An astronaut is orbiting a black hole with a mass of 2.0 × 10³¹ kg at a distance of 126 km from its center. The astronaut is positioned in the spacecraft so that his 0.10-kg cheeks are 0.050 m on either side of the orbital circle. What is the net tidal force pulling his cheeks apart?
G = 6.67 x 10^-11 N·m²/kg².

Question

Quizplus · Accepted Answer

The tidal force can be calculated using the formula for the differential gravitational force: ΔF = (2GmM/R^3) * d, where G is the gravitational constant, m is the mass of the cheeks, M is the mass of the black hole, R is the distance from the center of the black hole, and d is the separation between the cheeks. Plugging in the values: ΔF = (2 * 6.67 x 10^-11 N·m^2/kg^2 * 0.10 kg * 2.0 x 10^31 kg / (126,000 m)^3) * 0.050 m, we find that the net tidal force is approximately 10,000 N.

An Astronaut Is Orbiting a Black Hole with a Mass