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# Wednesday January 30 astro lecture.docx

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Brock University

Astronomy

ASTR 1P02

Bozidar Mitrovic

Winter

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Wednesday January 30, 2013
Astro Lecture:
Black Holes & Einstein’s General Theory of Relativity:
Black Holes
- if the core of a high mass star has mass above about 3M the degenerate
neutrons cannot prevent its gravitational collapse and it collapses into a
single point (so-called singularity)
- the escape velocity from a body (Earth, Moon, Sun, Star…) is the velocity that
an object has to have so that it can escape the gravitational confine of the
body
- for earth the escape velocity from it is about 11 km/s
- it can be shown that V*2esc (escape velocity) = 2GM/R (gravitational
constant)
- for given mass (M) Vesc increases with decreasing R
- singularity, escape velocity > the speed of light, escape velocity is equal to the
speed of light, event horizon, escape velocity < speed of light
- Schwarzschild Radius Rs is the radius of the event horizon
- Rs (in km)=3M (in solar masses)
- Example:
o For M=10 M Rs= 30km
o For M=20 M Rs=60 km
- Nothing, including light, can escape the region within the event horizon
hence the name “black hole”
How is one to detect a Black Hole?
- look for a binary system consisting of a regular star and an invisible object
with a mass of at least 3M
- [center of mass: is in the middle]
- third kepler’s law as formulated by Newton tells us that if you take the size of
the orbit cube and the orbital period squared you get the mass
o a*3/p*2 = Mpm
- from (1) and (2) one can find M and m
- also the invisible companion needs to be an intense source of x-rays
- stellar wind particles produced by the regular star system are accelerated by
the strong gravitational pull near the event horizon and as a result produce x-
ray radiation
- first discovered in 1971 by

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