Moon and Earth rotate about their common center of mass, which is located about RCM = 4700 km from the center of Earth. (This is 1690 km below the surface.) Take the distance from the center of the earth to the center of the moon to be 3.84x108 m, and the mass of the moon to be 7.35x1022 kg. a) Write an expression for the general acceleration due to the Moon’s gravity at the center of mass of the system (similar to how g is the general acceleration due to the Earth's
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
The Moon and Earth rotate about their common center of mass, which is located about RCM = 4700 km from the center of Earth. (This is 1690 km below the surface.) Take the distance from the center of the earth to the center of the moon to be 3.84x108 m, and the mass of the moon to be 7.35x1022 kg.
a) Write an expression for the general acceleration due to the Moon’s gravity at the center of mass of the system (similar to how g is the general acceleration due to the Earth's gravity at the surface of the Earth). Write your equation using variables from the problem statement as well as M as the mass of the moon, R as the distance between the center of the Earth and the center of the Moon, and any constants required.
b) Calculate this acceleration, in meters per second squared.
c) Calculate the centripetal acceleration of the center of Earth as it rotates about their common center of mass once each lunar month (about 27.3 d) in m/s2.
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