# Gravity as a force

PeroK
Homework Helper
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(b) Does it make any difference if he had dropped the Lunar Lander, instead of the hammer, along with the feather on our Moon? If it was the size of another moon, I believe it would be a Moon-quake?

It's perhaps not a very important point, but if you are talking about relatively small objects then they take the same time to fall. But, if both objects are large then they both fall towards each other significantly and will take less time to collide, given the same starting distance, than the case of a small object falling towards one of them.

mfb
Mentor
(b) You said the gravitational acceleration of an object is independent of its own mass, doesn't it mean the gravitational acceleration of the feather, the hammer,... and the Moon are all independent of their own masses?
Yes. F=MmG/r2, and if you look at the acceleration of one of the objects (e.g. the one with mass m), then a=F/m=MG/r2 which does not depend on m any more.
Since total mass of (Moon + hammer) is larger than the total mass of (Moon + feather)
The sum of masses does not matter. Only the product appears in formulas.
wouldn't the attraction force between the Moon and the hammer be greater?
The force is larger, but acceleration is force divided by mass, so the mass cancels in the calculation.
I believe the acceleration is dependent on the strength of the gravity field, not necessary the mass.
The strength of the gravitational field is given by the mass of the moon and the distance to it.
The mass is exactly the relevant part of the "composition".
(c) Logically, Moon would accelerate toward the hammer and the feather by mutual attracting force even it is undetectable, isn't it?
Sure.
I believe the easiest attraction force to experiment is magnetic attraction. For example, a free-moving large magnetic ball will also accelerate toward a free-moving small magnetic ball, only not as much, isn't it?
Depends on the relative orientation of the magnets. Magnets are not a good model for this reason.
What if David Scott set the feather on the top end, further from the ground, of the hammer, would the hammer accelerate away from the feather?
Theoretically yes, but the difference is completely negligible. At that level of precision the attraction between hammer and feather could be relevant as well.
My point is, do the sizes of objects matter?
No.

magnetic slim
Correction, magnetic slime.

the experiment gave an example of the general principle that the gravitational acceleration of an object is independent of its own mass.
David Scott's hammer feather drop, along with all other falling body experiments, shows:

The gravitational acceleration of an object is independent of it's shape, size, and surface; in addition to it's own mass, isn't it?

Andrew Mason
Homework Helper
Correction, magnetic slime,

David Scott's hammer feather drop, along with all other falling body experiments, shows:

The gravitational acceleration of an object is independent of it's shape, size, and surface; in addition to it's own mass, isn't it?
Gravitational acceleration is independent of its mass. It is not necssarily independent of its mass distribution, or size. For example, a 100 T mass in the form of a thin wire stretched from a satellite to the earth surface will experience different gravitational accelerations than a 100T mass located at the midpoint of the stretched wire.

AM

Gravitational acceleration is independent of its mass. It is not necssarily independent of its mass distribution, or size.
Can you explain:
- How abut the surface and shape?
- Didn't David Scott's hammer fell in sync with feather, the mass, size, shape, and surface are clearly very different?
- The different size, and weight, of the balls fall in uniform acceleration in all experiments I have learned, when the friction of the air is neglected?
- Galileo's inclined plane experiments show the uniform acceleration of different sizes of spheres, by times-squared law regardless of the sizes? I believe he had done very intensive studies on this, if not the most. Great man like him would not give up finding the truth in my view.
- I believe there are countless experiments out there. However, I have been searching for years. Would you kindly direct few falling body experiments that show otherwise? Video clips would be perfected, but anything will do. Thank you. Help, anyone?
My point is, do the sizes of objects matter?
No.
a 100 T mass in the form of a thin wire stretched from a satellite to the earth surface will experience different gravitational accelerations than a 100T mass located at the midpoint of the stretched wire.
What kind of difference, which mass would have higher gravitational acceleration, one at midpoint?
I wouldn't think it is feasible to perform such an experiment considering these reasonings:
- Mose satellites travel at much higher speed then surface of the Earth. Satellite tied to a stretched wire anchored on the ground would be a big issue, even geosynchronous satellite. I don't expect our technology will meet the challenge any time soon, do you?
- Mass at the altitude of satellite is about weightless. It would not fall unless it is pushed down and break the surface of the atmosphere. Isn't the interference is introduced by altering the initial free-fall?
- It would introduce the surface interactions of the object and the atmosphere upon reentry. Could it bounce off?
- Object at midpoint would begin at lower centrifugal force.
- Object at the satellite has next to zero air resistance to begin with. It's starting and en-route environment is different from the one at midpoint.
- Gravity anomaly, air, atmosphere friction, altitude, and weather over large distance would compound the issues. For example, temperature, humanity, and wind speed would be constant. Wire would sway, stretch, expand, and bend even it could hold. The set-up and environment of the experiment can not be controlled.
- Loss of mass could void the experiment. Wouldn't the one from satellite burn out beforehand?
- Isn't this similar experiment to Galileo's inclined plane, but high-tech overkill?
- Do you think the experiments already done, even Galileo and David Scott, cannot provide clear and sufficient clues?

Andrew Mason
Homework Helper
Can you explain:
- How abut the surface and shape?
- Didn't David Scott's hammer fell in sync with feather, the mass, size, shape, and surface are clearly very different?
- The different size, and weight, of the balls fall in uniform acceleration in all experiments I have learned, when the friction of the air is neglected?
- Galileo's inclined plane experiments show the uniform acceleration of different sizes of spheres, by times-squared law regardless of the sizes? I believe he had done very intensive studies on this, if not the most. Great man like him would not give up finding the truth in my view.
- I believe there are countless experiments out there. However, I have been searching for years. Would you kindly direct few falling body experiments that show otherwise? Video clips would be perfected, but anything will do. Thank you. Help, anyone?
The Galileo experiment, and astronaut Scott's demonstration of it, was not accurate enough to show variations in gravity due to mass distribution. A 15 kg dumbell and a .15 kg baseball held above the moon surface will accelerate toward the moon surface at the same rate unless you can measure the difference to about 1 part in 10^25. But if you could measure the acceleration to that level of accuracy, you would find that the dumbell's acceleration will vary slightly depending on its orientation, whereas the baseball's acceleration would not.

AM

mfb
Mentor
- Galileo's inclined plane experiments show the uniform acceleration of different sizes of spheres, by times-squared law regardless of the sizes? I believe he had done very intensive studies on this, if not the most. Great man like him would not give up finding the truth in my view.
An inclined plane is not a free fall. On an inclined plane, you have to consider the moment of inertia of the rotating objects.

The Galileo experiment, and astronaut Scott's demonstration of it, was not accurate enough to show variations in gravity due to mass distribution. A 15 kg dumbell and a .15 kg baseball held above the moon surface will accelerate toward the moon surface at the same rate unless you can measure the difference to about 1 part in 10^25. But if you could measure the acceleration to that level of accuracy, you would find that the dumbell's acceleration will vary slightly depending on its orientation, whereas the baseball's acceleration would not.AM
I believe you understand the reason why David Scott dropped hammer and feather, not 15 kg dumbell and .15 kg baseball.

1 part in 10^25 is a ridiculous claim. Variance that small you can not say it is the result of gravity, magnetic field, temperature, humility, spiral momentum of the Earth/Moon/Solar System, trillions and trillions of passing solar particles, electrons, neutrinos, and all possible variations of the environment as well as the testing objects, devices, including your breath, heartbeat, body temperature, shaking hands, and so forth.... Even you can prove, say 1 part in 10^10, you have to prove the testing environment, devices, and procedures are in perfect constant. Scientifically, you did not disprove Galileo, Scott, and all other experiments. The same principle applies to all experiments short of significance.
• How can you disprove gravitational acceleration is independent of the surfaces of the hammer and feather?
• How can you disprove gravitational acceleration is independent of the shapes of the hammer and feather?
• How can you disprove gravitational acceleration is independent of the sizes of the hammer and feather?
• Action at a distance of gravity remains debatable.
Other than that, attracting acceleration also has to be proven independent of it's mass, otherwise, gravitational acceleration is not equal to attracting acceleration.
An inclined plane is not a free fall. On an inclined plane, you have to consider the moment of inertia of the rotating objects.
Yes, you have to consider the moment of inertia of the rotating objects falling in spherical (3D directions) in mid space as well. There is no such thing as perfect sphere. However, it is a slow motion of gravity acceleration. I think it is brilliant to obtain the mathematic equation of gravitational acceleration. It is the same principle of high-speed photography in science.

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sophiecentaur
Gold Member
2020 Award
If he had dropped another moon what would have happened?
And if he had dropped the feather from the mid (neutral) point and if the moons had identical masses. The net gravitational force on the feather would be zero.The two moons would move towards each other, squashing the feather between them as they met. In the frame of one moon, the feather would have fallen half the distance that the other moon would have 'fallen' in the same time.
But the law that's in operation in the standard hammer and feather situation implies a uniform gravitational field (massive / flat planet); a much simpler case than for two moons.

Andrew Mason
Homework Helper
Scientifically, you did not disprove Galileo, Scott, and all other experiments.
It is not a matter of disproving Galileo's "equal times of fall" experiment. It is a matter of correctly stating its level of accuracy. If Newton law of universal gravitation is correct: ie. ##F = GMm/r^2## is correct, then it is just a matter of applying that law.

AM

PeterDonis
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2020 Award
For the same reason time always moves from past to future.

This can't be right, because gravity is still attractive if you reverse the direction of time. There are physical processes we know of that violate time reversal invariance, but gravity is not one of them.

PeterDonis
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The Galileo experiment, and astronaut Scott's demonstration of it, was not accurate enough to show variations in gravity due to mass distribution.

I assume you are talking about tidal gravity here? The general law that acceleration of a test object is independent of its mass (and mass distribution) assumes that tidal gravity is negligible. If tidal gravity is not negligible then you are right that this general law is no longer exactly correct.

PeterDonis
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If he had dropped another moon what would have happened?

This isn't really a comparable situation, because there is no way to drop another moon towards the moon while ignoring the effects of tidal gravity, whereas, as I noted in another post just now, the general law under discussion is only correct if tidal gravity is negligible. Also, another moon would not qualify as a "test object", and the general law under discussion only applies to test objects. Test objects, by definition, have negligible gravitational effects themselves, and that is obviously not true for another moon.

Andrew Mason
Homework Helper
I assume you are talking about tidal gravity here? The general law that acceleration of a test object is independent of its mass (and mass distribution) assumes that tidal gravity is negligible. If tidal gravity is not negligible then you are right that this general law is no longer exactly correct.
Yes. Tidal forces. I assume that is what you mean by tidal gravity. Tidal forces, due to differences in the gravitational forces/unit mass acting on different parts of a body due to differences in position in the gravitational field of the other gravitating body, have the tendency to pull a body apart, which is the opposite of how one thinks of gravity.

AM

PeterDonis
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2020 Award
Tidal forces. I assume that is what you mean by tidal gravity.

Yes.

Tidal forces, due to differences in the gravitational forces/unit mass acting on different parts of a body due to differences in position in the gravitational field of the other gravitating body, have the tendency to pull a body apart

Not always. Radial tidal forces in the field of a spherical mass do this, but tangential ones don't; they have a tendency to push a body together. But both of these are different from the effect of the Newtonian "force" of gravity, which has no effect at all on the internal structure of a body, neither pulling apart nor pushing together.