Neptune was discovered due to irregularities in Uranus' orbit. At closest approach, these two planets are about 10 AU apart
a) What is the force of gravity between these two objects? b) How does that compare to the force of gravity between the Sun and Uranus (approximately 20 AU from the Sun)?
a) F = G M m / d2 = 6.7 × 10-11 m3 kg-1 s-2 ? 8.7 × 1025 kg ? 1.0 × 1026 kg / (10 ? 1.5 × 108 km)2 =
2.6 × 1023 N
b) As in a, but mass and distance change:
F = G M m / d2 = 6.7 × 10-11 m3 kg-1 s-2 ? 8.7 × 1025 kg ? 2.0 × 1030 kg / (20 ? 1.5 × 108 km)2 =
1.3 × 1027 N
That's about 5000 times the force between Uranus and Neptune. It is impressive that the hand calculations and observations of Uranus were accurate enough that this perturbation of Uranus' orbit led to the discovery of Neptune.
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