Imagine that the moon is held in place in its orbit about theEarth by electrical forces rather than by gravity. What is thenecessary electrical charge -Q that would be on the Earth and the+Q that would be on the moon to hold the moon in a circular orbitof 27.3 days? The Earth-Moon distance is 384,000 km and the mass ofthe moon is 7.35x10^22kg. Imagine that the moon is held in place in its orbit about theEarth by electrical forces rather than by gravity. What is thenecessary electrical charge -Q that would be on the Earth and the+Q that would be on the moon to hold the moon in a circular orbitof 27.3 days? The Earth-Moon distance is 384,000 km and the mass ofthe moon is 7.35x10^22kg.
Explanation / Answer
electric attarctive force = centripetal force KQ ^ 2 / r^ 2 = mrw ^ 2 Q ^ 2 = mr^3 w ^ 2 / K where m = mass of moon is 7.35x10^22kg r= The Earth-Moon distance = 384,000 km = 384 * 10 ^ 6 m w = angularspeed = 2 / T T = period =27.3 days = 27.3 * 24*3600 s So, w = 2.663 * 10 ^ -6 rad / s K = coulomb's cosnatnt = 8.99 *10 ^ 9 N m ^ 2 / C ^ 2 plug the values Q ^ 2 = 3.284 * 10 ^ 27 Q = 5.73 * 10 ^ 13 C