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ASTR 2030 Homework #3 (due October 16th at the start of class)!
Please answer all parts of each question using complete (word and math)
sentences and showing your work. Always list your sources and collaborators.
Late homework will not be accepted.!
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(1) The X-ray-emitting object Hercules X-1 is generally thought to be an
accreting neutron star in a binary system, whereas the X-ray emitter
Cygnus X-1 is believed to be a black hole. Give two examples of how
astronomers can (sometimes) determine whether an X-ray-emitting object
is a neutron star or black hole. (2 points)!
(2) Give one reason why isolated (not in a binary system) radio pulsars are
known not to be spinning white dwarfs. (1 point)!
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(3) Give one reason why isolated radio pulsars are not consistent with being
spinning black holes. (1 point)!
(4) White dwarf supernovae are observed in all types of galaxies, whereas the
core collapse supernovae that result in the formation of neutron stars are
typically seen in galaxies that contain many recently formed stars. Explain
why this is so (Chapter 2 of the BR textbook may be useful here). (3 points)!
(5) The formula for the Schwarzschild radius of a black hole (the radius of the
event horizon, if the hole is non-spinning) is:!
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RS =
2GM
c2
where G = 6.67 x 10-11 m3 / (kg s2). The Earth has a mass of 6 x 1024 kg.
Suppose that small Earth-mass black holes exist. What would their
Schwarzschild radius be? Express this in centimeters and name an
everyday object of similar size. (2 points)!
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(6) You are the scientific consultant for the next James Bond movie, in which
the villain develops a device able to (slightly) squeeze the Sun. The villain
plans to hold the Earth to ransom, saying that the stronger gravity at the
surface of the squeezed Sun will cause the Sun to collapse. Is the villain’s
threat credible? Explain why or why not. (3 points)!
(7) The force of gravity (in the Newtonian approximation) on a mass m, at the
surface of a body of mass M and radius R, is given by!
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F=
GMm
R2
A neutron star has a mass that is 500,000 times greater than that of the
Earth, and a radius that is 600 times smaller. By what factor would the
force of gravity increase if you were standing on the surface of this
neutron star as compared to on the surface of the Earth? (3 points)!
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