B Does an orbiting mass exert force on what it is orbiting around?

[Alkamist]

I'm trying to get this concept straight in my head. Take, for example, the International Space Station; it is orbiting the Earth in considerable gravity, yet the inhabitants feel weightless. So they cannot be exerting a force on the Earth aside from their own minuscule gravitational pull right?

If this is true, could you in theory have a very focused gravitational field (caused by energy or super dense matter or something) and be orbiting it very quickly in a tight circle while feeling as if you are standing still?

 

[olgerm]

An orbiting body(that has mass) does exert force on body it is orbiting around. International Space Station does exert force on Earth. look up Newton's law of universal gravitation

 

[Christopher Grayce]

That's correct, the astronauts (and ISS itself) do not exert a force on the Earth other than their own gravitational pull, but you might want to bear in mind that the force of gravity is the *product* of the two masses, so the force between the astronauts and the Earth is quite significant, as far as gravity goes, since the Earth mass is huge. The reason they don't feel it is because they are in free fall -- they are falling towards the Earth all the time at the maximum possible rate. (The reason they don't hit the ground is that they are simultaneously shooting horizontally around the Earth, and they go so fast horizontally that they "miss" the ground due to the curvature of the Earth, and keep falling.)

They can still tell they're orbiting and not standing still, however, and not just by looking out the window. Because of the slight variation in orbital speed between the parts of their bodies closest to the Earth and the parts furthest away, they will feel a slight tug stretching them, called the tidal force. Around the Earth, and for something as small as an astronaut, the tidal force is too small to feel. But if they were in a small orbit around a very dense body, as you imagine, this tidal force would become very strong and they would definitely feel it -- indeed, if the orbit were small enough, the tidal force would pull them apart.

 

[Nugatory]

I'm trying to get this concept straight in my head. Take, for example, the International Space Station; it is orbiting the Earth in considerable gravity, yet the inhabitants feel weightless.

Yes. They are in free fall, moving under the influence of gravity with nothing to oppose it. Compare with what you feel standing on the surface of the earth: the ground is pushing up on your feet (because it resists being compressed by gravity pulling you down against it) - that upwards force is what you feel as weight.

So they cannot be exerting a force on the Earth aside from their own minuscule gravitational pull right?

The force they are exerting on the Earth is the same as the force the Earth is exerting on them. Look at Newton's force law $F=Gm_1m_2/r^2$; you get the same result whether $m_1$ is the Earth and $m_2$ is a person the space station or the other way around. Of course the Earth is much more massive than they are, so is affected much less by the same force.

If this is true, could you in theory have a very focused gravitational field (caused by energy or super dense matter or something) and be orbiting it very quickly in a tight circle while feeling as if you are standing still?

Yes, if by "feeling as if you are standing still" you mean feeling weightless. No matter how strong the gravitational force, you won't feel it; you'll only feel forced that stop you from moving freely under its influence.
(Tidal forces, which are caused by differences in the strength of the gravitational field from point to point are a different matter. Near a black hole the difference between the force on your head and on your feet - remember that factor of $1/r^2$ in the force law - may be large enough to tear you apart)

 

[Alkamist]

Thank you for the replies. So in free fall, you are experiencing force pulling you toward earth, but you don't feel it because it is essentially uniform across every atom in your body?

 

[russ_watters]

Thank you for the replies. So in free fall, you are experiencing force pulling you toward earth, but you don't feel it because it is essentially uniform across every atom in your body?

Yep!

 

[sophiecentaur]

Thank you for the replies. So in free fall, you are experiencing force pulling you toward earth, but you don't feel it because it is essentially uniform across every atom in your body?

Yes - up to a point but the phrase 'micro gravity' is more appropriate when in an orbiting spaceship ( rather than 'zero gravity') . With no disturbances of the air inside the ISS, small objects will move about detectably when released in the cabin because the Earth-side of the (rigid) ship is moving slower than it would if in free orbit and the Far- side of the ship is moving a tad faster and a 'free' object will be unconstrained by the structure of the ship and it can follow its own (slightly different) orbit.

 

[Nugatory]

With no disturbances of the air inside the ISS, small objects will move about detectably when released in the cabin because the Earth-side of the (rigid) ship is moving slower than it would if in free orbit and the Far- side of the ship is moving a tad faster and a 'free' object will be unconstrained by the structure of the ship and it can follow its own (slightly different) orbit.

These are the "tidal forces" that @Christopher Grayce and I mentioned above; they arise because the gravitational force varies slightly with distance so will be different on different parts of the orbiting space station because they're at slightly different distances from earth.

[Sophie already knows this, of course. This comment for other people reading the thread and seeing his post]