4
$\begingroup$

This is a hypothetical question. Thank you for your time and efforts.

A signal is sent from a transmitter on Mercury's surface while it is at its greatest western or eastern elongation. The signal is aimed at a spacecraft in orbit around the Moon at the time of a total lunar eclipse. At the time that the signal is sent, the spacecraft is within the Earth's umbra. There are no artificial satellites available to help pass the signal on. Will the signal be successfully received?

I understand that it will take the signal about 8 minutes to travel from the transmitter on Mercury to the vicinity of the Moon. I understand that, as the solar system stands, Earth may never witness a total lunar eclipse while Mercury is at its greatest western or eastern elongation.

Improve this question
$\endgroup$

2 Answers 2

Reset to default
10
$\begingroup$

A total eclipse occurs when a full moon coincides with an orbital node of the moon. That is to say it occurs entirely due to the relative position of the Moon to the Earth and Sun

An elongation of Mercury depends on the position of Mercury relative to the Earth and Sun. There is no resonance or any other relationship between the orbit of the Moon and the Orbit of Mercury.

So although it will be rare. There are two elongations of Mercury in 116 days, and there are about 60 or so total lunar eclipses per century, so you would expect about one lunar eclipse-elongation of Mercury coincidence per century.

For example, on Dec 31 2028, there will be a total lunar eclipse on the same day as the greatest western elongation of Mercury.

So that said, Mercury would be in line-of-sight of the eclipsed spacecraft orbiting the moon, as it would be at least 18 degrees from the sun, and the Earth (which is covering the sun) only has a diameter of about 2 degrees. There would be nothing to block the signal. So the signal would be received

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thank you so much for this very useful answer, James K! I do appreciate your time and attention. Thank you also for correcting my assumption that total lunar eclipses will never occur when Mercury is at an elongation. Very interesting! $\endgroup$
    – JM Yaden
    Oct 14, 2022 at 5:53
5
$\begingroup$

Thought it would be easier to visualize. Here I used the "worst case" values with Mercury's elongation at parhelion, Earth at aphelion, and the Moon at perigee.

This also assumes they're all in the same plane, but the inclination of Mercury's orbit and the Moon's orbit means the Earth actually blocking the line of site between the two would be pretty rare.

In the first image, the Earth-Moon distance and the Earth diameter are to scale (but not the Moon diameter). The second image is a zoomed-out view, the distances are to scale, but the planet/moon diameters are not (because they'd be smaller than a single pixel).

Zoomed

Earth-Sun-Mercury

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thank you so much for these images, Greg Miller. Yes, it is plain to see that a radio message would not be obstructed by the Earth in this scenario. I appreciate your time! $\endgroup$
    – JM Yaden
    Oct 14, 2022 at 16:48

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .