Using the data below, calculate the gravitational field of a satellite in orbit

Question

Using the data below, calculate the gravitational field of a satellite in orbit about a star at a distance of twice the star's radius. The star's stats are given by: M 200 astir 10^6 M_earth R = 10^8 m What is the surface gravity of the star? What is the escape velocity of a 1000kg mass in this orbit, r = 2 R? Calculate the Schwarzschild radius if the star's escape speed is equal to the speed of light. What is the event horizon of a black hole? Sketch the black hole's geometry. Describe what happens to an object as it passes the event horizon.

Explanation / Answer

2.1)
given

M = 200*10^6*Mearth

= 200*10^6*5.98*10^24

= 1.196*10^33 kg

R = 10^8 m

at r = 2*R

g = G*M/r^2

= 6.67*10^-11*1.196*10^33/(2*10^8)^2

= 1.994*10^6 m/s^2

2.2)

on the surface,

g = G*M/R^2

= 6.67*10^-11*1.196*10^33/(10^8)^2

= 7.98*10^6 m/s^2

2.3) Ve = sqrt(2*G*M/r)

= sqrt(2*g*r)

= sqrt(2*1.994*10^6*2*10^8)

= 2.82*10^7 m/s

2.4) Rs = 2*G*M/c^2

= 2*6.67*10^-11*1.196*10^33/(3*10^8)^2

= 1.77*10^6 m

2.5) Event horizon is imaginary spherical surface with the radius of Rs.

If object passes through event horizon it can escape from the blockhole.

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