astro264 hw Ch S2 and S3
Which two statements are the basic premises for the special theory of relativity?
(1) The laws of nature are the same for everyone. (2) The speed of light is the same for everyone.
Rank the objects based on the amount that spacetime is curved (relative to flat spacetime) very near the surface (or event horizon) of each of the objects, from least to greatest.
(based on strongest gravity) least curvature- red giant, main sequence star, neutron star- most curvature
According to general relativity, which of the following statements are true?
-Fast orbiting pairs of neutron stars lose energy that is carried away by gravitational waves. -The universe has no center and no edges. -Gravity arises from curvature of spacetime. -Time runs slightly slower on the ground floor of a building than the top floor. -Crossing the event horizon of a black hole means leaving the observable universe.
The following are predictions made by the theory of relativity.
-Observers in different reference frames may disagree about whether two events in two different places occur simultaneously. -E = mc2 -No material object sent outward from Earth can reach or exceed the speed of light. (NOT Observers in different reference frames may disagree about the basic laws of nature.)
Which of the following accurately describe some aspect of gravitational waves?
-The existence of gravitational waves is predicted by Einstein's general theory of relativity. -Gravitational waves are predicted to travel through space at the speed of light. -Gravitational waves carry energy away from their sources of emission. -The first direct detection of gravitational waves came in 2015.
Which of the following five statements do both you and Al agree are true?
-The green light and red light travel at the same speed. -The green light reaches Al before the red light reaches him. -The green light and red light reach you at the same time. (NOT The green light and red light both flash at the same time and Al is the one who is moving)
Use the appropriate relativity formula given in the text to answer the following. Isabella is moving by you at a speed of 0.8c. Although 1 minute passes on your watch, how much time will you see pass on her watch?
36 seconds
Because they are obvious only at speeds that we never experience in our daily lives.
Because it has been verified by many observations and experiments.
Why do the predicted consequences of the special theory of relativity seem so strange to most of us?
Because they are obvious only at speeds that we never experience in our daily lives.
Einstein's general theory of relativity predicts that two orbiting neutron stars should radiate gravitational waves. How does the fact that the orbital period is getting shorter support this prediction?
Gravitational waves must carry some energy away from the system, and this loss of energy must cause the orbits to get smaller over time.
You and Al are both floating freely in your spaceships. Suppose that Al is moving away from you at 85 km/hr. You throw a ball in his direction at a speed of 75 km/hr. According to Al, which of the following is going on?
He sees you moving away from him at 85 km/hr and the ball moving away from him at 10 km/hr.
Bob is in a spaceship going by you at 90% of the speed of light, but in an upright standing position. Bob measures his mass to be 50 kg, his height to be 2.0 meters, and his waist size to be 80 cm. What would you say about his measurements?
His mass is more than 50 kg, his height is still 2.0 meters, and his waist size is less than 80 cm.
This figure shows an airplane traveling east to west along Earth's equator at the same speed that Earth rotates from west to east. Viewed from the Moon, what does the airplane do?
It remains stationary while Earth rotates beneath it.
Consider a binary system of two neutron stars. How should the emission of gravitational waves affect this system?
It should cause the orbits of the two objects to decay with time.
People on Earth would, of course, simply see the airplane fly westward at 1,670 km/hr. What is the significance of the difference in viewpoints between people on Earth and people on the Moon?
It shows that motion is relative not absolute.
Suppose your normal resting heart rate is 60 beats per minute. Now, suppose you board a spaceship that travels away from Earth at 90% of the speed of light. While on the ship, you measure your heart rate. What will it be?
It will still be 60 beats per minute.
Suppose you measure the density (mass per volume) of an object moving by you at high speed. How will its density compare to the density it would have at rest in your reference frame?
Its density would be higher.
Consider the image of a cluster of galaxies below. What does it show that is explained by Einstein's general theory of relativity?
Light from galaxies behind the cluster distorted as light is bent through the curved space near the cluster.
Are there any circumstances under which you would measure a moving object's length to be longer than its rest length?
No, you will always measure a moving object's length to be shorter than its rest length.
Imagine that the Sun could be turned into a black hole without changing its mass. How would Earth's orbit change?
Spacetime would become more curved at Earth's orbit.
What did scientists notice during the total solar eclipse of 1919 that provided evidence in favor of Einstein's general theory of relativity?
Stars whose light passed near the Sun appeared out of position.
How does the explosion of a nuclear bomb provide evidence for the theory of relativity?
The bomb converts rest-mass energy into thermal energy in accord with E = mc2, which is part of the theory of relativity.
In what way do observations of binary star systems support the special theory of relativity?
The fact that the stars appear distinct supports the idea that the speed of light is unaffected by the motion of the stars.
What does Al say about the lights as they illuminate you?
The green light illuminates you at the same time as the red light because although the green light flashes first, you are traveling away from it.
Again consider the scenario from a previous problem. A sprinter named Ben has challenged a beam of light to a race in the 100-m dash. The race is held in a stadium full of spectators. At the start signal, a laser beam is turned on at the start line, pointed down the track. At the same instant, Ben bursts out of the starting blocks at 99% of the speed of light (0.99c). According to Ben, what happens?
The light beam moves out ahead of him at the full speed of light, winning the race easily.
A sprinter named Ben has challenged a beam of light to a race in the 100-m dash. The race is held in a stadium full of spectators. At the start signal, a laser beam is turned on at the start line, pointed down the track. At the same instant, Ben bursts out of the starting blocks at 99% of the speed of light (0.99c). According to the spectators watching in the stands, what happens?
The light beam wins the race, but barely; it is going 1% of the speed of light faster than him.
A spaceship is moving past you at a speed close to the speed of light. If you could somehow watch the people inside it over a long period of time, what would you conclude?
They are aging more slowly than you.
You are racing away from Earth in a super space ship in which you can continually increase your speed by firing engines that never quit. Which of the following best explains how people on Earth will perceive your speed?
They will see your speed getting closer and closer to the speed of light but never reaching it.
Tom is going to your left at 90% of the speed of light and Joan is going to your right at 90% of the speed of light. What will Tom say about you and Joan?
You are moving away from him at 90% the speed of light. Joan is moving away from him at as speed that is faster than 90% of the speed of light but slower than the whole speed of light.
Suppose that, at rest, both you and a passenger on the other spaceship have the same heart rate of 60 beats per minute. How will you and the passenger on the other spaceship observe each other's heart rates as you pass by in your spaceships?
You would observe that the passenger in the other spaceship has a slower heart rate than you do, and she would observe that you have a slower heart rate than hers.
Which of the following correctly describes what we mean by a great circle on the surface of Earth?
any circle whose center is at the center of Earth
According to relativity, at the center of a(n) ___spacetime becomes infinitely curved.
black hole
LIGO detects gravitational waves because the lengths of its arms change as gravitational waves pass by. About how much are these lengths expected to change when LIGO detects gravitational waves from the merger of two neutron stars or two black holes?
by an amount smaller than the diameter of a proton
Given such small length changes (as noted in Part D), what can give scientists confidence that they have really detected a gravitational wave signal?
detecting the same changes at more than one location
The equivalence principle asserts that __________ are exactly equivalent.
effects of gravity and effects of acceleration
_____ is the boundary of a black hole beyond which a spacecraft could not even in principle transmit a radio signal to observers outside the black hole.
event horizon
we can travel at the speed of life
false, freddie mercury was a ****ing liar
Astronauts are weightless in the International Space Station because they are in a
free float flame
_____applies even to cases in which gravity or accelerations are present.
general theory of relativity
A star that happens to be hidden behind the Sun might become viewable during a solar eclipse due to the bending of light known as____
gravitational lensing
Spectral lines of hydrogen on a white dwarf appear at longer wavelengths than the same lines observed in the spectrum of the Sun, illustrating what we call____
gravitational redshift
____is the slowing of time that you observe when you look at an object with a strong gravitational field.
gravitational time dilation
Two neutron stars orbiting each other at close distance will gradually spiral in toward each other because they lose orbital energy to___
gravitational waves
Suppose the binary neutron star system did not emit gravitational waves. Which of the following shows what the data would look like in that case?
horizontal line
The observation that you will measure the length of an object moving relative to you as being shorter than the same object at rest is an example of____
length contraction
With current technology, we expect to be able to detect (directly) gravitational waves from a binary system of two neutron stars or two black holes __________.
only from the instant when the two objects merge into one
the rate at which time passes on any object moving relative to you depends __________.
only on the object's speed toward or away from you
A situation that at first does not seem to make sense is a___
paradox
When the Space Shuttle and Space Station are docked to each other, astronauts in these two spacecraft will make the same measurements about space and time because they are in the same ___
reference frame
_____tells us that objects in motion have greater mass than they do when at rest.
special theory of relativity
An observer on the Moon would observe astronauts on a spaceship passing by at 0.9c to age more slowly due to___
time dialation
If we could build a spaceship capable of traveling at a speed near the speed of light, passengers on the ship could make a journey to a star that is 500 light-years away within their lifetimes.
true
When we look at pictures of distant objects in the universe, the images of the objects often are distorted by gravitational lensing.
true
Where does an object on an elliptical orbit experience the greatest acceleration?
where spacetime has the most curvature
if a ____can really exist, it might be able to connect two widely separated locations in the universe.
wormhole
