(a) The magnitude of gravitational force between the moon and planet is [tex]1.721 \times 10^{20} \;\rm N[/tex].
(b) The acceleration of moon towards the planet is [tex]6.36 \times 10^{-3} \;\rm m/s^{2}[/tex].
(c) The acceleration of planet towards the moon is [tex]2.29 \times 10^{-5} \;\rm m/s^{2}[/tex] .
Given data:
The mass of planet is, [tex]m_{1}=7.503 \times 10^{24} \;\rm kg[/tex].
The mass of moon is, [tex]m_{2}=2.703 \times 10^{22} \;\rm kg[/tex].
The average distance between the centers is, [tex]d = 2.803 \times 10^{8} \;\rm m[/tex].
(a)
The magnitude of gravitational force between the moon and planet is,
[tex]F = \dfrac{G \times m_{1} \times m_{2}}{d^{2}} \\\\F = \dfrac{6.67 \times 10^{-11} \times 7.503 \times 10^{24} \times 2.703 \times 10^{22}}{(2.803 \times 10^{8})^{2}} \\F =1.721 \times 10^{20} \;\rm N[/tex]
Thus, the magnitude of gravitational force between the moon and planet is [tex]1.721 \times 10^{20} \;\rm N[/tex].
(b)
The acceleration of moon towards the planet is obtained as,
[tex]F = m_{2} \times a\\1.721 \times 10^{20} = 2.703 \times 10^{22} \times a\\a = 6.36 \times 10^{-3} \;\rm m/s^{2}[/tex]
Thus, the acceleration of moon towards the planet is [tex]6.36 \times 10^{-3} \;\rm m/s^{2}[/tex].
(c)
Now, the acceleration of planet towards the moon is obtained as
[tex]F = m_{1} \times a'\\1.721 \times 10^{20} = 7.503 \times 10^{24} \times a'\\a' = 2.29 \times 10^{-5} \;\rm m/s^{2}[/tex]
Thus, the acceleration of planet towards the moon is [tex]2.29 \times 10^{-5} \;\rm m/s^{2}[/tex] .
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