## APAS 1010

### Problem Set #3

DUE TUESDAY MARCH 18, 1997

1. 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 measured 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 nearest neighbor?
2. 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.
3. What is the size of a black hole with the mass of our universe as measured in light years?
4. 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?
5. 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!!
6. 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 the speed?
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 wavelength shift?