Astronomy: Black Holes and Neutron Stars Worksheet

Question 1

Explain how a massive star can become a neutron star or a black hole at the end of its life.

Accepted Answer

A massive star can run out of nuclear fuel and collapse under gravity. If the collapsed core is supported by neutron pressure, it becomes a neutron star. If the core is too massive for any known pressure to stop the collapse, it becomes a black hole.

Question 2

A black hole has a mass of 10 solar masses. Use the approximation that the Schwarzschild radius is about 3 kilometers for each solar mass. Calculate the Schwarzschild radius of this black hole.

Accepted Answer

The Schwarzschild radius is 10 times 3 kilometers, so the radius is about 30 kilometers.

Question 3

Define the event horizon of a black hole and explain why it is important.

Accepted Answer

The event horizon is the boundary around a black hole where the escape velocity equals the speed of light. It is important because anything that crosses it cannot escape back to the outside universe.

Question 4

A neutron star has a mass of 1.4 solar masses and a radius of 12 kilometers. Use 1 solar mass = 2.0 x 10^30 kilograms. Estimate its average density using density = mass divided by volume and volume = 4/3 pi r^3. Use pi = 3.14.

Accepted Answer

The mass is 2.8 x 10^30 kilograms and the radius is 12,000 meters. The volume is about 7.2 x 10^12 cubic meters, so the average density is about 3.9 x 10^17 kilograms per cubic meter.

Question 5

A pulsar rotates 30 times each second. Calculate its rotation period in seconds.

Accepted Answer

The period is 1 divided by 30, so the pulsar completes one rotation in about 0.033 seconds.

Question 6

Explain why many neutron stars are observed as pulsars.

Accepted Answer

Many neutron stars have strong magnetic fields and emit beams of radiation from their magnetic poles. If those beams sweep across Earth as the star rotates, we observe regular pulses, so the neutron star is seen as a pulsar.

Question 7

Use escape velocity = square root of 2GM/R to estimate the escape velocity from a neutron star with mass 2.8 x 10^30 kilograms and radius 1.2 x 10^4 meters. Use G = 6.67 x 10^-11 N m^2/kg^2.

Accepted Answer

Substituting the values gives an escape velocity of about 1.8 x 10^8 meters per second. This is about 60 percent of the speed of light.

Question 8

Compare a white dwarf, a neutron star, and a black hole in terms of density and final core mass.

Accepted Answer

A white dwarf is the least dense of the three and forms from lower mass stellar cores. A neutron star is much denser and forms from a more massive collapsed core. A black hole forms when the collapsed core is so massive that gravity overwhelms all known support, making it the most extreme compact object.

Question 9

A star's core collapses from a radius of 10,000 kilometers to a radius of 10 kilometers. If angular momentum is conserved, explain what happens to its rotation rate.

Accepted Answer

The rotation rate increases greatly because the core becomes much smaller. When a collapsing object keeps the same angular momentum, a smaller radius causes it to spin faster, like an ice skater pulling in their arms.

Question 10

Describe two types of evidence astronomers can use to detect a black hole even though it does not emit light directly.

Accepted Answer

Astronomers can detect a black hole by observing stars orbiting an unseen massive object and by observing X-rays from hot gas in an accretion disk. They can also detect gravitational waves from black hole mergers.

Question 11

Two neutron stars orbit each other and merge. Describe one major signal or result that astronomers may observe from this event.

Accepted Answer

Astronomers may observe gravitational waves from the inspiral and merger. They may also observe a bright electromagnetic event called a kilonova, which can produce heavy elements such as gold and platinum.

Question 12

Explain why time dilation is stronger near a black hole than far away from it.

Accepted Answer

Time dilation is stronger near a black hole because gravity is much more intense close to its mass. According to general relativity, clocks closer to a very massive compact object run more slowly compared with clocks far away.

Astronomy: Black Holes and Neutron Stars

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