The distance between the Sun and Jupiter is [tex]7.78\cdot 10^{11}m[/tex]
Explanation:
The magnitude of the gravitational force between two objects is given by
[tex]F=G\frac{m_1 m_2}{r^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
[tex]m_1, m_2[/tex] are the masses of the two objects
r is the separation between them
In this problem, we have:
[tex]F=4.14\cdot 10^{23} N[/tex] is the gravitational force between the Sun and Jupiter
[tex]m_1 = 1.99\cdot 10^{30} kg[/tex] is the mass of the Sun
[tex]m_2 = 1.89\cdot 10^{27}kg[/tex] is the mass of Jupiter
Solving the equation for r, we find the distance between Jupiter and the Sun:
[tex]r=\sqrt{\frac{Gm_1 m_2}{F}}=\sqrt{\frac{(6.67\cdot 10^{-11})(1.99\cdot 10^{30})(1.89\cdot 10^{27})}{4.14\cdot 10^{23}}}=7.78\cdot 10^{11}m[/tex]
Learn more about gravitational force:
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