Physics
X-ray pulses from Cygnus X-1, a celestial x-
ray source, have been recorded during high-
altitude rocket flights. The signals can be
interpreted as originating when a blob of ion-
ized matter orbits a black hole with a period
of 7.84 ms.
If the blob were in a circular orbit about
a black hole whose mass is 13.5 times the
mass of the Sun, what is the orbit radius?
The value of the gravitational constant is
6.67259 × 10−11 N · m2/kg2 and mass of the
Sun is 1.991 × 1030 kg.
Answer in units of km.
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Answers
The orbit radius can be found using Kepler's Third Law, which is also known as the mathematical expression of Newton's Law of Gravity: T^2 = (4*Pi^2*r^3)/(G*m) where T is the orbital period, r is the orbital radius, G is the gravitational constant, and m is the mass of the celestial object. Plugging in the given values, we get: 7.84 ms^2 = (4*Pi^2*r^3)/(6.67259*10^-11 * 1.991*10^30) Multiplying both sides by 6.67259*10^-11*1.991*10^30, we obtain: 6.67259*10^-11*1.991*10^30*7.84 ms^2 = 4*Pi^2*r^3 Rearranging, we obtain: r^3 = (6.67259*10^-11*1.991*10^30*7.84 ms^2)/(4*Pi^2) Taking the cube root of both sides, we get r = [ (6.67259*10^-11*1.991*10^30*7.84 ms^2)/(4*Pi^2) ]^1/
