Question

1. 1) Strength of the electric force
   The earth and the moon exert attractive gravitational forces on one another according

   to Newton's law of gravitation. However, since the earth and the moon are electrically neutral (that is, the net charge of each planet is zero), they do not exert electrical forces on one another.

   Assume now that someone (aliens) removes some number N of electrons from both the earth and the moon, so that the two bodies now exhibit electrical repulsion due to their mutual positive charge q.

   1. a) Calculate the charge q (in Coulombs) that the earth and moon would each have to accumulate in order for the repulsive Coulomb force to balance the attractive gravitation force, thereby allowing the moon to leave the earth's orbit

   2. b) How many extra protons on each celestial body does the charge calculated in part (a) represent?

   3. c) Now estimate the number of protons making up the entire earth (explain your reasoning!), and then compare this number to the number of extra protons as calculated in part (b). Assuming the moon has charge q as calculated above, what percentage of all protons making up the earth would need to lack an electron in order to overcome gravity, thereby causing to moon to leave orbit? Would the aliens need to strip off a small or large portion of the earth's electrons in order to accomplish this feat?

Answer 1

Mass of the Earth

Mass of the Moon   

Now,

Part-a

The electric force will be equal to the Gravitational force,

therefore

by plugging all the values we get

which gives us

Part-b

The number of protons in the charge accumulated would be

which gives us

protons