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Earth Moon pair: find the system center of mass and gravity point to produce zero field

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SEE ATTACHMENT #1 for a diagram showing parameters.

Consider the earth, mass M= 5.98 E 24 kg, and the moon, mass m= 7.35 E 22 kg, as a system with distance d= 3.84 E 8 m between their centers.

Find the distance between the c.m. (center of mass) of the system, and the point where the gravity field of the earth cancels that of the moon to produce zero field.

Solution Summary

The system's center of mass and gravity point to produce zero fields are found. The expert provides a diagram to show the parameters. In a step by step solution, the problem is explained and solved.

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Step 1.
Recall that the gravity field of a body of mass M, exterior to its surface and at a distance r from its center, is toward the body, and is expressed by:
(1) g = G M / r^2 in which G is the universal constant 6.67 E -11 nt m^2 / kg^2

Step 2.
For the fields to cancel at a point x meters from Earth and d-x meters from the ...

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