# Calculating Transit Windows

## Calculating Transit Windows

Assume I have a planet with a known orbital period

*P*, a known periastron ephemeris*T*_{peri}in JD, a known eccentricity*e*, and a known stellar radius*R*_{star}. How would I go about estimating when a possible transit would occur (*T*_{transit})? (we're assuming*b*= 0)._________________

*Caps Lock: Cruise control for 'Cool'!*

**Sirius_Alpha**- Admin
- Number of posts : 3495

Location : Earth

Registration date : 2008-04-06

## Re: Calculating Transit Windows

The transit occurs when the true anomaly

Convert the true anomaly to the eccentric anomaly

where atan2(

Convert to the mean anomaly using the Kepler equation:

The time since periastron is given by

Time of eclipse can be found in a similar way but setting

*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*=*E*−*e** sin(*E*)The time since periastron is given by

*T*_{transit}−*T*_{peri}=*M*/2π **P*.Time of eclipse can be found in a similar way but setting

*ν*= 3π/2 −*ω***Lazarus**- dG star
- Number of posts : 2846

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.

_________________

*Caps Lock: Cruise control for 'Cool'!*

**Sirius_Alpha**- Admin
- Number of posts : 3495

Location : Earth

Registration date : 2008-04-06

Page

**1**of**1****Permissions in this forum:**

**cannot**reply to topics in this forum