Question

The mass of planet Jupiter is $1.9\times {10}^{27}$kg and that of the Sun is $1.99\times {10}^{30}$kg. The mean distance of Jupiter from the Sun is $7.8\times {10}^{11}$m. Calculate the gravitational force which Sun exerts on Jupiter. Assuming that Jupiter moves in circular orbit around the Sun, also calculate the speed of Jupiter. $G=6.67\times {10}^{-11}$ $N{m}^{2}k{g}^{-2}$.

• A. $=5\times {10}^{23}$N
• B. $=4.15\times {10}^{23}$N
• C. $=15\times {10}^{23}$N
• D. $=1\times {10}^{23}$N

Answer 1

The correct option is B. $=4.15\times {10}^{23}$N.

Mass of Jupiter$=1.9\times {10}^{27}㎏=M_1$

Mass of Sun$=1.99\times {10}^{30}㎏=M_2$

Mean distance of Jupiter from Sun$=7.8\times {10}^{11}m=r$

$G=6.67\times {10}^{-11}N㎡{㎏}^{-2}$

Gravitational Force, $F=\frac{G{M}_1{M}_2}{r^2}$

$F=\frac{6.67\times {10}^{-11}\times 1.9\times {10}^{27}\times 1.99\times {10}^{30}}{{(7.8\times {10}^{11})}^2}$

$F=4.16\times {10}^{23}N$

Let the orbital speed of the jupiter be $v$.

The necessary centripetal force required to move in a circular orbit is provided by the gravitational pull acting on the jupiter.

Therefore, Centripetal force = Gravitational force

$\frac{m{v}^2}{r}=F$

$⟹v=\sqrt{\frac{Fr}{m}}$

$⟹v=\sqrt{\frac{4.16\times {10}^{23}\times 7.8\times {10}^{11}}{1.9\times {10}^{27}㎏}}$

$⟹v=1.3\times {10}^{4}m/s$.