In this problem, you will calculate the location of the center of mass for the earth-moon system, and then you will calculate the center of mass of the earth-moon-sun system. the mass of the moon is 7.35×1022 kg , the mass of the earth is 6.00×1024 kg , and the mass of the sun is 2.00×1030 kg . the distance between the moon and the earth is 3.80×105 km . the distance between the earth and the sun is 1.50×108 km .

Assuming that the earth is the center of all coordinates. The center of mass of the earth will be located at the coordinate

To calculate the center of mass of the Earth-moon we require to proceed to the calculations given by,

Where

= Mass of earth

= Distance to center of mass for earth

= mass of moon

= Distance from moon to earth (to center of mass)

Replacing the values we have

We extrapolate this procedure to the sun, but now including the three bodies, in this way

So we have the two center of mass:

System Earth-Moon equal to km

System Earth-Moon-Sun equal to km

the moon affects the earth gravitation ally, causing certain motions of that body and also producing tides in its ocean and atmosphere. the tidal wave in our atmosphere is, however, far too minute to be an effective cause in any known meteorological phenomenon.

explanation:

more than, less

less than, more