Treating Sun and Earth as symmetric spheres, find the center of mass of the Eart

Question

Treating Sun and Earth as symmetric spheres, find the center of mass of the Earth-Sun system. Assume that x=0 in the center of the Sun.Where is this point in relation to the Sun's surface?Treating Earth and Moon as symmetric spheres, find the center of mass of the Earth-Moon system. Assume that x=0 in the center of the Earth. Where is this point in relation to the Sun's surface?Treating Earth and Moon as symmetric spheres, find the center of mass of the Earth-Moon system. Assume that x=0 in the center of the Earth.

Explanation / Answer

mass of the sun is M = 1.99*1030 kg mass of the earth is m = 5.97*1024 kg radius of the sun is R = 6.95*108 m radius of the earth is r = 6.38*106 m distance between the sun and earth is d = 1.49*1011 m distance between the centers of the earth and sun is D = 1.5*1011 m Let x = 0 at the center of the sun The center of mass of the earth-sun system is Xcm = (Mx1 + mx2)/(M+m) Xcm = [(1.99*1030 kg)(0) + (5.97*1024 kg)(1.5*1011 m)]/[(1.99*1030 kg)+(5.97*1024 kg)] Xcm = 4.49*105 m The center of mass is inside the sun
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mass of the moon is M = 7.36*1022 kg mass of the earth is m = 5.97*1024 kg radius of the moon is R = 1.74*106 m radius of the earth is r = 6.38*106 m distance between the moon and easrth is d = 3.84*108 m distance between the centers of the earth and moon is D = 3.92*108 m Let x = 0 at the center of the earth The center of mass of the earth-moon system is Xcm = (mx1 + Mx2)/(M+m)
Xcm = [(5.97*1024 kg)(0) + (7.36*1022 kg)(3.92*108 m)]/[( 7.36*1022 kg)+(5.97*1024 kg)]
˜ 4.60 x 106 km from the center of the earth.


mass of the moon is M = 7.36*1022 kg mass of the earth is m = 5.97*1024 kg radius of the moon is R = 1.74*106 m radius of the earth is r = 6.38*106 m distance between the moon and easrth is d = 3.84*108 m distance between the centers of the earth and moon is D = 3.92*108 m Let x = 0 at the center of the earth The center of mass of the earth-moon system is Xcm = (mx1 + Mx2)/(M+m)
Xcm = [(5.97*1024 kg)(0) + (7.36*1022 kg)(3.92*108 m)]/[( 7.36*1022 kg)+(5.97*1024 kg)]
˜ 4.60 x 106 km from the center of the earth.

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