Can a planet's moon rise at the same time every night?

In order for this to be possible, the moon would have to be in the same place relative to the planet and the star throughout the day - in other words, if you drew a line from the center of the star through the center of the planet, then drew a line from the center of the planet through the center of the moon, you would have two lines that intersected at an angle that is forever constant.

For those who got past that first paragraph sentence, there are two places that would work: the Lagrangian points $L_1$ and $L_2$. The five Lagrangian points are laid out like this:

The "holes" and overall shape of space here is an analogy for gravity wells, so ignore that, but treat the green lines connecting the star, planet and points as rigid - in other words, as the planet revolves around the star, the green lines rotate with it, as do the Lagrangian points.

$L_1$ and $L_2$ will satisfy your scenario. However, $L_1$ should be discarded because putting the moon there would make it only appear in the daytime! So we'll take $L_2$.

The problem is that the only stable Lagrangian points are $L_4$ and $L_5$ notice how the others are near the metaphorical depressions of space. This indicates that if an object at them shifts, it will move away. For $L_4$ and $L_5$, the object will merely return.

To stay at $L_1$ or $L_2$, stationkeeping is required. So you'd have to attach thrusters to your moon to keep it in the same place! Alternatively, put it in a Lissajous orbit. You'll still need some thrusters, but it should be stable. Here's what the orbit will look like:

This kind of orbit would be very tough - if not impossible - to put a very massive object in.

Two moons would make this job nearly impossible, because if they were near each other, they'd most likely perturb each other's orbits and ruin any stability. Your odds of getting this to work for one moon are slim to none; your odds for two moons are slightly worse.

Or you can use a little handwavium to solve all your technical difficulties!

posted almost 10 years ago

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