Aplanet is in an elliptical orbit around a distant star. at periastron (the point of closest approach to the star), the planet is rp=4.50×108 km from the star and is moving with a speed of vp=18.5 km/s . when the planet is at apastron (the point of greatest distance from the star), it is ra=9.10×108 km from the star. how fast is the planet moving at apastron? va=? km/s

9.15 km/s

Explanation:

rp = 4.5 x 10^8 km

vp = 18.5 km/s

ra = 9.10 x 10^8 km

va = ?

According to the conservation of angular momentum constant.

Let m be the mass of planet

m x rp x vp = m x ra x va

4.5 x 10^8 x 18.5 = 9.10 x 10^8 x va

va = 9.15 km/s

acceleration = (change in speed) / (time for the change)

change in speed = (20-120)= -100 m/s.

1.5 min = 90 sec

acceleration = -100/90 = -1.11 m/s^2.

we don't care about the 150kg or the 2,500 meters. they don't make any difference.

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