BLACK HOLE MASs Section: Your Name: Team Name: Purpose (Answer the following que

Question

BLACK HOLE MASs Section: Your Name: Team Name: Purpose (Answer the following question related to the lab's purpose.) Kepler's second law implies that an orbiting star moves faster when close to a black hole and slower when farther away. Why is this? Explain by recalling the properties of gravity- (4 pts) 1. Procedure (Answer the following question about the procedure.) What sort of star works best for measuring the mass of the black hole: one with a short period or one with a long period? Explain. Does the mass of the star itself matter? Explain why or why not (4 pts) 1.

Explanation / Answer

1. kepler's second law implues that stars move faster when they are closer to black holes

this happens because gravitational field is a conservative field

so when the orbiting star is closer to the black hole, its potential energy decreases ( increases in magnitude with -ve sign), and hence consequenctly its KE must increase, eaning it travels faster when it is closer to the black hole as compared to when it is further away

1. for measuring mass of the black hole

let it be M

then time period of rotaiton of a satr around it = T

then

T = 2*pi*r/v ( for circular orbit)

now, v^2 = GM/r

r = GM/v^2

hence

T = 2*pi*GM/v^3

M = Tv^3/2*pi*G

dM = v^3*dT/2*pi*G

whwere v^3 is a constant

which depends on mass and diustacne from the star

hence

dM = (2*pi*GM/Tv^2)^3*dT/2*pi*G = (4pi^2G^2M^3)dT/T^3v^6

hence star with longer time period has less error in dM and mass of star itself does not matter

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