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A rocket is launched from earth to explore our solar system and beyond. As the rocket moves out of the earth's atmosphere and into deep space, the gravitational constant. g. decreases and approaches zero, and the gravitational potential energy of the rocket:

A. also decreases and approaches zero.

b. continually increases.

c. remains constant.

d. increases at first and then decreases and approaches zero.

I thought at first, the relationship between g and height would be the important factor so i thought that since Force of gravity goes by the inverse square, as you increase height, or distance of the rocket from earth in this case the r^2 value effectively decreases the value for g from 9.81 m/s^2 --> something much smaller as you get far away to other solar systems as the question implies, but as g gets smaller, h, from Ug=MGH gets bigger, but since H=R (maybe this is where my assumption was wrong) the rate at which g gets smaller and h gets bigger based on the distances, it seemed to me like at some point the gravitational potential energy would stop increasing (i thought a pretty large distance away from the center of the earth when this would happen cuz i think of it like 2 functions ones linear and ones exponential (mgh v. gmm/r^2) and they would eventually intersect and then i thought of how that could apply to the work energy theorem and i started getting confused) but either wayso i thought about it for a while and i picked letter D. the answer from the book was........ (spoiler bellow)

B., the explanation given was:

Energy is required to separate attracting bodies. The rocket is attracted to earth by gravity. Gravity is a conservative force so the added energy goes into potential energy.

Doesn't make sense to me.