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monitta
3 years ago
9

19. A satellite goes along an elliptical path around earth. The rate of change of area swept by the line joining earth and the s

atellite is proportional to (a) r/2 (c)r3/2 (d) r2
Geography
1 answer:
grigory [225]3 years ago
4 0

Answer:

r^\frac{1}{2}

Explanation:

Angular momentum, L = m v r

areal velocity = \frac{dA}{dt}

according to kepler's 2nd law

\frac{dA}{dt}=\frac{L}{2m}

since, we know that

v=\sqrt{\frac{Gm}{r} }

areal velocity= \frac{mvr}{2m} = \frac{vr}{2}

now substituting value of v in areal velocity we get

\frac{1}{2}\sqrt{GMr}

hence from above equation of rate of change of area swept i.e. areal velocity is proportional to   r^\frac{1}{2}

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