Black Holes Flashcards
• Define the term “escape speed” and explain how it changes with the mass of a body and the distance from that body
◦ Escape speed is the speed required for a projectile to break free from an objects gravity
‣ Eg the escape speed from the surface of the earth is 11.2km/s
◦ The pull of gravity depends on the mass of th embody and the distance from the centre of gravity of that mass
‣ Eg. If the sun is compressed, its mass will remain the same, but the distance between a point on then surface and the centre will get smaller and smaller
‣ So if the mass of an object is large but the distance from the centre of gravity from that mass is smaller the mass is compressed and the pull of gravity for an object on the shrinking surface will get stronger
‣ BASICALLY, same mass falling into smaller sphere = escape speed grows
How do you calculate escape speed?
Escape velocity = square root of (2xGx(M/R))
- M is the objects mass
- R is starting distance above the objects centre
- if starting from surface, use objects radius
What is gravitational constant
6.67x10^-11
• Describe what happens to bodies which attempt to orbit with speeds above and below the escape speed
◦ Only objects that are launched with a speed greater than the escape velocity will escape the body’s gravitational pull
‣ Important to note that escape speed means that something travelling away from the surface of a large body AT THIS SPEED will not require any more force to escape the body’s gravitational pull.
• This means that escape speed for something like a rocket that has continual forces is different
• But if something is travelling at a speed lower than the escape speed, it might need additional force to push it through
‣ THINK ABOUT IT LIKE ROLLING A BALL UP A HILL. - if earths gravity is like a ball making a dent in a rubber sheet, you need a certain speed to roll the ball so that it will reach the peak and roll over the edge
• Define the term “Schwarzschild radius” in terms of the escape speed and the speed of light.
t is the radius of the event horizon (the circle’s circumference divided by 2pi
‣ It depends on its mass - more mass = larger radius
‣ Cross the event horizon, and there is no way of getting out of the black hole - bc you would have to move beyond the speed of light to exit the black hole
‣ This is the distance from the centre at which the escape speed equals the speed of light
◦ This also means that as you cross the event horizon, and revel further and further to the singularity, the more and more fast you have to be than the speed of light in order to get out of the black hole
◦ Therefore, as mass increases, the Schwartzschild radius increases
• Explain why black holes are not “cosmic vacuum cleaners”
◦ Don’t think about it as having a ton of gravity because its a black hole, it has the same as whatever it formed from
◦ You can think of it as spacetime flowing into the black hole at the speed of light
◦ Eg if you turned the sun into a black hole, earths orbit would not change
• Describe the observational evidence for the existence of black holes, including the black hole at the center of our galaxy
◦ X-ray binaries
◦ A binary star is a pair of stars that orbit one another - eg Sirius A and Serius B which orbit one another
‣ In binary star systems, one dies before the other - and the other star will steal matter from the other, forming an accretion disk and an reach incredibly high temperatures
‣ X-ray telescope was created and they found those binary star systems - by measuring the star orbiting the invisible one showed that the unseen object had a mass that was compressed into a tiny area and surrounded by an accretion disc
◦ Studying the motion of stars near the very centre of our galaxy - orbit around Sagittarius A* - a supermassive black hole
‣ Can use the motion of these stars to calculate the mass of this unknown thing - found the black hole
◦ Gravitational wave detector to find black hole mergers
‣ two tubes that are 4km long, perpendicular to one another
‣ Somewhere in the universe, some things are moving around making gravitational waves, and one day they reach earth and the entire planet goes woah ripple ripple as they pass through
‣ So one arm gets shorter or longer by measurement as this wave passes through - measure the arms with lasers
‣ By correlating gravitational wave observations from detectors around the globe, very secure detections of incredibly distant black hole mergers can be made
◦ Direct imaging using the event horizon telescope
• Draw a diagram to explain gravitational lensing and relate it to observational evidence for the existence of black holes
- Light from the background galaxy is lensed by the spacetime curvature of the foreground galaxy, permitting us to see things we would normally not see
- gravitational lensing is when massive objects bend the space around them forcing light to follow its curved contours
- then we can prove the existence of black holes by looking at the gravitational lensing effect of objects behind the black hole
- wouldn’t see the black hole but lensing effect would prove there is a massive object bending light in the contours of spacetime
• Distinguish between stellar-mass and supermassive black holes
◦ Stellar mass black holes have masses about 3-50 times the mass of our sun
◦ Supermassive black holes can be around millions to billions of times the mass of the sun
‣ We have microscopic black holes
‣ Stellar mass black holes
‣ Intermediate mass black holes - 100-100,000 solar masses
‣ Supermassive black holes - millions/billions of solar masses
Describe what would happen to Earth if the Sun was replaced by a 1 solar mass black hole
Nothing, its mass would not change so its gravitational pull would not change
Schwarzschild radii of some objects:
The Milky Way: 0.3 light years
The sun: 3km
Jupiter: 3m
Earth: 1cm
Strawberry: 10^-29m
Schwarzschild radius equation
R = 2GM/c^2
What is the speed of light
3 x 10^8 m/s
Cygnus X-1 was the
First stellar mass black hole to be discovered observationally
- emits x rays due to the accretion disk around the black hole stealing matter from the companion star
- is a binary star system with a black hole and blue supergiant star
