Part A: At what height above Earth\'s surface is the gravitational acceleration
ID: 2264149 • Letter: P
Question
Part A: At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 0.60%? Part B At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 6.0%? Part C At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 60%? Part A: At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 0.60%? Part B At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 6.0%? Part C At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 60%? Part B At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 6.0%? Part C At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 60%? Part C At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 60%?Explanation / Answer
(a)GMm/(RE+h)^2 = 0.006*GMm/RE^2
so, (RE+h)^2=(1000/6)RE^2
so, RE+h = 12.91RE
where RE=6.38*10^6 m
so, h=11.91*R = 11.91*6.38*10^6=75985.44km
(b)GMm/(RE+h)^2 = 0.06*GMm/RE^2
so, (RE+h)^2=(100/6)RE^2
so, RE+h = 4.0824RE
where RE=6.38*10^6 m
so, h=3.082*R = 11.91*6.38*10^6=19666.24km
so, (RE+h)^2=(10/6)RE^2
so, RE+h = 1.291RE
where RE=6.38*10^6 m
so, h=0.291*R = 11.91*6.38*10^6=1856.544km