The gravity force between Jupiter and Io will be 6.343 × 10²² N.
<h3>What is Newton's law of gravitation?</h3>
Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.
Given data;
Mass of Jupiter,![\rm m_j = 1.9 \times 10^{27} \ kg](https://tex.z-dn.net/?f=%5Crm%20m_j%20%3D%201.9%20%5Ctimes%2010%5E%7B27%7D%20%5C%20kg)
Mass of moon of Jupiter,
]
The gravitational constant is,![\rm G = 6.67 \times 10^{-11 } \ m^3 kg^{-1} s^{-2}](https://tex.z-dn.net/?f=%5Crm%20G%20%3D%20%206.67%20%5Ctimes%2010%5E%7B-11%20%7D%20%5C%20m%5E3%20%20kg%5E%7B-1%7D%20%20s%5E%7B-2%7D)
Distance between Jupiter and Io, R = 421,700 km = 4,217,00,000 m
The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.
The gravitational force is found as;
![\rm F = G \frac{ m_J m_{I_0}}{R^2} \\\\\ F = (6.67\times 10^{-11}) \frac{( (1.9\times 10^{27})\times (8.9\times 10^{22} )} { (421700000)^2}\\\\ F_g = 6.343 \times 10^{22} \ N](https://tex.z-dn.net/?f=%5Crm%20F%20%3D%20G%20%5Cfrac%7B%20m_J%20m_%7BI_0%7D%7D%7BR%5E2%7D%20%5C%5C%5C%5C%5C%20F%20%3D%20%286.67%5Ctimes%2010%5E%7B-11%7D%29%20%5Cfrac%7B%28%20%281.9%5Ctimes%2010%5E%7B27%7D%29%5Ctimes%20%288.9%5Ctimes%2010%5E%7B22%7D%20%29%7D%20%7B%20%28421700000%29%5E2%7D%5C%5C%5C%5C%20F_g%20%3D%206.343%20%5Ctimes%2010%5E%7B22%7D%20%5C%20%20N)
Hence, the gravity force between Jupiter and Io will be 6.343 × 10²² N.
The complete question is
"Jupiter has a mass of 1.9 × 1027 kg, and its moon Io has a mass of 8.9 × 1022 kg. Their centers are separated by a distance of 421,700 km what is the force of gravity acting on Io? "
To learn more about Newton's law of gravitation, refer to the link.
brainly.com/question/9699135.
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