How long will a satellite, placed in a circular orbit of radius that is ((1/4)) text th the radius of a geostationary satellite, take to complete one revolution around the earth?

Question

How long will a satellite, placed in a circular orbit of radius that is ((1/4)) text th the radius of a geostationary satellite, take to complete one revolution around the earth? (A) 12 hours (B) 6 hours (C) 3 hours (D) 4 days

Tardigrade Admin · Accepted Answer

From Kepler's third law T2 propto R3 or T propto R3 / 2 ∴ (T1/T2)=((R1/R2))3 / 2 (T1/T2)=((4 R1/R1))3 / 2 T2=(T1/8)=(29/8)=3 h

Q. How long will a satellite, placed in a circular orbit of radius that is $(\frac{1}{4})^{th}$ the radius of a geostationary satellite, take to complete one revolution around the earth?

12 hours

6 hours

3 hours

4 days

From Kepler's third law
$T^{2} \propto R^{3}$
or $T \propto R^{3/2}$
$∴ \frac{T _{1}}{T _{2}} = (\frac{R _{1}}{R _{2}})^{3/2}$
$\frac{T _{1}}{T _{2}} = (\frac{4 R _{1}}{R _{1}})^{3/2}$
$T_{2} = \frac{T _{1}}{8} = \frac{29}{8} = 3 h$

Q. How long will a satellite, placed in a circular orbit of radius that is (41​)th the radius of a geostationary satellite, take to complete one revolution around the earth?