Question

Satellites A and B are orbiting around the earth in orbits of ratio R and 4R respectively. The ratio of their areal velocities is-

Answer 1

Using Kepler's second law we have:

Arealvelocity=

time

Areaswept

=

dt

2

1

r(rdθ)

=

2

1

r

2

ω=

2

1

rv=constant

Thus we get,

2

1

r

GM

r (from

r

mv

2

=

r

2

GMm

)

Thus we get

Areal velocity ∝

r

Thus for the planets with radius in ratio of 1:4 we get radii in the ratio of 1:2