Question

The mass of the jupiter is $1.9\times {10}^{2}kg$ and that of sun is $1.99\times {10}^{30}kg.$ The mean distance of jupiter from the sun is $7.8\times {10}^{11}m$. Speed of jupiter is (assuming that jupiter moves in circular orbit around the sun)

Answer 1

Given that,

Mass of Jupiter, $m_j=1.9\times {10}^{27}Kg$

Mass of sun, $m_s=1.99\times {10}^{30}Kg$

Distance from Jupiter and sun is $d=7.8\times {10}^{11}m$

Gravitational force between two masses is

$F=\frac{G{m}_1{m}_2}{d^2}$

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

$F=4.14\times {10}^{23}N$

Now, the gravitational force is balanced by centripetal force

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

$4.14\times {10}^{23}=\frac{1.99\times {10}^{30}\times v^2}{7.8\times {10}^{11}}$

$v^2=161604m/s$

$v=402m/s$