Calculating Transit Windows

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Calculating Transit Windows

Post by Sirius_Alpha on 16th August 2012, 12:39 pm

Assume I have a planet with a known orbital period P, a known periastron ephemeris Tperi in JD, a known eccentricity e, and a known stellar radius Rstar. How would I go about estimating when a possible transit would occur (Ttransit)? (we're assuming b = 0).

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Re: Calculating Transit Windows

Post by Lazarus on 21st August 2012, 4:27 pm

The transit occurs when the true anomaly ν = π/2 − ω (working in radians)

Convert the true anomaly to the eccentric anomaly E using

E = atan2(√(1−e^2) * sin(ν), e + cos(ν))

where atan2(y, x) is the angle coordinate of the point (x, y). (Ensure you check which way round the atan2 function you are using takes the arguments)

Convert to the mean anomaly using the Kepler equation:

M = Ee * sin(E)

The time since periastron is given by

TtransitTperi = M/2π * P.

Time of eclipse can be found in a similar way but setting ν = 3π/2 − ω
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Re: Calculating Transit Windows

Post by Sirius_Alpha on 25th September 2012, 8:24 pm

Thank-you for this. I will have to play around with this and see what I can do. It's much appreciated.

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