Astronomy 1020 Stellar Astronomy Spring_2015 Day-37.

Astronomy 1020Spring_2015

Day-37Stellar Astronomy

Happy 25th Birthday

Course Announcements• Final exam (and Exam-4) is (are)

scheduled on Wednesday, May 6, 10:30-12:30pm

• LABS:• ALL LABS ARE Due: Wed. 29th at class time • Lab Make-up Day: TUESDAY 4/28 – E118

• OLY Lenses & Telescopes and the Spectrometer will be set up. All others can be done on a computer prior to coming.

• L-Ts since the other collection (so far): • 37, 41, 45, 117, 119, 121, 133

If the mass of a neutron star exceeds 3 M, it will collapse into a black hole.

Not even light can escape the gravitational pull of a black hole.

Can form directly from Type II supernova (if massive enough) or from accretion by a neutron star in a binary system.

Makes us question our assumptions about the nature of space and time.

An event describes something that happens at a specific location and specific time.

Special relativity describes the relationship between events in space and time.

Combines those two aspects into a four-dimensional spacetime.

Something that must be analyzed using special relativity is called relativistic.

Newton’s laws don’t apply to the universe, but they are not wrong; they are contained in special relativity.

There are many important implications of special relativity.

These apply to many areas of physics, including very small scales.

Here are five important implications:

1. Mass and energy are the same thing.

• Matter can be converted into energy and vice versa.

2mcE

2. The speed of light c is the ultimate speed limit.

3. “At the same time” is relative.• Perceived information is dependent on relative

motion.

4. Time passes more slowly in a moving reference frame time dilation.

5. An object is shorter in motion than it is at rest length contraction.

Human space travel is currently difficult. Current technology can make ships travel

at speeds of 20,000 m/s. Would take over 50,000 years to get to our

nearest neighbor star, Proxima Centauri. Moving at high speeds takes a lot of

energy.

The general theory of relativity describes how mass distorts the geometry of spacetime.

Asks us not to think of gravitation as a force, but rather the result of the shape of spacetime that objects move through.

The greater an object’s mass, the more it will bend the spacetime around it.

Special relativity: You can’t tell the difference if you’re in a spaceship at rest or moving at a constant velocity.

Both are valid inertial reference frames.

General relativity: You can’t tell the difference between being stationary on Earth and accelerating at 9.8 m/s2 in a spaceship.

Equivalence principle.

An object in spacetime follows the geometry of spacetime as the object moves.

Imagine spacetime as a rubber sheet. Path = geodesic (shortest distance

between 2 points). Falling objects have curved geodesics.

General Relativity

There are many consequences of general relativity. Here are four:

1. Mercury’s orbit is not completely stable— it precesses about 43 arseconds per century.

General Relativity

2. Light will also follow curved space and be bent around massive objects. This gravitational lensing can displace and

distort an object’s image.

General Relativity

3. Time runs more slowly near massive objects general relativistic time dilation. Results in gravitational redshift of light coming

from near those massive objects.

General Relativity

4. Gravitational waves should move through spacetime like ripples through the rubber sheet. Should move at the speed of light. Have not yet been observed. LIGO (Laser Interferometer Gravitational-

Wave Observatory) is looking.

General Relativity A black hole is a

singularity—all the matter has collapsed to one point.

Infinitely dense. It is a bottomless well

in the fabric of spacetime.

General Relativity Once you get too

close, no geodesics lead out, not even for light.

The boundary of no return is called the event horizon or the Schwarzschild radius.

Event horizon of a 1 M black hole = 3 km.

Extreme tidal forces would rip an object or human apart as it fell in.

Gravitational time dilation and redshift become infinite.

Black holes should lose energy by Hawking radiation: Virtual particles come into existence near it, and one falls into the black hole while the other becomes real and leaves.

Black holes can be found by effects of their gravity.

Can exist in X-ray binary systems. Rapidly varying X-ray sources require a very

small, very massive object.

It is possible that some gamma-ray bursts (GRBs) are given off by the creation of black holes.

The intense amount of radiation would spell trouble for life on a planet in its way.

Earth’s motion produces the aberration of starlight.

Slight change in stars’ positions reveals Earth’s relative motion.

Analogy: falling rain or snow as seen from a moving car.

CONNECTIONS 18.1CONNECTIONS 18.1

The boxcar experiment shows that two events that are simultaneous for a stationary observer may occur at separate times for someone in a different frame of reference.

Consequence of the speed of light being constant for all observers, moving or not.

MATH TOOLS 18.1MATH TOOLS 18.1

The Lorentz factor tells you how much time dilation or length contraction occurs when something is moving at a given speed.

The Lorentz factor is always ≥ 1. If you are traveling at a high speed through

space, you will make your trip in a shorter distance and shorter time than as observed by someone on Earth.

MATH MATH TOOLSTOOLS 18.2 18.2

General relativity does not show that Newton’s laws are incorrect.

Newton’s laws turn out to actually be approximations of the more detailed general theory of relativity when you consider a weak gravitational field, such as Earth’s or the Sun’s.

New theories should incorporate the old, correct ideas.

CONNECTIONS 18.2CONNECTIONS 18.2

Scientists check theories by considering their limits.

General relativity reduces to Newton’s laws in the limit of being far from a mass.

PROCESS OF SCIENCEPROCESS OF SCIENCE

You can find the total mass of two objects in an X-ray binary by considering the general form of Kepler’s third law, knowing their separation and orbital period.

For a blue supergiant and a compact object separated by 0.2 AU with a period of 5.6 days:

MATH TOOLS 18.3MATH TOOLS 18.3

Concept Quiz—Event Horizon

What is the event horizon of a supermassive black hole with a mass of 4 x 106 M?

A. 3 km

B. 12 km

C. 12 million km

D. 4 x 1015 km

Concept Quiz—Special Relativity

If you are stationary on Earth and you watch your friend fly by in a spaceship at half the speed of light, your friend will appear _____.

A. to have a stretched-out length, with time passing more quickly

B. to have a shorter length, with time passing more slowly

C. to have a stretched-out length, with time passing more slowly

D. to have a shorter length, with time passing more quickly

Concept Quiz—General Relativity

According to general relativity, why does the Moon orbit Earth?

A. The Moon and Earth have equal gravitational forces, but the Moon’s acceleration is greater than Earth’s.

B. The Moon is being acted on by a gravitational force to keep it in the warp in spacetime created by Earth.

C. The Moon is in a stable circular geodesic in the warp in spacetime created by Earth.

D. General relativity says that Earth is orbiting the Moon.

In everyday life, your perspective is easily related to someone else’s.

In such an inertial frame of reference, the usual laws of physics apply.

Velocities simply add. Newton’s laws should

apply to the universe.

Things are different at high speeds.

All observers will see that light moves at a speed of c, regardless of their motion.

Motion must be analyzed differently, using Einstein’s special theory of relativity.

Usually, perceived speeds depend on objects’ relative motion, but nothing can go faster than c!

Example: If a spaceship is going by Earth at a speed of c/2 and emits light, we’ll still see the light pass by Earth at a speed of c, not c + c/2.