If you know the mass of a star and an object\'s perihelion distance (closest app

Question

If you know the mass of a star and an object's perihelion distance (closest approach to the star) and aphelion distance (farthest point from the star), then using conservation of energy and angular momentum you can solve for the speeds of that object at perihelion and at aphelion. Comet Lovejoy, discovered in 2011, is a sun-grazing comet that had closest approach to the sun at 8.3X10^8 m, (the radius of the sun is 7.0X10^8 m) and an estimated farthest distance from the sun at 2.4X10^13 m.

1.) What are the minimum and maximum speed of Comet Lovejoy?

2.) What is the expected orbital period of Comet Lovejoy, assuming its close approach to the sun did not impact its orbit?

Explanation / Answer

(a) If r and R are the minimum and maximum distances

and v and V are the minimum and maximum velocities,

then CoM gives us

mvR = mVr

v = V(r/R)

and CoE gives us

0.5mv^2 - GmM/R = 0.5mV

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