Gravitational Acceleration near a Massive Black Hole

[mb85]

The radius Rhand mass Mh of a black hole are related by Rh = 2GMh/c^2, 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 / r^2 (it is, for large black holes). (a) What is ag at ro for a very large black hole whose mass is 1.61 × 10^14 times the solar mass of 1.99 × 10^30 kg? (b) If an astronaut with a height of 1.66 m is at ro with her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet?


Rh = 2(6.67x10^-11)(3.204x10^44)/ (3.0x10^8)^2
Rh = 4.75 x 10^17

So then, Ag = GM/ (1.001Rh)^2
Ag = (6.67x10-11)(3.204x10^44)/(1.001 x 4.75x10^17)^2
Ag = 0.0945 m/s^2

I find myself having trouble with part B. How do i relate them?

I did Ag = (6.67x10^-11)(3.204x10^44)/(1.66 x 4.75x10^17)^2
Ag = 0.0344 m/s^2
So i did the difference btwn answer A and B and got .0601 m/s^2

But i know its wrong. Can someone help me out? Thanks!

 

[Astronuc]

In part B,

calculate a_g at r_o and at (r_o + 1.66 m).

This assumes the astronaut's feet are at r_o.

 

[mb85]

So isn't Ro part A's answer?

and when you say Ro + 1.66, does that mean...
Ro =(1.001+1.66)Rh?

 

[Astronuc]

So isn't Ro part A's answer?

and when you say Ro + 1.66, does that mean...
Ro =(1.001+1.66)Rh?

According to the problem, in part A, one is to calculate a_g at r_o.

In part B, find the between a_g(r_o) and a_g(r_o+1.66m).

It should be something like A * (1/r_o² - 1/(r_o+1.66m)²), where A is some constant.