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Haul Me Up or Haul You Down?

We've been imagining that we're sitting in a geostationary satellite. That's a satellite that orbits the equator at the same speed and direction as the earth turns. That means it's always over the same spot of land, as if it were floating in the sky 22,500 miles up. We let down a rope to pull up some supplies. Will this work?

Nope. No conceivable rope would be strong enough to support its own weight at such a distance. Let's just pretend a rope could reach the ground and be tied to a box of supplies, and we have a big winch on the satellite to pull it up again. What are we forgetting?

Yep, the satellite itself. A geostationary satellite stays in the same spot with respect to the ground, but it still isn't attached to anything! So, will the satellite pull up the supplies or will the supplies pull down the satellite?

The answer is, a little bit of both. If the satellite is vastly more massive than the supplies, it could lift them without noticeable effect. However, no matter how massive it is, the satellite will always move a little bit toward the supplies. Even small deviations can spell disaster for a satellite, which can be thrown off course significantly by being forced into a different, undesirable altitude.

The more massive the supplies, the more the satellite will move. If the supplies are exactly as massive as the satellite, the two will meet halfway, if the satellite hasn't crashed yet! Twice as massive or more and the supplies will simply pull down the satellite altogether.

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