# How often do satellites pass the moon?

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1. Jan 30, 2016

### Mr. Fizzix

So, I have really no background in astrophysics (other than touching on some areas in general physics and calculus). I understand that asking questions such as the one in my title, that I would need to be more specific, and I will attempt to be as specific as I can.

I understand that most satellites take around 90 minutes to orbit the Earth (once the orbit has "stabilized" so to speak), variable by what angle it orbits, at what altitude and possibly other factors. Let's say 90, and that it is orbiting on the same "plane" (not sure if this term is a generalization) as the moon. Now, I know that the moon orbits the Earth once every 27.322 days. I would assume they orbit the Earth in the same direction? So, how often would this satellite, one the same plane of the moon's orbit, "pass" the moon (that is, if a line was was drawn from the Earth's center to the moon's center, how often would it cross it).

This seems like such a basic question that I should be able to solve, but for some reason it is giving me a headache. Thank you in advance.

Brent

2. Jan 30, 2016

### Janus

Staff Emeritus
General solution:
$$T = \frac{1}{\frac{1}{P_s}-\frac{1}{P_m}}$$

Where Ps is the orbital period of the satellite*
and Pm is the orbital period of the Moon

*assuming the satellite has a nearer orbit than the Moon and orbits in the same direction.

3. Jan 30, 2016

### Mr. Fizzix

90.206 minutes. I was expecting it to be just a little bit above 90 (confirmed). It appears that this is within the error of satellite's variation in orbit times. Thank you for this, appreciate it.

4. Jan 31, 2016

### tony873004

I like to call it the "one over one over formula". This formula is seen a lot in math and science.
You can paint a house in 3 hours. I take 1000 hours to paint the same house. If we joined efforts, how long would it take?
A quick analysis shows that although I do contribute, I'm not much help to the team, so while the answer will be less than 3 hours, it won't be much less.
1 divided by 1/3 + 1/1000 is 2.991 hours.