An astronaut stands at a position on the Moon such that Earth is directly over h

Question

An astronaut stands at a position on the Moon such that Earth is directly over head and releases a Moon rock that was in her hand.
(a) Which way will it fall?

towards the earth or towards the moon ?

(b) What is the gravitational force exerted by the Moon on a 2.4 kg rock resting on the Moon's surface?
? N
(c) What is the gravitational force exerted by the Earth on the same 2.4 kg rock resting on the surface of the Moon?
? mN
(d) What is the net gravitational force on the rock?
? N ; towards the earth or moon?

Explanation / Answer

a)
The rock will fall to the moon for the same reason that the austronaut stays on the moon. The force of gravity decreases exponentially as the distance between the two objects increases. Here's the proof.
b) Fgrvty=G(mrockmmoon)/r2=(6.67X10-11)(2.4)(7.35X1022)/(1.74X106)2 =3.876N c)
Fearth=G(mrockmearth)/r2=(6.67X10-11)(2.4)(5.7X1024)/(3.84X109)2 =6.185 * 10-5N d)
FN=Fmoon-Feath = 3.8759N towards the moon. basically no influence at all from the earth. a)
The rock will fall to the moon for the same reason that the austronaut stays on the moon. The force of gravity decreases exponentially as the distance between the two objects increases. Here's the proof.
b) Fgrvty=G(mrockmmoon)/r2=(6.67X10-11)(2.4)(7.35X1022)/(1.74X106)2 =3.876N c)
Fearth=G(mrockmearth)/r2=(6.67X10-11)(2.4)(5.7X1024)/(3.84X109)2 =6.185 * 10-5N d)
FN=Fmoon-Feath = 3.8759N towards the moon. basically no influence at all from the earth. =6.185 * 10-5N d)
FN=Fmoon-Feath = 3.8759N towards the moon. basically no influence at all from the earth.

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