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# Introduction to gravity

AP.PHYS:
INT‑3.C (EU)
,
INT‑3.C.1 (EK)
,
INT‑3.C.1.1 (LO)
NGSS.HS:
HS‑PS2‑4
,
HS‑PS2‑5
,
HS‑PS2.B.1
,
HS‑PS2.B
,
HS‑PS2
Basics of gravity and the Law of Universal Gravitation. Created by Sal Khan.

## Want to join the conversation?

• •   It is the same principle as an airplane that is taking off. It has the thrust and the lift and so can resist gravity. In the case of the bird the lift comes from all of the individual feathers and the thrust comes from the bird flapping its wings or finding a hot air current to find lift on. That is another story though.
• Where does gravity ultimately come from? Do masses naturally have gravitational forces associated with them? Since you can convert Mass into Energy (E=MC^2), why doesn't energy, such as light, have gravity? I've read some where that gravity is theorized to be the resultant force of the big bang. It is not objects are attracted to each other, but everything in the universe is trying to move back toward the origin of the universe. Kind of like Newton's 3rd law. Please explain :D •   @terryjbrennan You are incorrect. Photons are, by nature, massless. That is why they are able to travel at the speed of light (C) and not just below it. Anything with mass cannot move at the speed of light.

@kokocipher In answer to your question "where does gravity ultimately come from," according to the General Theory of Relativity, the most widely accepted and most accurate theory used to explain our observations of gravity, gravity is the result of objects with mass bending space time. All objects bend spacetime, and more massive/dense objects bend it more steeply. That is they have a stronger gravitational pull. Since mass == energy (E=MC2)energy will indeed bend space time, if there is enough energy in a small enough space.

However, consider the following. It requires the mass of an entire moon or planet to have an effect strong enough for you to feel. Since E=MC2 the amount of energy required to bend space the same amount (that is to have a gravitational influence that humans could detect without instruments) is unfathomable. If there's energy that dense it tends to collapse into matter. Indeed, this is what happens in our particle accelerators such as the LHC.

As for black holes, they are locations in space where there is mass dense enough to bend spacetime so steeply that it would require movement faster than the speed of light to escape. Due to the nature of our Universe it is impossible to exceed the speed of light (I'm aware that sounds vague, but it would take a good hour to explain in more detail). Therefore, nothing, not even light, can escape.
• Where does the Big G come from and why is it that specific number? • •  helium has very less density so it apparently floats in air because air has a greater density. just as how ice floats on water because ice as a lower density than water. the same way helium has less density than air so it floats and does not defy gravity.
• Gasses have very high kinetic energy. DO they escape earth's gravitational pull? • On very rare occasions. A gas molecule, like any other escaping projectile, requires enough velocity (escape velocity) to leave from an orbiting path around the earth. I suppose if a gas molecule in the atmosphere received enough energy (and turned to a near plasma state) it would be possible.
One issue is that while individual gas molecules have high kinetic energies, they are characterized by randomly colliding with other gas molecules at high speeds. So you wouldn't really see any synchronized movement of molecules away from the earth's surface--while some are moving away, others are moving towards the earth, and they collide with each other.
• • This was basically a three step process. 1) First of all, you have Newton's Law of Universal Gravitation, that states that the force of attraction due to gravity between two masses, m and M, at a distance r, is given by F=GmM/r^2, where G is a constant called the gravitational constant. 2) Second, you know that all objects on the Earth's surface will fall with a constant acceleration, known as g. From Newton's second law of motion, F=ma, you get that mg=GmM/R^2, where M is the Earth's mass and R is the Earth's radius. Do a little algebra, and you get that M=gR^2/G. g is measured, and so is R. All you need is G (and love). 3) Enters Cavendish, who measured the gravitational attraction between two spheres of known mass and distance, therefore finding G. You plug in the values, and you get M. Awesome!
• I am a little confused at this point so my question might be invalid but lemme give it a try :
An apply thrown in the air also attracts the earth but due to the mass of the earth the acceleration on earth is negligible , but then if a huge amount of apples were thrown from a single point on earth then would the earth move towards the apples due to the combined force of all the apples thrown in the sky?? • If photons are massless particles, then why does gravity bend light? • I'm gonna go a step further than Newton :D and ask why do things have to follow the Universal Law of Gravitation? I mean, like, what causes this gravitational force? For e.g., electrostatic force is created due to charges... then gravitational force is caused due to what?? • Hello,

This might be slightly off-topic, but I had a doubt I couldn't clarify.

Say, two objects of masses M and m are placed at rest in vacuum, a distance R away from each other and the only forces acting upon them are each others' gravitational forces. If they start accelerating towards each other, how long would it take for them to collide?

I tried solving it through integration and failed. (Equating initial P.E. and final K.E. didn't work well (for me) either.) The best expression for time I could come up with was,
``t = ____√(2R^3)____      3∙√(G(M+m))``
Since this is a made up question, I have no clue whether it is correct or not (probably isn't), so I would appreciate it if someone could help out.

[Edit: Through a bit of trial and error, I think I got the right answer as
``t = ____√(2R^3)____,      √(3∙G(M+m))``
though I am not sure how to derive it.

Note: I replace the numerator with `√(2((Re+h)^3 - Re^3))`, where Re is the radius of the earth
h is the height above the surface of the earth,
M and m are the masses of the earth and another object.

I compared the result with the result from `h = ut + 1/2(at^2)` , and got an answer within 4 decimal places (for h << R). Still not sure how I got the √3 in the denominator, though.]

Thank you • Let's take a different approach.

Imagine the two masses are in orbit with mass M and m.

Orbit is just continous freefall, which is why the ISS experiences no gravity (or microgravity).

We make the orbits very very eecentric, long and skinny so the semi minor axis is 0, leading to a straight line across the semi major axis.

The bigger mass, M, has a higher F_g but in return, it has a higher inertia. The lower mass, m, has a lower F_g but has a lower inertia and moves quite easily towards the big mass.

Like a pendulum, these two forces cancel equally, leaving the distance 1/2 the distance between them, or in other words R/2.

These are the objects: O ---> F_g * F_g <- o

So they will meet at the center, R/2.

But remember, these are just regular circular orbits. But, the mass of the smaller object has enough mass to shift the center of mass of the system, in other words bring the barycenter out of the main object.

The semi major axis of these objects are just half the distance between their circular orbits, ignoring the barycenter.

So its: a_1 + a_2: a_2 + a_1 for the big mass and small mass, respectively.

But then we need to include the barycenter, so we need to take the average of those semi-major axes because the barycenter is exactly half the distance between those objects.

So: (2a_1 + 2a_2)/2 = a_1 + a_2. Since before we made these orbits very long and skinny, these were ciruclar orbits so a_1 and a_2 are the same distance, 1/4 of the total distance.

The orbit equation for their time which is part of
Kepler's Laws is: T = 2pi*sqrt(a^3/GM)

But we need to remind ourselves that this is a 2 body problem.

If we look at F = ma, this is only for 1 object.

For 2 objects, we need to include both so the F = ma equation turns out to be this:

summation(F) = summation(m)a.

So we need to add the two forces of the objects and the two masses of the objects to get the total acceleration.

In this case, we want the total time, so we need to apply the same logic.

a is semi major axis by the way.

So: T = 2pi*sqrt[summartion(a)^3/G*summation(M)]

So: T = 2pi*sqrt[(1/4R+ 1/4R)^3)/G(M + m)]

Which is: 2pi*sqrt[(R/2)^3/G(M+m)]

Thus: 2pi*sqrt[(R^2/8)/G(M+m)]

...a complex fraction where if we simplify it:

T = 2pi*sqrt[R^3/8G(M+m)]

But we want half the time for the collision, so divide that by 2:

T = pi*sqrt[R^3/8G(M+m)]

You could do further simplyfing

If you would like to get better details, it is explained well in this video: youtube.com/watch?v=F0zUOcZN6sI

Hope this helps!