The radius Rhand mass Mh of a black hole are related by Rh = 2GMh/c2, where c is the speed of light. Assume that the gravitational acceleration agof an object at a distance ro= 1.001Rh from the center of a black hole is given by ag = G M / r2 (it is, for large black holes). (a) What is ag at rofor a very large black hole whose mass is 1.69 × 1015 times the solar mass of 1.99 × 1030 kg? (b) If an astronaut with a height of 1.73 m is at rowith her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet ahead-afeet?

The radius Rhand mass Mh of a black hole are related by Rh = 2GMh/c2, where c is the speed of light. Assume that the gravitational acceleration agof an object at a distance ro= 1.001Rh from the center of a black hole is given by ag = G M / r2 (it is, for large black holes). (a) What is ag at rofor a very large black hole whose mass is 1.69 × 1015 times the solar mass of 1.99 × 1030 kg? (b) If an astronaut with a height of 1.73 m is at rowith her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet ahead-afeet?

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Question

The radius R_hand mass M_h of a black hole are related by R_h = 2GM_h/c², where c is the speed of light. Assume that the gravitational acceleration a_gof an object at a distance r_o= 1.001R_h from the center of a black hole is given by a_g = G M / r² (it is, for large black holes).

(a) What is a_g at r_ofor a very large black hole whose mass is 1.69 × 10¹⁵ times the solar mass of 1.99 × 10³⁰ kg?
(b) If an astronaut with a height of 1.73 m is at r_owith her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet a_head-a_feet?

Definition Definition Rate at which light travels, measured in a vacuum. The speed of light is a universal physical constant used in many areas of physics, most commonly denoted by the letter c . The value of the speed of light c = 299,792,458 m/s, but for most of the calculations, the value of the speed of light is approximated as c = 3 x 10 8 m/s.

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