Tidal effects in the Earth-Moon system are causing the Moon\'s orbital period to

Question

Tidal effects in the Earth-Moon system are causing the Moon's orbital period to increase at a current rate of about 35 ms per century. Assuming the Moon's orbit around the Earth is circular, to what rate of change in the Earth-Moon distance does this correspond? Hint: Differentiate Kepler's third law, the equation T^2=(16*pie^2 * r^3)/ GM These answers are INCORRECT: 3.2*10^-5 m/s.........7.5*10^-10 m/s ........ 1.1*10^-11 m/s ...... 8.86*10^-8 m/s ........... 8.9*10^-8 m/s...... 8.8*10^-8 m/s ........ 9.0*10^-8 m/s

Explanation / Answer

T= sqrt((4*pie^2 * r^3)/GM) = 2 * 3.1416 * (r^3/GM)^0.5

T = 2 * 3.1416 * (r^3)^0.5 (1/(6.67e-11*5.97e24))^0.5

T = 3.1487e-7 (r^3)^0.5

dT/dr = 3.1487e-7 * (0.5) * (3 r^2) * (r^3)^-0.5

dT/dr = 3.1487e-7 * (0.5) * (3) * (r)^0.5

dT/dr = 3.1487e-7 * (0.5) * (3) * (384400e3)^0.5

dT/dr = 0.009260069 s/m

dr = 35e-3/0.009260069

dr = 3.77967 meters per century

v = dr/t = 3.779669/(100*365.25*24*60*60) = 1.1977e-9 m/s

Please rate correct answer first. Thanks a lot

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