Tidal forces can be extreme near a black hole: the black hole\'s gravitational f

Question

Tidal forces can be extreme near a black hole: the black hole's gravitational force is stronger on the part of an object closer to the black hole and weaker on the part of the object farther from the black hole. This differential force will literally pull objects apart, a process dubbed "spaghettification." The tidal acceleration a experienced by an object of size d that is distance R away from a mass M is a = 2GMd/R^3 Consider a black hole that is 0.85 solar masses. A 1.7-m tall, 79 kg astronaut is 125 km away from the blackhole. What tidal acceleration does she experience? The tidal acceleration for this astronaut is Number _____ times the acceleration due to gravity on Earth.

Explanation / Answer

given
tidal acceleration a, esperienced by an object of size d at distance R away from the mass M is given by
a = 2GMd/R^3

so, black hole mass, M = 0.85 solar masses = 0.85*1.98*1030 = 1.69065*10^30 kg
G = 6.67*10^-11 ( universal gravitation constant)
d = 1.7 m tall
R = 125 km = 125,000 m

so, a = 2*6.67*10^-11*1.69065*10^30*1.7/125,000^3 = 196,303.6707 m/s/s

the tidal accelerationis n times the gravity on earth
where n = 196303.670784/9.81 = 20,010.56 times

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