton.

Speaker 2 (21:45):
Interesting, all right, Well, then what's the current value of
what we think G or uppercase G is.

Speaker 1 (21:50):
So it's a really tiny number. It's six point six
seven times ten to the minus eleven, and the units
on it are kind of weird. It's meters cubed divided
by kilograms times seconds squared. It's this very small number
like ten to the minus eleven.

Speaker 2 (22:07):
WHOA, So that's one of the reasons kind of why
gravity is so weak too, right, because the G is
such a.

Speaker 1 (22:12):
Small number, that's exactly the reason why gravity is so weak.
If G was much much bigger, gravity would be much
more powerful. And so this number is the number for
G in our universe, and we don't know are there
other universes out there with different values for G that
have like much more powerful gravity and they all collapsed
into black holes to a few seconds after being birthed.

(22:32):
Are the universes out there with even weaker g's and
those universes still haven't even made stars because there isn't
a powerful enough gravity to pull that stuff together. We
just don't know if there are other options for this
thing and why we have this value. But you're right,
it completely controls the strength of gravity. And what's super
weird about it being so small is that the other
forces have much bigger constants, which is why gravity is

(22:55):
so much weaker than all of the other forces.

Speaker 2 (22:57):
Well, I feel like you're blaming the gravitational constant here,
but it could also just be like things don't have
enough mass, Like maybe things were more massive, do you
know what I mean, and then the force of gravity
would be stronger.

Speaker 1 (23:08):
Yeah, exactly. There's a subtlety there in how you compare
different forces, Like how do you compare electromagnetism and gravity. Well,
you take objects that have mass and have charge, like protons,
and you hold them apart at a certain distance, and
you calculate their relative strengths. And so, for example, if
you hold two protons like a centimeter apart, then you

(23:29):
discover that gravity is ten to the thirty three times
weaker than the electromagnetic force. But you might say, hold
on a second, that's just because protons have almost no
mass and a big charge. If we lived in a
universe where protons had tiny charge and huge masses, then
you would say gravity is stronger. And yeah, you're absolutely right,
But the kind of things that exist in our universe

(23:50):
tend to have a certain amount of mass per charge,
and that means that gravity ends up being really really
weak compared to electromagnetism. So yeah, blame it on the constant,
or blame it on the particles. But it's somebody's fault.

Speaker 2 (24:02):
It's somebody's fault that the things that you don't weigh more,
or that you do weigh a lot.

Speaker 1 (24:07):
Everything is somebody's fault, somebody else's fault. Right in this case,
I think it is a fair comparison to say, typical
particles in the universe, what is their relative gravity versus
their relative electromagnetic repulsion? And what you find is that
they're not even close. Right, Like gravity is weaker. It's
not even a little bit weaker or a lot weaker.
It's ridiculously weaker. It's ten to the thirty three times weaker.

(24:29):
It's like negligible compared to the force of electromagnetism. And
that's due to this constant, Like electromagnetism has its own constant,
and it's just a much bigger number, right.

Speaker 2 (24:39):
I think what you mean is like if I had
two protons out there in space and I bring them
close together, like the force of electromagnetism, that's going to
be repelling them is like thirty two orders of magnetude
more than the force of gravity bringing them together exactly.
All right, well, let's dig into what it takes to
measure the gravitational constant G. It's pretty hard, right because

(25:00):
as we're as we're saying, gravity is super weak.

Speaker 1 (25:02):
Yeah, there's like three reasons why measuring big G is
actually really really hard. Number one is what you said
that gravity is weak. You know, it's not easy to
measure these things because you need big masses. You can't
really measure the gravity between two protons. It's so small
that you could never really measure it. So you need
bigger and bigger objects. And that brings you to the
second reason why it's so difficult, which is that it's

(25:24):
hard to shield gravity from other things. Like you're always
going to be feeling the gravity of everything else around you,
you know, like your laboratory and the mountains and the Earth.
So it's hard to get like an isolated system to
study gravity.

Speaker 2 (25:38):
What do you mean isolated? Like because the Earth is
pulling you down with gravity, but you can still maybe
measure gravity. It's side to side, right, like if I
just put two balls on my table technically, they are
being attracted to each other by gravity. Couldn't I measure that?

Speaker 1 (25:50):
Yeah, you certainly could. But they're also being attracted by
the gravity of your wall, and the gravity of the
tree outside, and the gravity of the mountains nearby. And
that's not true for other forces. Like for electromagnetism, you
can you have positive and negative charges, and so you
can shield things. You can like balance all the forces
out so that electromagnetism is effectively zeroed out and study

(26:11):
it at small scales. But for gravity, there's no way
to shield your laboratory from the gravity of your surroundings
unless you get like really really far away from everything.

Speaker 2 (26:20):
What do you mean, Like, I can't just conduct my
experiment on a really tall tower or you know, at
the top of a mountain, or maybe even on a satellite.

Speaker 1 (26:28):
Yeah, on a satellite would be great. The further you
can get from other masses, the better you could do
this experiment. So if you did your experiment measuring the
gravitational strength between two objects, like out in the middle
of a super bubble, far away from everything, that would
be great. But that's one of the challenges, right we
don't have the way to do that experiment out in
the middle of space. We have to do our experiments
here in the vicinity of Earth, which has its own gravity.

Speaker 2 (26:51):
Well, it sounds like maybe the difficulty is in like
isolating it. It's more like it's super weak, right, because
like you could do it through this experiment out in
a satellite, right and and you know the as it
goes around the Earth, things would cancel out anyways. Right.

Speaker 1 (27:04):
Yeah, it's just one reason why it's difficult. The primary
reason I think is that gravity is just so weak.
You know, you're trying to measure a very very small
effect and it's swamped by all sorts of other effects.
You know, if you have, for example, two masses and
you want to measure their gravity between them, then you
have to hope that there are no other forces bigger
than the gravitational force also operating on those masses that

(27:25):
would just swamp your measurement. You know, if there's like
a tiny residual electric charge on these masses because you
touch them and you got static electricity on them, it
will be so much more powerful than the gravitational force
you're trying to measure that it will just swamp your measurements.

Speaker 2 (27:39):
Well, maybe we should paint a picture here for people, like,
how would you even design an experiment like this? Like,
let's say I'm proposing to you, Daniel, that we go
up in the Space Shuttle or we go out in
a rocket out to the International Space Station. I'm going
to take two Billard balls, put them, you know, ten
centimeters apart, and then I'm going to watch how long
it takes them to get attracted to each other by gravity.

(28:00):
Wrong with that experiment?

Speaker 1 (28:01):
Yeah, you could do that, that would work. Nothing that's
wrong with that experiment except that it requires going up
to space, and also you have to account for all
the other masses nearby, right, Like the space station is
also going to be tugging on these things, and the
space station is probably a lot more massive than the
balls you brought. You can't bring super duper heavy balls
up into space because you have limitations on the expense

(28:23):
due to the launches.

Speaker 2 (28:24):
You mean, like I said, I have those two balls
leading in front of me. They're being pulled together by
the gravity they have with each other, but maybe they're
also being pulled apart a little bit by the space
station around them, right, Or like if my fellow astronauts
it's to the right of me or to the left
of me. It might influence how those two balls come
together exactly.

Speaker 1 (28:42):
And because you're trying to measure something very very small,
then you need to be very very accurate about your measurements,
and small changes in your results can lead to large
changes in the results that you get.

Speaker 2 (28:53):
What if I just do it a lot, or what
if I tell everyone to stay still not move in
the space station? Wouldn't that give me a pretty good experiment?

Speaker 1 (29:04):
Yeah, that would measure it. I don't think that would
come close to the precision we have today. And also
it would be really expensive. Everything out in space is
very expensive and very complicated.

Speaker 2 (29:13):
All right, What are some of the other reasons that
make it difficult?

Speaker 1 (29:16):
I think the last reason is just that there's no
like relationship to the other constants, you know, the other forces.
We think there might be some relationship with them. Electromagnetism
and the weak forces can get bundled together into the
electroweak force, and there's some unity there. We have theories
about how the strong force might connect with that, and
so we have like a unity of the forces. But
gravity is by itself. We don't know how to bring

(29:38):
gravity into quantum physics, so we have no like way
to predict or like constrain the value of this force.
You really just have to go out and measure it.
There's no other way to analyze it, right.

Speaker 2 (29:49):
I always thought the hard thing about measuring the gravitational
constant was that you know, to get a measurement of it,
you sort of need to know like in our biller
ball example, you sort of need to know exactly what
the masses of those biller balls are. But it's hard
to know what the mass of something is if you
don't already know the gravitational constant. Right, isn't that one
of the big problems. It's like a chicken and egg problem,

(30:10):
like how do you measure gravity. To measure gravity, you
need to know the mass of something. But to the
mass of something you need to weigh it, which you
need for which you need to know the gravitational constant.

Speaker 1 (30:19):
Yeah, in the end, it comes down to what do
you know? First? If you know the masses of two objects,
you can measure the force between them, and then you
get big G. If you know big G and the forces,
then you can measure the masses between them. So the
basic story of measuring big G is finding a scenario
where we already for other reasons, know the masses of
two objects that we can use to measure big G.

(30:42):
That's the struggle. That's why we can't, for example, have
looked at the Earth in the sun hundreds of years
ago and used those to determine big G because we
didn't know the masses of the Earth and the Sun.
To derive the masses of the Earth and the Sun
from like their relative motion, you have to know the
force between them, and you'd have to know big G.

Speaker 2 (30:58):
Well, maybe a step as through then, like what's the
history of trying to measure this universal constant?

Speaker 1 (31:03):
So it goes all the way back to Newton right.
Newton described this relationship between stuff and there was a
constant there, and he suggested how you might measure this constant.
He said, maybe if you had, for example, like a
pendulum basically a heavy ball on a string, and you
brought it near something massive like a mountain, then you
might be able to measure the deflection of that ball

(31:24):
as it's like tugged on by the mountain. Interesting bit
of history, though, is that Newton didn't write down big G.
He never wrote that down doesn't appear in his works
because Newton was working at a time before we expressed
our theoretical laws in terms of algebraic expressions. Back then,
all of our physics was done in terms of sentences

(31:44):
rather than in terms of algebra.

Speaker 2 (31:46):
I thought you were going to say, he did it
in a time before we started body shaming our letters.

Speaker 1 (31:52):
No, So if you go back and like read the Principia,
you know, he expresses his law of gravity in terms
of a sentence. You know, he says it will be
mutually gravitating towards each other at a rate relative to
the reciprocal the square of their distances. You know, he
doesn't summarize at all in terms of mathematics. So he
never actually wrote down Big G. It wasn't until a
couple hundred years later that I started being called big G.

(32:14):
But Newton had the basic idea. He's like, if you
know the mass of a mountain and the mass of
a pendulum, maybe you could make this measurement.

Speaker 2 (32:21):
Right, But again that's kind of the problem that you
don't really know the mass of the mountain.

Speaker 1 (32:25):
Well, what you could do is measure the mass of
the mountain. You could say I know the density of rock,
and I could measure the volume of the mountain and
so from that I could estimate the mass of the mountain.
And this is actually what people did. The first measurements
of big G come from holding a pendulum near a
mountain in Scotland and seeing how it deflected.

Speaker 2 (32:44):
No way, this actually.

Speaker 1 (32:45):
Works, This actually works. Yes, it was a huge project.
This was done in the seventeen seventies. There's a mountain
in Scotland and it's a good choice because it's like
isolated from other mountains. It just sort of like sticks
up and like a nice symmetrical shape, which means that
it was not super complicated to describe its shape and

(33:06):
calculate its volume. And also it's like got really steep slopes,
so you get kind of close up to its center
of mass. Take the maximum effect. And there's like a
whole team of people that spent like years up there
making very precise measurements of pendula with heavy masses on
them and measuring their deflection and surveying the mountain to
try to estimate its volume as precisely as possible. It's

(33:27):
a huge project.

Speaker 2 (33:28):
Wait, what so like if I hang a Billard ball
from a string right and hold it in front of me.
It's going to hang straight down. But as I walk
towards a big mountain, it's going to start to lean
or get pulled and actually start swinging that way.

Speaker 1 (33:43):
Yeah, it will get pulled towards that mountain, so its
resting position will not be straight down. If you follow
the string up, it will not point perfectly towards the zenith.
It will be slightly deflected. And the bigger the mass
of the mountain, or the bigger the value of big G,
the stronger the deflection. So if you know the mass
of the mountain, then you can measure big g s.

(34:04):
This is the whole game, is knowing the masses of
two things and then measuring the forces between them. There's
a fun little wrinkle here, though. You might think that
you also need to know the mass of the earth,
because that's also pulling on your pendulum. But if you
know the volume of the mountain and the volume of
the Earth, which we do, then the angle of deflection
of the pendulum depends on the relative densities of the

(34:27):
Earth and the mountain, which one is denser. So really
the experiment measures the density of the Earth, which wasn't
known at the time. Of course, knowing the density of
the earth and the volume lets you calculate the mass
of the earth, and therefore let you get big g m.

Speaker 2 (34:44):
I guess you could use this to like measure people's
masses too. Like if you walk around a better ball
on the string and just kind of walk around and
get it close to people, you could technically right measure
their mass.

Speaker 1 (34:55):
Technically, yes, you could measure their mass.

Speaker 2 (34:58):
And be like, hey, big Daniel, I mean uppercase Daniel.

Speaker 1 (35:01):
If somebody had like accidentally ingested a lot of heavy metal,
you could detect it. Yeah, absolutely all right.

Speaker 2 (35:06):
So that was in the seventeen hundred And they did
this and what did they find? What value did they
come up with?

Speaker 1 (35:11):
So they made a measurement of this thing and they
got the number right to within about twenty percent. So
they measured this, which is I think pretty awesome. Like
this is a hard piece of work. There's one guy
who spent just like years calculating the volume of this
mountain from all these survey measurements. He turned it into
prisms and calculated the volume of each of those and
added them all up. And you know, this is before

(35:33):
computing and before any sort of modeling. This is in
the seventeen hundreds. He's working by like lamp light and
with a quill. But they got the right number within
twenty percent. So it's pretty impressive. And that also means
that they made the first real measurement of the density
of the Earth. They found that it was four and
a half times the density of water and almost twice

(35:53):
the density of that mountain in Scotland. That was a
bit of a surprise because we didn't know the internal
structure of the Earth in Newton's time. Some people thought
the Earth was like a huge hollow shell. So this number,
so much higher than the density of the mountain, was
a really fascinating early clue that the Earth has a
really very dense core. It's a really very cool result

(36:16):
with pretty basic tools.

Speaker 2 (36:18):
Wow. Pretty cool. And so let's get maybe into some
of the other ways that people have measured this as
well as maybe the most recent measurements and see how
they measure up and it's weigh them together. But first
let's take another quick break. All right, we're talking about

(36:43):
the universal gravitational constant. We know that it's kind of
weak compared to the other forces, But it's super monumentally
important in the universe because it basically determines how stars
and planets form, how galaxies form, basically determines the whole
structure of the universe.

Speaker 1 (37:00):
Yeah, exactly, it's one of the parameters on that control
panel of the universe that tells us why our universe
is this way and not some other way.

Speaker 2 (37:09):
And so we're talking about how you actually measure this
because it's tricky because a gravity is so weak, but
also b you need to know the masses of things
before you can measure this constant. But to measure the
masses of things, you sort of need to know the constant.
And so people have tried different ways. They did it
first in the seventeen hundreds and they got within twenty percent.
What was the next step?

Speaker 1 (37:29):
So that method holding a pendulum near a mountain worked,
but it was pretty imprecise because the mountain is like
a big fuzzy object. We don't really have a strong
handle on its density. You know, is it all the
same rock all the way through? What exactly is the
volume of it? And so people decided to shrink the
experiment down to something smaller that they could control. But
then you need a lot more precision because in the

(37:51):
effect it's going to be a lot lot smaller. So
instead of having one pendulum and a mountain, instead they
basically have two pendulam But if you just have like
two billion balls hanging near each other, the force between
them is so small that you're not going to be
able to measure any sort of deflection. So there was
a geologist, John Mitchell who came up with a really
clever way to measure a very very tiny force between

(38:14):
two billiard balls.

Speaker 2 (38:15):
Essentially, how'd they do it?

Speaker 1 (38:17):
So what they do is they have a pair of
these balls on a rod, and then they hang that
rod from a string, and then they bring two other
massive balls closer to these two balls on the rod,
and they measure how strongly the rod is attracted to
these other massive balls by measuring how far the string twists.
So instead of measuring like the deflection from the vertical,

(38:39):
which is a tiny, tiny amount, they can measure like
how far this thing has twisted this string it's hanging from.
So it's called a torsion balance.

Speaker 2 (38:49):
Right, you're talking about a setup that's like what do
you call those like ornaments? You hang them from your ceiling.

Speaker 1 (38:53):
It's a mobile.

Speaker 2 (38:54):
A mobile, Yeah, that's kind of what you're talking about, right,
Like you make a mobile out of two biller balls
where you put them on a rod, and then you
hang the row from the center of it on a
string from the ceiling, and then you sort of see
how this mobile swings or turns when you put mass
bigger masses next to or near the to bigger ball exactly.

Speaker 1 (39:14):
And so now you're measuring the angle of rotation of
your mobile basically as it turns towards the other balls.
And that's a little bit easier to measure than the
deflection relative to some vertical where you need to like
calibrate it to the stars. Here, you know how much
force it takes to twist this string. You can calibrate
that when the balls aren't around, And then you bring

(39:36):
the balls in and you see, like how much do
they twist the string? What is the equilibrium position between
the force that's trying to bring the mobile back to
its resting position and the force from the balls that's
pulling on it in the other direction.

Speaker 2 (39:48):
The twisting of the string also tends to want to
bring it back to a neutral position, right.

Speaker 1 (39:54):
Exactly If you just like twisted this thing up and
let it go. They would spin back eventually to its
resting position. And so just the way like a pendulum
is deflected by the mountain, here, this whole balance is
twisted a little bit by the presence of these other masses.

Speaker 2 (40:09):
Interesting, and so they did this kind of at the
end of the seventeen hundreds, and how close did they get?

Speaker 1 (40:13):
So Yeah, so this idea was by John Mitchell, a geologist. Unfortunately,
John Mitchell built the whole experiment and then died before
he could really use it. And it was Cavendish who
inherited this thing and did a bunch of really really
careful experiments, and he's the one for whom this experiment
is known. Unfortunately, Mitchell's sort.

Speaker 2 (40:30):
Of lost line sounds very suspicious.

Speaker 1 (40:33):
Yeah, lost to history, but you know Cavendish.

Speaker 2 (40:37):
Seventeen hundred murder, Mystery Physics, it's a winning podcast episode, True.

Speaker 1 (40:41):
Crime Science exactly. Anyway, he got a very precise measurement.
He measured it to within one percent of the true value.
And this was a big elaborate thing. It was like
a two meter wide box that this whole thing was in,
and he had to be enclosed in there to avoid
like air currents. He could only observe it through these
tiny little holes through which there were lenses. So it's
really elaborate setup, but it worked. And this is in

(41:02):
the late seventeen hundreds, and that was the most precise
measurement for about one hundred years.

Speaker 2 (41:07):
Wow, it's pretty impressive what happened at one hundred years later.

Speaker 1 (41:10):
So for the nexte of years, the folks who were
using the mountain method tried to beat Cavendish but failed.
They kept trying, like different mountains and different surveys, and
they spent lots of money and lots of time, and
sometimes they drank too much and actually like burned down
their whole facility. It's a very colorful history if you
look into it. But they never succeeded in beating Cavendish,
and wasn't until people improved on his torsion balance method.

(41:30):
But one hundred years later a scientist named CV Boys
was able to bring down the uncertainty, and people made
a little bit of progress over the next few decades,
so that like by the nineteen thirties we had a
measurement of it to within a tenth of one percent
and That sounds pretty good, right, But remember, like this
is a fundamental constant of the universe. Other constants we've

(41:52):
measured to like one part in a billion, so having
this down to like one part in one hundred or
one part in a thousand is not very impressive. It's
one of the worst measured physical constants in the universe.

Speaker 2 (42:04):
Oh man, are you physics shaming those experimenters?

Speaker 1 (42:07):
Now, I'm doing exactly the opposite. I'm saying, this is
so hard. It's a really, really difficult measurement. You know,
in order to do this, you have to completely isolate
your setup from everything else. You have to come up
with clever ways to account for everything to measure the
bias in your experiment. You know. The more recent measurements
people have been doing in the last few decades involve
clever tricks like put a mirror on the wire and

(42:30):
instead of measuring the angle of the balls, which is
really small, shine a laser on the mirror. Use the
motion of the laser spot to measure how much the
wire has twisted. These kind of tricks and all sorts
of other techniques to reduce the electrostatics on these balls.
It's really impressive. Amount of work.

Speaker 2 (42:46):
I guess my main question is you're saying, like, we're
getting closer to the true measurement or the true value
of this constant. But how do you know what the
true value is? Like, how do you know you're only
tenth of a percent off or ten percent off? Like,
how do you know what act is supposed to be?

Speaker 1 (43:01):
Yeah, that's a great point, and we don't know what
it's supposed to be. There's no prediction, right, so any
number could be the right number. And in the history
of these measurements, typically what happens is you have a
first measurement which is sloppy and rough, and then you
improve it and you get more and more precision. So
if you look at these things over time, they tend
to converge towards one value, which we say, oh, that
must be the true value. In reality, it doesn't always

(43:22):
work like that. We have some cases in history where
the value seems to converge to one number and then
it shifts, and that's because people know about the previous
results and they sort of want to reproduce the previous results.
So if like one of the first results was off
by a bit, then there's like an implicit bias in
people's experiments that tend to like find mistakes and bugs
until their number agrees with the previous number. It takes

(43:44):
a little bit more bravery and courage to disagree with
an established measurement. So you see those sort of like
jumps sometimes in the history of a measurement. This one
is particularly interesting because as the measurements have gotten more
and more precise, like in the last ten or fifteen years,
it's been a real cottage industry of making these measurements,
they've started to disagree. So now we have a bunch

(44:04):
of measurements of the gravitational constant with fairly small uncertainties
that disagree with each other by more than the uncertainties.

Speaker 2 (44:12):
Interesting, So I think maybe when you say, like they
got within point one percent, you're not saying that that
it's not by point one percent. You're saying like their
confidence in their measurement is down towero point one percent,
like they think they're within that range. Right, It's more
like a measure of confidence.

Speaker 1 (44:29):
Yeah, they usually quote and uncertainly they say it's this
number within a certain range. But we can also compare
their measurement to our current best understanding of what the
value is, so we can analyze their historical accuracy by
comparing it with modern measurements.

Speaker 2 (44:42):
And so, is there no way to like derive this
from the equations of the universe or to you know,
tie back to some other more fundamental thing like the
mass of an electron, for example, or something.

Speaker 1 (44:53):
No, there is not. There's no way to derive this.
It's totally unrelated to every other physical constant and every
other process in the universe. The gravitational constant doesn't just
control gravity. It only controls gravity. It doesn't determine anything
else in the universe. So there's no other way to
figure it out. The only way to do it is
to measure the force of gravity between two things. And

(45:15):
to do that you got to know their masses.

Speaker 2 (45:17):
M we can't tell by you know, how light bends
around a black hole or something like that, or around
the sun.

Speaker 1 (45:24):
Yes. Actually, as our calculations in general relativity get more
and more precise, we may be able to do things
like seeing how space is bent in the vicinity of
strong gravity, which might be able to give us a
new handle on how to measure this constant.

Speaker 2 (45:38):
Pretty cool, But I guess until then that means like,
if our measurement of G is off by point one percent,
that means that any calculation that we make using G
is also off by at least that point one percent, right.

Speaker 1 (45:50):
Mm hmm. Yeah. These days, we're down to about five
times ten to the negative five as a fractional uncertainty
on big G, so you know, like a few parts
per million, which is much more precise than historically but
still by far the worst measured constant. And you're right,
it means that we can't make very precise predictions about
what happens near black hole because they depend on big G.

(46:13):
So you need super precise measurements to nail big G
so we can then make super precise predictions.

Speaker 2 (46:19):
It kind of sounds like maybe we'll never know the
true value of G.

Speaker 1 (46:22):
It might be because the true value of G has
an infinite number of digits in it. In that sense,
will never know the true value of anything, even like
you know the mass of an electron or any other parameter,
because it has an infinite number of digits and you
can't have an infinite amount of experiments or an infinite
number of graduate students to measure them.

Speaker 2 (46:38):
What I guess what I mean is like, at some
point you do need to know the masses of the
things involved in your experiment, and so but that for
that you also kind of need g and so there's
as maybe going to be a little uncertain because of that.

Speaker 1 (46:48):
There's always going to be uncertainty exactly, and because we
don't know this one very well, it makes everything in
gravity more uncertain.

Speaker 2 (46:55):
All right, Well, sounds like there's still a lot of
room for people to come up with some interesting experiment
to measure this exactly.

Speaker 1 (47:02):
You might think it's a historical quantity, but people have
been measuring these things in the last five ten years.
It's like an area of active research understanding Newton's constant
for gravity.

Speaker 2 (47:14):
So I guess the next time you weigh yourself and
you're like, what, I weigh this much, you can maybe
blame it on the uncertainty of the gravitational constant.

Speaker 1 (47:22):
That's right, blame Newton.

Speaker 2 (47:24):
I guess that still doesn't help you explain why you're getting.

Speaker 1 (47:26):
Old or why you're getting more silver.

Speaker 2 (47:27):
All right, Well, we hope you enjoyed that and maybe
thought a little bit more about what we know about
the universe and we still don't know and how we
still don't know very basic things about it, like how
much you weigh or how much how hard the Earth
is pulling domin you.

Speaker 1 (47:41):
So for those of you looking to crack a deep
secret of the universe, this is one of those frontiers.
Maybe you'll find a reason why G has to be
a certain value, or maybe you'll come up with a
super clever experiment to nail it down very.

Speaker 2 (47:54):
Precisely, and then everyone will go ge whiz, I mean
big g wheez I mean uppercase. All right, thanks for
joining us, see you next time.

Speaker 1 (48:11):
Thanks for listening, and remember that Daniel and Jorge Explain
the Universe is a production of iHeartRadio. For more podcasts
from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever
you listen to your favorite shows.