Teaser - no relativity required (promise!)

Based on your information and not bothering to look up the math. acceleration inversely proportional to black hole mass a = k *1/m k = a * m = 15 million mass * 1 million g acceleration = 15 million million mass * g acc m = k / a = 15 million million mass * g acc / 1 g acc = 15 million million solar mass.

This answer does not make sense.

Now what I don't understand is your claim that it is 'inversely proportional'. I would think that it should be 'directly proportional'.

F = m * a

• F_blackhole = F_space_craft
• M_blackhole = 15 M Sol
• a_blackhold = a_bh
• M_spacecraft = M_sc
• a_spacecraft = 1 M g
• F_bh = M_bh * a_bh = 15 M Sol * a_bh
• F_sc = M_sc * a_sc = M_sc * 1 M g

Solve for M_sc

Solve for Force on space craft

a_sc = 1 g

Solve for Mass of black hold.

M_bh = F / a = 15 Sol * a_bh / a_bh = 15 Sol

This answer seems reasonable. Therefore they must be directly proportional and not inversely proportional!

The trick lies in the "... 1% (by radius) outside of a non-rotating black hole's event horizon." of the question. This event horizon radius (r_e) grows linearly with the mass (M) of the black hole:

r_e = 2GM/c^2, where G is Newton's gravitational constant and c is the speed of light.

So direct proportionality for the acceleration against the mass cannot work...

Greetings Nick:

To prevent this dangling as a loose end, your original answer: "... 15 million million solar mass" is correct! It is a simple proportionality, provided that you stay a at constant fractional distance outside of the event horizon radius – the more massive the hole, the farther you are from it's center…

What is the "Score" after my name for?

You have to direct this question at the administrator/moderators of this forum. I guess it comes from an algorithm working on the number of accepted threads that you started... or whatever!