Using the data below, calculate the gravitational field of a satellite in orbit
ID: 1558093 • Letter: U
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.