Would a Very Large Mass (e.g. the Moon) Fall with g?

[John Mohr]

Today, I had a thought experiment where I began to puzzle over inertia of very large masses being dropped.

Imagine a scenario where the Moon was suspended 100 m from the surface of the Earth alongside a marble at the same height. Now ignoring air resistance and the gravity exerted by the Moon on the marble, let's suppose they were "dropped" from that point. Would they hit the Earth's surface at the same time?

My thoughts were that the Moon would lag behind and hit the surface after the marble due to it's great inertia. Also, one would noticeably feel the Earth falling "up" towards the Moon.

Would anyone else like to weigh in on this?

 

[Dale]

Imagine a scenario where the Moon was suspended 100 m from the surface of the Earth alongside a marble at the same height.

Is the bottom of the marble at the same height as the bottom of the moon? Or is the center of the marble at the same height as the center of the moon?

 

[miltos]

In any case, moon and marble will move with the same acceleration towards earth

Also, one would noticeably feel the Earth falling "up" towards the Moon.

That's true. You would also notice tide and wind currents-atmospheric pressure changes by just approaching moon to earth

 

[PeroK]

Today, I had a thought experiment where I began to puzzle over inertia of very large masses being dropped.

Imagine a scenario where the Moon was suspended 100 m from the surface of the Earth alongside a marble at the same height.

Given the Moon is $3,500km$ in diameter, that's not a scenario I can imagine.

A superdense marble with the mass of the moon, perhaps.

 

[John Mohr]

Is the bottom of the marble at the same height as the bottom of the moon? Or is the center of the marble at the same height as the center of the moon?

Good question! I visualized the bottom of the marble at the same point as the bottom of the Moon (so that both would cover the same distance).

 

[John Mohr]

Given the Moon is $3,500km$ in diameter, that's not a scenario I can imagine.

A superdense marble with the mass of the moon, perhaps.

Ah yes, this would be a good idea PeroK. Something like the material of a neutron star with the volume of a marble.

 

[Dale]

Good question! I visualized the bottom of the marble at the same point as the bottom of the Moon (so that both would cover the same distance).

So then the marble will hit first, not because it has less inertia, but because its center of mass is closer so the gravitational field is stronger.

 

[Dale]

Ah yes, this would be a good idea PeroK. Something like the material of a neutron star with the volume of a marble.

In this scenario they would hit at the same time.

 

[John Mohr]

So then the marble will hit first, not because it has less inertia, but because its center of mass is closer so the gravitational field is stronger.

Ah yes Dale, very cool. I would agree for this scenario as the center of mass and center of gravity would be a quite different points.

 

[lekh2003]

Ah yes Dale, very cool. I would agree for this scenario as the center of mass and center of gravity would be a quite different points.

But if I may add, the only reason they hit at the same time is because the superdense marble is pulling on Earth which changes the outcomes for both the marbles. If we tried the experiment twice, once with the superdense marble and once with the regular marble, then the superdense marble with hit the Earth in less time.

 

[rcgldr]

Choosing the common and non-accelerating center of mass of Earth plus moon as the reference frame, then the acceleration of the moon towards that common center of mass is due to Earth's gravity field. The Earth would also be accelerating towards the common center of mass due to the moon's gravitational field. The combined masses affect the rate of closure, but not the rate of acceleration towards a common center of mass.

 

[John Mohr]

I'm not sure if it's because I've watched too many Star Wars movies of star destroyers crashing down to the surface's of various planets slowly, but it seemed to me like the inertia would take time to overcome.