If the Moon would rotate around the Earth with double its current speed.
What would happen then? Would it get further from the Earth or it would be possible to keep its distance from Earth?
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$\begingroup$ Why has this question been downvoted? $\endgroup$– Jim421616Nov 29, 2020 at 18:53
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$\begingroup$ @Jim421616 Impossible hypothetical scenario questions are generally off-topic here. But I think this question is ok since it's (mainly) just asking about basic celestial mechanics. $\endgroup$– PM 2RingNov 29, 2020 at 21:16
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$\begingroup$ Can you clarify your question regarding "twice as fast". Orbital mechanics work such that as bodies orbit faster, they need to have a higher orbit. But the higher orbit has more distance to cover and that means that while moving "faster" they require more time to complete a full orbit. Are you referring to the velocity ... or the period of the orbit taking half as long to complete an orbit? $\endgroup$– Tim CampbellNov 30, 2020 at 4:53
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1$\begingroup$ @TimCampbell no orbital mechanics works such that as bodies orbit faster they need to have a lower orbit. $\endgroup$– James KNov 30, 2020 at 7:01
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No. The orbital speed is related to the distance of the moon by the equation
$$v=\sqrt{\frac{GM}{r}}$$
Where G is a constant, M is the mass of the Earth (adjusted for the mass of the moon) and r is the average distance of the moon(wikipedia).
So there are two interpretations of your question: firstly what would happen if we gave the moon a big push that doubled its speed? Well this would cause the moon to change its orbit from a roughly circular to an open orbit. The moon would sail off into space (slowing down as it is dragged back by the Earth, and end up orbiting the sun). The escape velocity is $\sqrt2$ times the orbital velocity, so if you are in orbit, and double the speed, you are sure to escape.
If you gave it a more gentle push it would enter an elliptical orbit. The speed would then be non-constant. If you increased its speed by 10% it would move 10% faster at perigee, but slower at apogee and on average its speed would actually be less than before.
The only way to increase the speed is to decrease the distance to the moon. If you reduced the distance by a factor of 4 (to about 95000km). This would cause the moon to double its speed.
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$\begingroup$ What if you give a push so it moves just 10% faster? 1.1 is lower than sqrt 2 $\endgroup$– Joe JobsNov 28, 2020 at 17:35
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$\begingroup$ Edited to discuss a 10% increase in speed. $\endgroup$– James KNov 28, 2020 at 17:44
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2$\begingroup$ @Joe If you did have the resources to double the Moon's orbital speed around the Earth you'd have to apply the required force rather carefully, over a long time span. Otherwise, you're likely to break it &/or melt it. $\endgroup$– PM 2RingNov 29, 2020 at 21:21
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$\begingroup$ Say a satellite is in orbit at 400 km. And then it uses thrusters to raise to 800 km. That means the satellite will reduce its linear speed simply because it raised its orbit? How can that happen? It is counter intuitive. Basic logic says it needs to fire thrusters in opposite direction to lose speed $\endgroup$– Joe JobsNov 30, 2020 at 15:28
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1$\begingroup$ You are in an orbit at 400km, you fire a burst of thrusters, increasing your linear speed. You then glide out, slowing down until you reach 800km, you are now going much more slowly, so you fire another burst of thusters to get into a circular orbit. You have increased speed again, but your final speed is still slower than when you started. $\endgroup$– James KNov 30, 2020 at 19:21