Calculating Black Hole Mass Limit for Gravitational Acceleration Change

[omegas]

Homework Statement

Calculate the black hole mass limit such that the change in the gravitational acceleration at a distance 50R_s over a small interval of 2m doesn't exceed 10m/s². Use Newton's Theory of Gravity in the calculation.

Homework Equations

Schwarszchild Radius:

R_s = 2GM / c²

Newton's Theory of Gravity:

F = GMm / r²

The Attempt at a Solution

Totally lost. I'm an American study abroad student in New Zealand and am completely lost with these assignments. Don't know where to go for help.

 

[BerryBoy]

Firstly, write down the expression for how the acceleration due to gravity changes with distance (from Newton's equations), then times this by 2 [metres] and force it to equal ten (the limit that the field can change) ie

$$\Delta r \left. \frac{\rm{d} g}{\rm{d} r} \right\vert_{r=50 R_\rm{s} }} =10 \rm{\, ms}^{-2}$$

where $$\Delta r = 2 \rm{\, m}$$

Does this help??

 

[omegas]

Thanks. I did the calculations, but I keep getting a negative number. I set my r = 50R_s and for my dg/dr I get -2GMr^-3. So when I solve for M is keep getting a negative number.

 

[BerryBoy]

A change in the gravitational acceleration can be positive or negative and we are not told whether to move 2 m away or towards the black hole, so solve for the absolute change (i.e. don't worry about the negative sign the solution still answers the problem).