The average distance separating Earth and the Moon (center to center) is 384 000

Question

The average distance separating Earth and the Moon (center to center) is 384 000 km. Use the data in Table 7.3 to find the net gravitational force exerted by Earth and the Moon on a 3.00 104 kg spaceship located halfway between them.
1 N


Useful Planetary Data Body Mass (kg) Mean Radius (m) Period (s) Distance from Sun (m) T2/r3 (s2/m3)
Mercury 3.18 1023 2.43 106 7.60 106 5.79 1010 2.97 10-19
Venus 4.88 1024 6.06 106 1.94 107 1.08 1011 2.99 10-19
Earth 5.98 1024 6.37 106 3.156 107 1.496 1011 2.97 10-19
Mars 6.42 1023 3.37 106 5.94 107 2.28 1011 2.98 10-19
Jupiter 1.90 1027 6.99 107 3.74 108 7.78 1011 2.97 10-19
Saturn 5.68 1026 5.85 107 9.35 108 1.43 1012 2.99 10-19
Uranus 8.68 1025 2.33 107 2.64 109 2.87 1012 2.95 10-19
Neptune 1.03 1026 2.21 107 5.22 109 4.50 1012 2.99 10-19
Pluto ~1.4 1022 ~1.5 106 7.82 109 5.91 1012 2.96 10-19
Moon 7.36 1022 1.74 106 - - -
Sun 1.991 1030 6.96 108 - - -

Explanation / Answer

The average distance separating Earth and the Moon (center to center) is r = 384 000 km = 384 * 10^6 m The net gravitational force exerted by Earth and the Moon on a 3.00 *10^4 kg spaceship located halfway between them is F = F -F' where F = force on ship due to earth = GMm / (r/2)^2 G = Gravitational constant = 6.67* 10^ -11 Nm^ 2/ kg^ 2 M = mass of earth = 5.98 * 10 ^ 24 kg m = mass of ship = 3* 10^4 kg F ' = force on ship due to Moon = GMm / (r/2)^2 M ' = mass of Moon = 7.36 × 1022 kilograms plug the values we get F = [Gm /(r/2)^2 ] [ M - M '] = [4Gm / r^2 ] [ M-M'] = 0.3206* 10^3 N

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