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

Options

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

Answer

A

Explanation

From Kepler's lae, `T^(2)propR^(3)`
or `((T_(2))/(T_(11)))^(2)=((R_(2))/(R_(1)))^(3)=((1.01R)/(R))^(3)`
`=(1+001)^(3)`
or `(T_(2))/(T_(1))=(1+001)^(3//2)`
`=1+((3)/(2)xx001)`
or `(T_(2)-T_(1))/(T_(1))=(1.5)/(100)=1.5%`