# Gravitational force of the Earth and Moon

• B
A person of mass 60kg will weigh around 100N on the moon. This is roughly equivalent to the gravitational force on a 10kg object on Earth.
Even if the forces acting on both are about the same, we don't see 10kg objects floating around on Earth whereas a man weighing 60kg can easily float on the moon. Why?

## Answers and Replies

stockzahn
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Imagine an evacuated room on earth, so no air in it. Now from the top of the room you drop a bowling ball and and a feather at the same moment. Which of the two objects does reach the bottom first?

A.T.
Even if the forces acting on both are about the same, ...
How is force related to acceleration?

Imagine an evacuated room on earth, so no air in it. Now from the top of the room you drop a bowling ball and and a feather at the same moment. Which of the two objects does reach the bottom first?

Both reach at the same time. Ok, now I get it. Irrespective of mass, the objects on Earth would speeding toward it at a constant acceleration. And on moon this value is just 1/6th of the Earth's. Thank You.

Now then, what is the effect of Earth's gravitational force? Since the force on objects of different mass are different, something about them should be different, isn't that so?

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stockzahn
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Both reach at the same time.

So the mass/weight doesn't seem to make a difference. That's why no object is "floating" on earth and all objects are "floating" on the moon. Now the question remains, why is that. The reason is that not only the graviational force is proportional to the mass of the object, but also its inertia. Mathematically you can express that like this:

$$ma=mg$$

, where ##m## is the mass of the object, ##g## the gravitational acceleration and ##a## the acceleration. The equation just states that the graviational (weight) force acting on the object equals the resistance of the object to change its state of movement (inertia). Independent on the mass of a certain object, the acceleration only depends on the acting graviation - therefore the higher gravitation of the earth increases the speed of the object faster than the weaker gravitation of the moon.

So the mass/weight doesn't seem to make a difference. That's why no object is "floating" on earth and all objects are "floating" on the moon. Now the question remains, why is that. The reason is that not only the graviational force is proportional to the mass of the object, but also its inertia. Mathematically you can express that like this:

$$ma=mg$$

, where ##m## is the mass of the object, ##g## the gravitational acceleration and ##a## the acceleration. The equation just states that the graviational (weight) force acting on the object equals the resistance of the object to change its state of movement (inertia). Independent on the mass of a certain object, the acceleration only depends on the acting graviation - therefore the higher gravitation of the earth increases the speed of the object faster than the weaker gravitation of the moon.

That was much helpful. Thank You.

On Earth, objects of different masses do experience different gravitational force. But the effect we can observe, i.e. the acceleration is the same. So isn't there anyway we would 'feel the difference'?

stockzahn
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On Earth, objects of different masses do experience different gravitational force.

Yes, and it is proportional to their mass.

But the effect we can observe, i.e. the acceleration is the same. So isn't there anyway we would 'feel the difference'?

Yes, in absence of any other force (e.g. drag due to air).

So isn't there anyway we would 'feel the difference'?

I'm not sure if I understand what you mean. One can feel the difference between varying accelerations, I'm pretty sure you could feel the difference between the acceleration you are experiencing on the earth and on the moon respectively. Also the human body cannot stand too high accelerations, and one has to train to withstand them, like astronauts or (jet) pilots have to.

akhila_k
Yes, and it is proportional to their mass.

Yes, in absence of any other force (e.g. drag due to air).

I'm not sure if I understand what you mean. One can feel the difference between varying accelerations, I'm pretty sure you could feel the difference between the acceleration you are experiencing on the earth and on the moon respectively. Also the human body cannot stand too high accelerations, and one has to train to withstand them, like astronauts or (jet) pilots have to.

What I meant was, two bodies falling freely on Earth wouldn't know that they've different masses and hence different forces acting on them, because they're experiencing the same acceleration. Isn't that so?

stockzahn
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What I meant was, two bodies falling freely on Earth wouldn't know that they've different masses and hence different forces acting on them, because they're experiencing the same acceleration. Isn't that so?

That's right, they couldn't know just by observing each other, since the evolution of their velocities is identical. Still though, the heavier object experiences a larger force.

That's right, they couldn't know just by observing each other, since the evolution of their velocities is identical. Still though, the heavier object experiences a larger force.
Ok. Now I get it. Thank you so much.

jbriggs444
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What I meant was, two bodies falling freely on Earth wouldn't know that they've different masses and hence different forces acting on them, because they're experiencing the same acceleration. Isn't that so?
If the objects are in free fall, the acceleration that they feel is zero. They will feel as if they are weightless.

There is a term, "proper acceleration" which refers to the acceleration you can feel. The acceleration that you can see (for instance by watching the ground come up and smack you in the face) is called "coordinate acceleration".

If you are free falling on Earth, you experience 0 gees of proper acceleration while having 1 gee of downward coordinate acceleration relative to the Earth's surface.

If you are standing still on Earth, you experience 1 gee of upward proper acceleration while having 0 gees of coordinate acceleration relative to the Earth's surface. Your proper acceleration is the result of the floor pushing upward on your shoes.

If you are free falling on the moon, you experience 0 gees of proper acceleration while having 1/6 gee of downward coordinate acceleration relative to the moon's surface.

If you are standing still on the moon, you experience 1/6 gee of upward proper acceleration while having 0 gees of coordinate acceleration relative to the moon's surface. Your proper acceleration is the result of the moon's surface pushing upward on your boots.

akhila_k and m4r35n357
Even if the forces acting on both are about the same, we don't see 10kg objects floating around on Earth whereas a man weighing 60kg can easily float on the moon. Why?

It has already explained that this is not a matter of mass but of gravitational acceleration only. However, you can fake a similar behaviour on Earth. If you want a car look like driving on the Moon, than make a movie of it driving with f = sqrt(gEarth/gMoon) the speed and play it in slow motion.

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sophiecentaur
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It's typical of human beings to take for granted the way people walk on the Moon - it was 'obvious' in retrospect. But it was certainly not predicted by Hollywood until people actually had been seen walking. There was a Film (Countdown 1967) that was released only just before the Apollo project and James Caan was shown, walking around quite 'normally', as on Earth. The credibility of that film was shot as soon as Armstrong and pals were seen doing it properly. A shame because the basic story was very good - at least as good as Capricorn One, in which, in the plot, no one actually walked on the Moon. Both story lines were basically Political. (You should watch both of them.)

That in itself is a great argument against the Moon Landing Conspiracy because Armstrong and Aldrin would have been walking as if on Earth if they weren't actually there at the time

If the objects are in free fall, the acceleration that they feel is zero. They will feel as if they are weightless.

There is a term, "proper acceleration" which refers to the acceleration you can feel. The acceleration that you can see (for instance by watching the ground come up and smack you in the face) is called "coordinate acceleration".

Thank you. This is new information for me.