# Where can I find formulas or calculators for apparent moon sizes?

(New here!) As I am setting up the astronomic framework of my new world, I have real issues finding information, formulas and calculators to get the actual size (diameter or radius) or apparent size (disk size) of my moons.

I know my roche limit and the hill sphere of my planet, and I have 3 placed moons in given distances from my planet and their orbital period, but how do I go on with actual size and apparent size of a moon? Doesn't that depend on mass too? I need to know how big my moons must be, for example so that one of them covers the sun disk for an eclipse with a corona, and for other reasons.

Any known links to calculators or formulas regarding this topic?

For completion, these are my moon datas at the moment, the planet is roughly like earth (1 earth mass, 0.9 radius):

Moon 1 - distance: 19.110 km, orbital period: 7.27 hours

Moon 2 - distance: 171.990 km, orbital period: 196.4 hours

Moon 3 - distance: 509.000 km, orbital period: 1001.76 hours

• Welcome to the site. Would your question not better be asked at astronomy.se ? – Burki Dec 5 '16 at 10:46
• Welcome to Worldbuilding SE and Stack Exchange. Useful terminology: angle subtended. – a CVn Dec 5 '16 at 11:48
• @Burki thanks for the hint, I will use that place to let my system be "proofread" once I have collected the most data. – Polarelch Dec 5 '16 at 12:59
• @Polarelch Just so you know, Astronomy.SE and Physics.SE and the other hard sciences usually close questions about speculative or fictional systems. If you want your system to be proof-read, posting here at Worldbuilding with the reality check tag is best. – kingledion Dec 5 '16 at 14:16
• @kingledion thanks I was already wondering a bit. I'll post it here in a new thread then – Polarelch Dec 5 '16 at 15:02

## 1 Answer

This is really just basic trigonometry.

radius / distance = tan(angle / 2)


or rearanged for diameter:

diameter = distance * tan(angle / 2) * 2


For example: When you want your moon 1 to fill 0.5° of the sky (about as large as our moon), it needs to have a diameter of 19110km * tan(0.5 / 2) * 2 = 166 km.

• i have the impression that the question also asks for the actual diameter of the moon. – Burki Dec 5 '16 at 10:45
• @Burki I think that's what this method provides. – Philipp Dec 5 '16 at 11:37
• you need either the real diameter or the apparent size. I understood the question so that it asks how big a moon has to be to match the information provided for distance and orbital period. – Burki Dec 5 '16 at 12:05
• @Burki The orbital period is derived from distance and gravity. The size of an object doesn't matter for calculating its orbit. – Philipp Dec 5 '16 at 12:31
• Hmmm... i would have expected that there should be an upper and a lower limit for the density. We would not want the moon to be a star, and we would not want it to be pulled apart by the gravitational pull of the planet. But i guess that still leaves a wide enough range for it to be "any sensible size". – Burki Dec 5 '16 at 12:40