A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the fist one (approximately) by

Options

A. A)`1.5%`
B. B)`0.5%`
C. C)`3%`
D. D)`1%`

Answer

A

Explanation

From Kepler.s law, `T^(2)propR^(3)`
or `((T_(2))/(T_(1)))^(2)=((R_(2))/(R_(1)))^(3)`
`=((1.01R)/(R))^(3)`
`=(1+0.01)^(3)`
or `(T_(2))/(T_(1))=(1+0.01)^(3//2)`
`=1+((3)/(2)xx0.01)`
or `(T_(2)-T_(1))/(T_(1))=(1.5)/(100)=1.5%`