Problem Set #3
DUE TUESDAY MARCH 18, 1997
email your answer before midnight to email@example.com
- Our galaxy contains approximately 200 billion stars each with an
mass equal to that of the sun on the average.
- a. What is the size of a black hole with the mass of our galaxy as
in light years? (For conversion from km to light years look in the
appendix #2 of Snow.)
- b. How does that size compare to the distance between us and our
- The universe contains approximately as many galaxies as there are
stars in a galaxy. Using our galaxy as average, what is the mass of the
universe as measured in solar masses.
- What is the size of a black hole with the mass of our universe as
measured in light years?
- The Big Bang occurred some 12 billion years ago and the outer edge of
the universe has been expanding with the speed of light since then.
- a. How does the black hole compare in size with the universe?
- b. Could one say the universe is a black hole?
- The curvature of space can be measured by the sum of the interior
angles of a triangle. When drawn on a sphere, the sum depends upon the
size of the triangle. If it covers 1/4 of a hemisphere such that it
contains three 90 degree angles, the sum is 270 degrees.
- a. Imagine a triangle that covers 1/2 of a hemisphere: what is the
sum of its interior angles?
- b. Now, try to imagine a triangle that covers the entire sphere;
what is the sum of its interior angles? This would be what a triangle
drawn on a black hole would look like, if you could see it!!
- Gravitational red shifts result from the slowing down of time near
a gravitational object. For weak gravitational fields, the red shift =
z = 0.5*(v/c)^2 where v is the escape velocity.
- a. What is the red shift at the sun?
- b. If that red shift was caused by the Doppler effect, what would be
- c. If light has a wavelength of 6000A when the source is at rest (or
in empty space), what is the color of the light as a result of the
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