Planet z is in elliptical orbit about the star loki. at, Ask an Expert

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Planet Z is in elliptical orbit about the star Loki. At perihelion, the planet is moving at speed vp = 1.92x104 m/s at a distance of rp = 4.95x1011 m from Loki. At aphelion, the planet is at distance ra = 9.31x1011 m from Loki.
Assume the angular momentum of the planet is constant.

a) Find va, the speed of Planet Z at aphelion.

b) If the period of orbit of Planet Z is Τ = 6.11 years, find M, the mass of the star Loki.

You will need to find a, the semi-major axis of the orbit, which should be easy since you already know the aphelion and perihelion distance.

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