Question

A research satellite of mass 200 kg circles the earth in an orbit radius $\frac{3R_E}{2}$, where $R_E$ is the radius of the earth. Assuming the gravitational pull on a mass of 1 kg on the earth's surface to be 10 N, the pull on the satellite will be:

• A. 890 N
• B. 889 N
• C. 885 N
• D. 892 N

Answer 1

Answer: (B)

889 N

Force between earth and mass of 1 Kg is $F=\frac{G{M}_E\times 1}{R_E^2}=\frac{G{M}_E}{R_E^2}=10N$ ....(i)
Where $M_E$ is the mass of the earth and $R_E$ is the radius of the earth respectively.
Force between earth and satellite is $F^{\prime }=\frac{G{M}_E\times 200}{{\left(\frac{3}{2}{R}_E\right)}^2}$ ...(ii)
Divide (ii) by (i), we get $\frac{F^{\prime }}{F}=\frac{800}{9}$
$F^{\prime }=\frac{800F}{9}=\frac{800}{9}\times 10N$ ($\therefore$ F=10N (Given))
$=\frac{8000}{9}N=889N$