posted by Amy on .
Calculate the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth when the two forces are in direct competition, that is, when the Sun, Moon, and Earth are aligned with the Moon between the Sun and the Earth. (This alignment corresponds to a solar eclipse.) (The mass of the Sun is 1.99 1030 kg, the mass of the Earth is 5.97 1024 kg, the mass of the Moon is 7.344 1022 kg, the distance between the Sun and the Earth is 1.496 1011 m, and the distance between the Earth and the Moon is 3.844 108 m.)
magnitude of the force exerted on the Moon by the Sun
magnitude of the force exerted on the Moon by the Earth
The Law of Universal Gravitation states that each particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Expressed mathematically,
F = GM(m)/r^2
where F is the force with which either of the particles attracts the other, M and m are the masses of two particles separated by a distance r, and G is the Universal Gravitational Constant. The product of G and, lets say, the mass of the earth, M, is sometimes referred to as GM or µ (the greek letter pronounced meuw as opposed to meow), the earth's gravitational constant. Thus the force of attraction exerted by the earth on any particle within, on the surface of, or above it, is F = 1.40766x10^16 ft^3/sec^2(m)/r^2 where m is the mass of the object being attracted = W/g, and r is the distance from the center of the earth to the mass. The force of attraction which the earth exerts on our body, that is, the pull of gravity on it, is called the weight of our body, and shows how heavy our body is. Thus, our body, being pulled down by by the earth, exerts a force on the ground equal to our weight. The ground being solid and fixed, exerts an equal and opposite force upward on our body and thus we remain at rest. A simple example of determining this force, or our weight, is to calculate the attractive force on the body of a 200 pound man standing on the surface of the earth. Now the man's mass is his weight divided by the acceleration due to gravity = 200/32.2 = 6.21118 lb.sec^2/ft. The radius of the surface from the center of the earth is 3963 miles x 5280 ft/mile = 20924640 feet. Thus the attractive force on his body is 1.40766x10^16(6.21118)/20924640^2 = 200 pounds. What do you know? The mans weight. Now, the attractive force on the 200 lb. man 1000 miles above the earth would only be 1.40766x10^16(6.21118)/26204640 = 127 pounds and half way to the moon, only .22 pounds.
Now use the data you have defined to determine the force of the earth on the moon and the opposing force exerted on the moon by the sun.