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Suppose an artificial satellite is launched to orbit the moon. Ignore 3-body problem issues, just assume it follows a roughly titled elliptical orbit relative to the plane cutting through earth's equator.

The moon is tidally locked to the earth--that is, the moon's surface itself rotates with the same period the moon rotates around the earth.

My question is will this apply to the artificial satellite orbiting the moon? That is, will the orientation of the satellite's orbiting plane remain fixed or will it also rotate in the moon's 28 day cycle?

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If we ignore other bodies, the orbital plane will remain fixed. It will not turn along with the Moon as the Moon orbits. That would require a force acting on the satellite which is not in the orbital plane.

Orbits do precess in real-world examples, but that is under the influence of other bodies (or of uneven features of the body orbited), and it is usually on a much slower timescale than what we're talking about here.

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  • $\begingroup$ Oh, I see your answer now, I interpreted (and now after re-reading it I guess your answer applies better) that OP wanted to know if the satellite would basically always be between the moon and earth for example. But yes, OP asks if the orbital plane changes, not the orbital period. $\endgroup$ – José Andrade Jan 27 at 20:31
  • $\begingroup$ Thanks for the answer. So what if we do take into account the earth's gravity? Will it cause the orbital plane to rotate? $\endgroup$ – abnry Jan 27 at 22:09
  • $\begingroup$ If you take into account external perturbations the lunar orbiters right ascension of the ascending nodes changes over time according to Eq (4e) in the following document lpi.usra.edu/lunar/documents/NTRS/collection2/NASA_TP_3394.pdf $\endgroup$ – Rumplestillskin Jan 28 at 8:07
  • $\begingroup$ @abrny: if the Earth is idealized as a sphere, then no, it won't -again because there's no force that acts out of the orbital plane. If we take into account the irregularities of the Earth then the plane might change - but only at a very tiny rate. $\endgroup$ – Kristoffer Sjöö Jan 29 at 13:37
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No, because orbital speed is just dependent on the orbital altitude. Which means that you can find the orbital altitude that corresponds to the same effect as the spin-orbit lock of the earth-moon system, but at an arbitrary altitude that would not be the case.

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