Question

Explorer $38$, a radio-astronomy satellite of mass $200kg$ circles the earth in an orbit of average radius $\frac{3R}{2}$, where $R$ is the radius of the earth. Assuming the gravitational pull on the mass of $1kg$ at the earth's surface to be $10N$, calculate the pull on the satellite.

• A. $889N$
• B. $8.89N$
• C. $8889N$
• D. $88.9N$

Answer 1

The correct option is A $889N$

From Newton's law, we know that: $F=\frac{GMm}{R^2}$
or, $\frac{F}{m}=g=\frac{GM}{R^2}$

So, for earth, $g=\frac{GM}{R^2}$
For satelite, $g^{\prime }=\frac{GM}{r^2}=\frac{g{R}^2}{r^2}=\frac{g{R}^2}{(3R/2{)}^2}$
$\therefore g^{\prime }=\frac{4}{9}g$
$\Rightarrow g^{\prime }=\frac{40}{9}N/kg$
$\therefore$ Pull on the satellite,
$w=m{g}^{\prime }=200\times \frac{40}{9}=889N$