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## Calculating conjunctions

General physics and astronomy discussions not directly related to Celestia
Topic author
krypton
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Location: San Francisco

### Calculating conjunctions

How would one go about calculating the conjunctions of moons?
What I''m interested in is finding out how often two moons would appear in conjunction in their full phase. So, assuming the moons have nearly identical orbital planes,how often would the inhabitants of a planet see as shown below? Assume the small moon has an orbital period of 6.01 days and the larger moon has an orbital period of 17.21 days. I don't expect anyone to do the math for me, but I would like to know the formula for finding the answer. Thanks.

chornedsnorkack
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### Re: Calculating conjunctions

krypton wrote:How would one go about calculating the conjunctions of moons?
What I''m interested in is finding out how often two moons would appear in conjunction in their full phase. So, assuming the moons have nearly identical orbital planes,how often would the inhabitants of a planet see as shown below? Assume the small moon has an orbital period of 6.01 days and the larger moon has an orbital period of 17.21 days. I don't expect anyone to do the math for me, but I would like to know the formula for finding the answer. Thanks.

Frequency would be zero by definition.

The frequency of conjunctions is a trivial exercise:
the bigger moon covers 360 degree in 17,21 days, so the angular speed is 360/17,21=20,92 degrees per day
the smaller moon by same logic will have angular speed 59,90 degrees per day
it therefore is chasing the bigger moon at 59,90-20,92=38,98 degrees per day
and has a conjunction each 360/38,98=9,24 days.
Since the orbits are in nearly same plane, every conjunction also is a transit.
But transits at full phase will never happen. If a full transit did happen once then the next transit would be near new, and the third transit would be 18,48 days after first... and not full phase, because the second exact full phase of the bigger moon would have been 17,21 days after the first and the fourth exact full phase of smaller moon 18,03 days after the first. So the third transit happens 1,27 days after the second full phase of bigger and 0,45 days after fourth full phase of the smaller moon. Both will be large phase gibbous waning moons - actually exactly same phase because they are in the same direction, but not exactly full.
Since the ratios of the orbital periods will generally be irrational, there will never be an exact full phase transit. So it will be a matter of judgement - how close to full is full?

Topic author
krypton
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Location: San Francisco

### Re: Calculating conjunctions

I should have been more specific.
"Full"=+ or - 12 hours of full phase. (Assume a 24 hour day)
"Conjunction"= within one degree.

chornedsnorkack
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### Re: Calculating conjunctions

krypton wrote:I should have been more specific.
"Full"=+ or - 12 hours of full phase. (Assume a 24 hour day)
Still ambiguous. +-12 hours for the outer moon (spanning 21 degrees) or +- 12 hours for the inner moon (spanning 60 degrees)?

Topic author
krypton
Posts: 24
Joined: 13.04.2013
With us: 7 years 1 month
Location: San Francisco

### Re: Calculating conjunctions

Never mind. I got it.