# A Planet revolves around the sun in an ellipse orbit of semi major axis 2xm.The areal velocity of the planet when it is nearest to the sun is 4.4xm/s.The least distance between planet and the sun is 1.8x10m.Find the minimum speed of the planet in Km/s?.

1
by Hitura

2014-10-20T05:42:54+05:30

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See diagram:

AP = major axis of the elliptical orbit of the planet = 2 * 2 * 10¹² m

Nearest distance at Apihelon = AF = 1.8 * 10¹² m = Ra

The farthest distance at perihelon = PF = AP - AF = (4 - 1.8) 10¹² m
PF = 2.2 * 10¹² m = Rp

Let us denote the linear (aerial) velocity of the planet as Vp at Perihelon P and as Va  at Apihelon A.

The angular momentum of the planet around the Sun is conserved. Hence

M Rp Vp = M Ra Va

Vp = Ra Va / Rp = 1.8 * 10¹² * 4.4 * 10¹° / 2.2 * 10¹²

Minimum speed of the planet is = Vp = 3.6 * 10¹° meters/sec
= 3.6 * 10⁷ kilometers/sec = 36,000,000 km/s
36 million km per sec

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