a. Calculate the escape velocity of an object leaving a black hole with mass equal to 20 times the Sun's mass at a distance equal to the Earth's orbit (r = 1.5x 10¹¹ m) away from the singularity (the location of the black hole's center). Express your answer as a fraction of the speed of light c. Even though black holes have all of their mass concentrated at a single point in spacetime (called the singularity), the size of a black hole is often described using a distance called the Schwarzschild radius. This distance, r, is the distance at which the escape velocity is equal to the speed of light, c. Once an object or a light beam gets closer to the black hole singularity than the Schwarzchild radius, it cannot escape, because nothing can travel faster than c. b. Find the Schwarzchild radius of the 20 solar mass black hole.
a. Calculate the escape velocity of an object leaving a black hole with mass equal to 20 times the Sun's mass at a distance equal to the Earth's orbit (r = 1.5x 10¹¹ m) away from the singularity (the location of the black hole's center). Express your answer as a fraction of the speed of light c. Even though black holes have all of their mass concentrated at a single point in spacetime (called the singularity), the size of a black hole is often described using a distance called the Schwarzschild radius. This distance, r, is the distance at which the escape velocity is equal to the speed of light, c. Once an object or a light beam gets closer to the black hole singularity than the Schwarzchild radius, it cannot escape, because nothing can travel faster than c. b. Find the Schwarzchild radius of the 20 solar mass black hole.
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Transcribed Image Text:3.
a. Calculate the escape velocity of an object leaving a black hole with mass equal to 20 times
the Sun's mass at a distance equal to the Earth's orbit (r = 1.5x 10¹¹ m) away from the
singularity (the location of the black hole's center). Express your answer as a fraction of the
speed of light c.
Even though black holes have all of their mass concentrated at a single point in spacetime
(called the singularity), the size of a black hole is often described using a distance called
the Schwarzschild radius. This distance, r, is the distance at which the escape velocity is
equal to the speed of light, c. Once an object or a light beam gets closer to the black hole
singularity than the Schwarzchild radius, it cannot escape, because nothing can travel faster
than c.
b. Find the Schwarzchild radius of the 20 solar mass black hole.
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what does this mean? I dont know what is being squared and what is a new thought.
Transcribed Image Text:=V
Escape velocity=
v=2GMrG = 6.67×10-11M = 20×1.99×1030 kgr = 1.5×1011v = 2GMrv = 2×6.67×10-
11×20×1.99×10301.5×1011v=1.88×105 m/svc = 1.88×105 m/s3×108 m/svc = 6.27×10-
4 Schwarzchild radius =RsEscape velocity becomes cc = 2GMRsRs = 2GMc2Rs =2×6.6
7x10-11x20x1.99×10303×1082Rs = 58992.44 m Rs ≈58.99 km ≈59 km
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