Force Bal: 90%d Earth-Moon Gravitational Forces

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A satellite positioned 90% of the distance from Earth to the Moon experiences balanced gravitational forces from both celestial bodies. At this point, the gravitational pull from Earth is slightly stronger than that from the Moon due to the inverse square law of gravitation. The discussion emphasizes the need for a diagram to visualize the forces acting on the satellite. Participants are encouraged to demonstrate their calculations and reasoning rather than simply requesting answers. Understanding these gravitational dynamics is crucial for satellite positioning and orbital mechanics.
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Given that the distance between the Earth and the Moon is d = 3.84 x 10^8 m, show
that a satellite located exactly in-between the Earth and the Moon at a distance of
90% d from the Earth experiences no net force (at least when only the
gravitational force due to the Earth and the Moon at taken into account). Draw a
diagram showing the forces acting on the satellite.
 
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