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For a maths project I am working on, I need to be able to prove the equation for an elliptical orbit, related to Kepler's first law:

^{2}) (or should be as p can be replaced by that value)

Where:

r = distance from sun to any point on the orbit

p = semi latus rectrum

a = semi-major axis

e = eccentricity

θ = true anomaly (angle between a and r anticlockwise I think)

Can someone please help me to understand where these equations come from and also confirm that I have got my current facts straight?

Regards,

*Memocyl*