<p>Expanding on the question: Let's say I have a planet orbiting some star (earth-like, sun-like, for the sake of example). If this planet has two moons, M1 with orbital period of 30 earth-days and M2 with orbital period of 50 earth-days, how often will the center of these moons be collinear with the planet's center? What about if there were a third moon, with 70 earth-days orbit?</p>
<p>I tried solving for the intersection between the line formed by the two moons and the planet, but failed in simplifying the resulting equation.</p>

CC BY-SA 4.0
2021-07-22T03:40:29.923Z
Can we assume that the moon orbits are perfectly circular and coplanar?
PM 2Ring
CC BY-SA 4.0
2021-07-22T03:52:22.913Z
The key term for this kind of problem is "synodic period". See, eg https://astronomy.stackexchange.com/q/18380/16685 For your problem, you need half the synodic period, because the moons are collinear with the planet when their angular separation is 0° or 180°.
PM 2Ring
<natural-satellites><time><mathematics><moon-phases><orbital-resonance>
How to determine how often a planet's center will be collinear with its moon's?
PedroGaya
# How to determine how often a planet's center will be collinear with its moon's?

(Asked by: username_0 on 2021-07-22)

Expanding on the question: Let's say I have a planet orbiting some star (earth-like, sun-like, for the sake of example). If this planet has two moons, M1 with orbital period of 30 earth-days and M2 with orbital period of 50 earth-days, how often will the center of these moons be collinear with the planet's center? What about if there were a third moon, with 70 earth-days orbit?

I tried solving for the intersection between the line formed by the two moons and the planet, but failed in simplifying the resulting equation.

**Tags:** natural-satellites, time, mathematics, moon-phases, orbital-resonance
> **Comments:**
> **username_1**: Can we assume that the moon orbits are perfectly circular and coplanar?  
> **username_1**: The key term for this kind of problem is "synodic period". See, eg https://astronomy.stackexchange.com/q/18380/16685 For your problem, you need half the synodic period, because the moons are collinear with the planet when their angular separation is 0° or 180°.  

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