acceleration due to gravity

Question

The mass of a black hole is roughly 2.0x10^32 kg.

a. How far would you be from the center of one if your 1.2x10^3 kg spacecraft was experiencing a force of 6.432x10^15N?

b. What acceleration due to gravity would your spacecraft be experiencing?

Answer 1

Part a)

Use the following gravitational equation:

F=(GMm)/r^2

where,

G=6.67x10^-11 Nm²/kg² (gravitational constant_

M= 2.0x10³² kg (mass of black hole)

m=1.2X10³ kg (mass of spacecraft)

F= 6.432x10¹⁵ N

We find 'r'. Plug in the above numbers into the equation to get

6.432x10¹⁵=(6.67x10^-11 *2.0x10³²*1.2X10³)/r²

6.432x10¹⁵=(1.601x10²⁵)/r²

solve for 'r' and we get

r=4.989 x 10⁴ m

So you would be 4.989 x 10⁴ meters from the center

Part b)

Set F= 6.432x10¹⁵ N equal to 'mg' to get

6.432x10¹⁵ = mg

where m=1.2X10³ kg so that we get

6.432x10¹⁵=1.2X10³ *g

solve for 'g' and we get

g=5.36x10¹² m/s²

So your acceleration due to gravity would be g=5.36x10¹² m/s²