Can this orbit exist around the Earth and the Moon if the weight and speed of the satellite is ideal? I have added a picture below with the orbit drawn.

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    $\begingroup$ OK I see. Your question is about Earth orbits that go way beyond the Moon, and it doesn't necessarily involve Lagrange points. $\endgroup$ – uhoh May 11 '18 at 10:18
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    $\begingroup$ @uhoh yes you are correct $\endgroup$ – Muze May 11 '18 at 10:19
  • $\begingroup$ Your diagram kind of suggests that you are ignoring the fact that the moon revolves around the Earth, with a different period from the Earth revolving around the Sun. The Sun, Earth & Moon line up as you have shown them about once a month, but at other times they are in other positions $\endgroup$ – Steve Linton May 11 '18 at 10:35

Objects in that orbit would be subject to significant perturbations from the moon.

Without active maintenance, I can't believe it would be close to that orbit after a couple of years. Most likely it would eventually be ejected into a heliocentric orbit.

You can't put an object into a "perfect" orbit. There's too much other stuff out there (like Mars and Jupiter) that give things slight tugs and make them wander off. In the one you've shown, eventually the moon would toss it aside.

  • $\begingroup$ If the orbit has the same period as the Moon, the perturbations by it will be strictly cyclic, and as such, for certain orbits, may be cancelling each other out. $\endgroup$ – SF. May 11 '18 at 9:41
  • $\begingroup$ @SF. that's what halo orbits about the Earth-Moon Lagrange points are; geocentric orbits whose period are the same as the Moon's, such that lunar perturbations cancel out (average out) over the long term. $\endgroup$ – uhoh May 11 '18 at 10:26

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