# Calculating Transit Windows

## Calculating Transit Windows

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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Sirius_Alpha

Number of posts : 3802
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Registration date : 2008-04-06

## Re: Calculating Transit Windows

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

Lazarus
dF star

Number of posts : 3070
Registration date : 2008-06-12

## Re: Calculating Transit Windows

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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Sirius_Alpha

Number of posts : 3802
Location : Earth
Registration date : 2008-04-06