Limit of Black Hole

1. Apr 27, 2010

omegas

1. The problem statement, all variables and given/known data
Calculate the black hole mass limit such that the change in the gravitational acceleration at a distance 50Rs over a small interval of 2m doesn't exceed 10m/s2. Use Newton's Theory of Gravity in the calculation.

2. Relevant equations

Rs = 2GM / c2

Newton's Theory of Gravity:

F = GMm / r2

3. 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.

2. Apr 28, 2010

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??

3. Apr 28, 2010

omegas

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

4. Apr 28, 2010

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).