Mass of Jupiter is 1.9×10^30 kg and mass of the Sun is 2×10^30 kg. Calculate the distance between them if the gravitational force between them is 4.3×10^29N.
Solution
Solution:
Given,
Mass of Jupiter ( \(\rm m_{j}\) ) = \(\rm 1.9×10^{30} kg\)
Mass of Sun ( \(\rm m_{s}\) ) = \(\rm 2×10^{30} kg\)
Gravitational force between them ( \(\rm F\) ) = \(\rm 4.3×10^{29} N\)
Universal gravitational constant ( \(\rm G\) ) = \(\rm 6.67×10^{-11} Nm^{2}kg{-2}\)
Distance between them ( \(\rm d\) ) = ?
We know,
\(\rm F\)= $ \frac{Gm_1m_2}{d^2} $
\(\rm d^{2}\)= $ \frac{Gm_jm_s}{F} $
\(\rm d^{2}\)= $ \frac{6.67×10^{-11}×1.9×10^{30}×2×10^{30}}{4.3×10^{29}} $
\(\rm d\) = \(\rm 2.43×10^{10}\)
Hence, If mass of Jupiter is \(\rm 1.9×10^{30} kg\) , mass of the Sun is\(\rm 2×10^{30} kg\) and gravitational force between them is \(\rm 4.3×10^{29} N\) the distance between them is \(\rm 2.43×10^{10}\).