Exam 18: Relativity and Black Holes

A red giant star is found to be orbiting an unseen object with a short orbital period.By measuring the speed at which it orbits, astronomers deduce that the unseen object has a mass of 10 M_SUN.This object is probably a ________ because ________.

If you were to design a spacecraft that could travel to the galactic center fast enough that the astronauts aboard aged by only 25 years during the trip, how fast would the spacecraft have to go? (Note: The galactic center is 25,000 light years away.)

When do the predictions of special relativity match those of Newtonian physics?

Suppose that an object is moving and it is emitting light toward you, in vacuum.What would you notice about the light you observe?

How might we be able to detect events like colliding neutron stars even if we don't detect any light from them?

A 3-M_SUN star is seen orbiting with an unseen object with a period of 36 days and a semimajor axis of 1 AU.The mass of the unseen object is closest to

What are the possible effects that a gamma-ray burst (GRB) in our galaxy might have on life on Earth? Is this something we should be worried about in our lifetimes?

How would the Newtonian theory explain the orbit of Earth around the Sun? What would the explanation be in general relativity?

The event horizon of a black hole is defined as

A fast-moving muon decays in 2 *10 ^{- 4} seconds, as measured by an observer at rest.In the reference frame of the muon itself, its lifetime is in fact only 2 *10 ^{- 6} seconds.What is the muon's speed?

A gamma-ray burst (GRB), such as the one in the figure below, may be responsible for some of Earth's mass extinctions.GRBs are hard to study because they

What does gravity mean in relativity?

Earth's motion results in the apparent phenomenon of

The GPS system requires time accuracy of the order of a few tens of nanoseconds (ns) for the clocks aboard the satellites.At the high altitudes where the satellites are deployed, their orbital speeds are about 20,000 km/h.Show, considering special relativity alone, that corrections are needed in order to keep the surface of Earth and orbiting satellites synchronized to within the required accuracy.

Explain what four-dimensional spacetime means.

In the rubber-sheet analogy for spacetime, what would you expect for objects (such as golf balls) rolling around in the presence of a massive object that is stretching the rubber sheet?

Prior to the detection of gravitational waves, most black holes (excepting supermassive ones) were discovered through X-ray studies.From the figure below, what is different about the black holes detected through gravitational waves, and why might this be the case?