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So, a gravity assist in very simple terms is when an object uses a planet's gravity and rotating momentum to increase the objects speed.

If this is true, why doesn't the ISS get further and further away from us as it gains angular momentum from Earth? As I understand every once in a while, the ISS has to do a burn to get back into stable orbit around Earth because of the very thin atmospheric drag on the ISS. That would mean the ISS isn't increasing it's speed, it's slowing down.

On a separate but related question, if gravity assists do indeed work that way, isn't our moon stealing angular momentum from Earth every second it's in orbit around us? As I understand, the moon is gradually being tugged away from Earth, not by stealing Earth's angular momentum, but because the tidal effects of the moon on Earth bump the moon into a higher orbit.

Please, no math, keep it to worded answers. I just want to understand the concept behind the explanations.

Thanks!

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Gravity assist doesn't use relevant amounts of angular momentum of Earth's rotation, but almost exclusively Earth's orbital momentum, which may be interpreted as angular momentum of the Earth-Sun system. Hence the ISS doesn't convert relevant amounts of angular momentum from Earth's rotation to momentum of ISS (may be interpreted as angular momentum of the Earth-ISS system). There exists a couple of minor rotation-dependent effects, dependent on Earth's mass distribution, magnetic fields, etc.

Gravity assist can accelerate, or deaccelerate relative to Sun's (almost) inertial frame, depending on the velocity vectors of the planet and the probe/asteroid. Gravity assist applies mainly to flyby, or momentum-based propulsion.

The ISS orbits Earth (no flyby), hence gravity assist isn't applicable, with the exception of propulsion.

Since gravity assist doesn't work the way you presumed, it doesn't apply to the Moon. Nevertheless our moon is "stealing" angular momentum from Earth by tidal acceleration. Earth's rotation is slowing down by this effect; a day gets longer about 2.3 milliseconds per century by tidal friction due to Moon and Sun (but there are other effects, as well, changing the length of a day).

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@Jerard Can you post some references? I would love to read more on this. –  Err Mar 6 at 17:07
    
Disregard last comment. Thanks, Jerard! –  Err Mar 6 at 20:14

There are two types of gravity-assists. When an object passes behind another, it accelerates. When it passes in front of another, it decelerates.

When looking from the sun watching the movement of the ISS while it orbits the earth, you would notice that its relative speed to yourself doesn't appear to be constant. It seems to change based on its position on its orbit around earth. It would appear to move faster while traveling in the direction the earth is heading and slower while traveling in the oppsite direction. You could say that a satellite orbiting a planet gets two gravity-assists per orbit, one accelerating and one decelerating. In the end these two assists cancel each other out.

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The moon's orbital is increasing due to tidal acceleration. This will happens to satellites whose orbital radius is above geosynchronous orbit (about 36,000 km above earth's surface).

But ISS is well below geosynchronous orbit. So it experience tidal deceleration. It's being pulled closer to the earth like Phobos is slowly getting closer to Mars.

I would expect ISS' tidal deceleration to be tiny in comparison to deceleration from atmospheric friction though.

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