Calculate the position of the center of mass of the following pairs of objects. Use acoordinate system where the origin is at the center of the more massive object. Give youranswer not in meters but as a fraction of the radius as requested. Get data from insidethe front cover of your text.

Question

Earth Radius = 6.37x10^6 m

Moon Radius = 1.74x10^6 m

Jupiter Radius = 1.90x10^7 m

Earth to moon distance = 3.84x10^8 m

earth to sun 1.496x10^11m

jupiter to sun 7.78x10^11 m

(a) The Earth and the Moon. Give the answer as a fraction of the earth's radius.

(b) The Sun and the Earth. Give the answer as a fraction of the sun's radius.

(c) The Sun and Jupiter. Give the answer as a fraction of the sun's radius.

please show how to get it i am really stuck.

Answer 1

Just think of the planets as point masses on a lever. We want the lever to balance, where the fulcrum is the center of mass.

So, m1d1 = m2d2
or, m1/m2 = d2/d1

For earth-moon,
d = 3.84x10^8 = d1+d2
earth mass = 5.9742x10^24
moon mass = 7.3477x10^22

m1/m2 = 81.307
so, 82.307 * d1 = 3.84x10^8
d1 = 4.7228x10^6

So, the center of mass for the earth-moon system is 4.7228x10^6m from the center of the earth.

4.7228x10^6/3.84x10^8 = 0.0123 of earth radius

do similar work for the other systems

Answer 2

Oops. I figured as a fraction of the earth-moon distance, not the earth radius.

4.7228x10^6/6.37x10^6 = 0.74 of earth radius