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According to this link

Mars is hiding behind the Moon ... It’s a twice-a-year occultation; like the eclipse

When such situations happen, can we communicate with the Mars rovers, and in the future - a human colony on Mars?

Or it's a time (how long? few hours?) when such communication is blocked?

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Yes, it is possible.

  • Radius of Earth:$6,378 \mathrm{km}$
  • Radius of the Moon: $1,737\mathrm{km}$
  • Semimajor Axis of the Moon's orbit: $384,000 \mathrm{km}$
  • Minimum distance from Earth to Mars: $54,600,000 \mathrm{km}$

Since the maximum difference in distance between the Earth and the moon is roughly 0.7% the minimum distance between Earth and Mars, you can effectively ignore the tiny change in apparent size due to the Moon being 384,000 km closer when between Earth and Mars, and can compare their diameters directly.

As a result, the apparent size of the Moon is always smaller than the apparent size of the Earth when viewed from Mars. The Moon cannot simultaneously block line-of-sight from all points on the Earth's surface to Mars.

And any communication link from a point on Earth to Mars or back will include some kind of relay in the design, because roughly 50% of the time, Mars will be below the horizon from said point on Earth.

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    $\begingroup$ Sorry, but that logic is rather flawed - we don't have communications stations all over the earth, so have very limited ability to pick and choose which ones to use. Occasions when the moon is in the exact same plane as both Earth and Mars are going to be limited, though, reducing the effect. $\endgroup$ – Mike Brockington Dec 21 '20 at 13:26
  • $\begingroup$ @MikeBrockington What is wrong with bouncing the communication off a satellite? $\endgroup$ – stackoverblown Dec 21 '20 at 14:07
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    $\begingroup$ The question was is it possible to make such a link. This answer demonstrates that it is in fact possible, so I give it credit, it doesn't rely on what is actually there, just is it possible. $\endgroup$ – PearsonArtPhoto Dec 21 '20 at 14:35
  • $\begingroup$ @stackoverblown Mention of relaying wasn't part of the answer when I made that comment - it has been substantially altered since then. $\endgroup$ – Mike Brockington Dec 21 '20 at 15:49

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