Tides on the Earth are caused by the difference in the Moon\'s gravitational fie
ID: 1582634 • Letter: T
Question
Tides on the Earth are caused by the difference in the Moon's gravitational field at the far side and at the near side of the Earth. The side of the Earth facing the Moon experiences a greater gravitational force than the side facing away from the Moon. The distance from the Earth's enter to the Moon's center is 3.84 x 10 m and the radius ofthe Earth is·7·10 m. The mass of the Moon is 7.36 x 1022 kg. (a) Calculate the Moon's gravitational field at the side of the Earth facing the Moon (b) Calculate the Moon's gravltational fleld at the slde of the Earth faclng away from the Moon. (c) Calculate the Moon's gravitational field at the center of the Earth. (d) Sketch the Earth and include the three vectors from parts (a) through (c). (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (e) Qualitatively explain why there are two tides a day on most places on the Earth due to the Moon. (Because of friction, the high tides do not exactly line up with the Moon.)Explanation / Answer
a)
r = distance between earth and moon = 3.84 x 108 m
R = radius of earth = 6.37 x 106 m
rn = distance of the moon from near side = r - R = (3.84 x 108) - (6.37 x 106) = 3.8 x 108 m
m = mass of moon = 7.36 x 1022 kg
gravitational field is given as
E = Gm/rn2 = (6.67 x 10-11) (7.36 x 1022)/(3.8 x 108)2 = 3.5 x 10-5
b)
r = distance between earth and moon = 3.84 x 108 m
R = radius of earth = 6.37 x 106 m
rf = distance of the moon from farther side = r + R = (3.84 x 108) + (6.37 x 106) = 3.9 x 108 m
m = mass of moon = 7.36 x 1022 kg
gravitational field is given as
E = Gm/rn2 = (6.67 x 10-11) (7.36 x 1022)/(3.9 x 108)2 = 3.2 x 10-5
c)
gravitational field is given as
E = Gm/r2 = (6.67 x 10-11) (7.36 x 1022)/(3.84 x 108)2 = 3.3 x 10-5