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Pathways to Astronomy

Stephen E. Schneider

Chapter 68

Black Holes - all with Video Answers

Educators

Chapter Questions

01:14

Problem 1

Calculate the Schwarzschild radius of a $3-M_{\odot}$ object.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
01:26

Problem 2

Calculate your Schwarzschild radius. How does that compare to the size of an atom? How does it compare to the size of a proton?

Narayan Hari
Narayan Hari
Numerade Educator
05:19

Problem 3

Some galaxies show evidence of very massive black holes at their centers. Calculate the radius of a billion- $M_{\odot}$ black hole. Calculate its density in kilograms per liter. (Reminder: There are 1000 liters in a cubic meter.)

Matthew Miranda
Matthew Miranda
Numerade Educator
02:42

Problem 4

Calculate the density of a black hole with a billion $\left(10^{9}\right)$ times the mass of the Sun. (Use $4 / 3 \pi R_{\mathrm{S}}^{3}$ as the volume of the black hole.) Compare your result to the density of water, and explain whether larger black holes have higher or lower densities.

Allison Krajewski
Allison Krajewski
Numerade Educator
01:44

Problem 5

If a neutron star is $10 \%$ bigger than its Schwarzschild radius, how slowly would a clock run on its surface? (Use the formula $\gamma_{G}=1 / \sqrt{1-^{R_{S}} / R}$ to calculate the gravitational time-stretching factor.

Averell Hause
Averell Hause
Carnegie Mellon University
03:38

Problem 6

Suppose you observe two friends. One takes her spaceship to an orbit around a black hole a distance of $1.1 R_{S}$ from the $\sin$ gularity (i.e., $10 \%$ farther away from the singularity than the event horizon is). The other moves in a straight line at $0.1 \mathrm{c}$.
Which friend has the greatest time-stretching factor (as observed by you)? (See Unit 53 for the special relativity Lorentz factor).

Shoukat Ali
Shoukat Ali
Other Schools
01:15

Problem 7

What is the radius and density of $A 0620-00$, assuming that it is a $16-M_{\odot}$ black hole?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:19

Problem 8

Neutron-density matter is close to being incompressible. Assuming that it is, we can calculate how big a mass of neutron-density matter turns into a black hole.
a. Calculate the density $\rho$ of a $1.4-M_{\odot}$ neutron star, which has a radius of $10 \mathrm{km}$.
b. The mass of a neutron star is equal to its volume times its density. Using the density you found in (a), multiply it by the volume $\left(4 / 3 \pi R^{3}\right)$ and use the Schwarzschild radius for mula to determine the radius when $R=R_{S}$.
c. Use the radius you found in (b) to calculate the mass of this
neutron star.

ES
Eugene Schneider
University of Minnesota - Twin Cities