Astronomy 89 Chapter 12
What size would we have to shrink the earth for it to become a black hole?
1) v(esc) = sqrt2GM/r 2) c = sqrt2GM/r(black hole) 3) r=2GM/c^2
Escape velocity Equation
1/2mv^2 is greater than or equal to (GMm)/r or v(esc) = sqrt(2GM)/r
Gravitational waves from merging black holes
LIGO (Laster Interferometry Gravitational Wave Observatory) has detected signals that exactly match theoretical predictions of merging black holes
What do you think would happen to the Earth's orbit if the Sun suddenly turned into a black hole? Assume the mass of the black hole equals the mass of the Sun
Nothing If the Sun shrank into a black hole, its gravity would be different only near the event horizon. The rest of the solar system wouldn't notice (in terms of gravity)
No escape
Nothing can escape from within the event horizon because nothing can go faster than light. No escape means there is no more contact with something that falls in. It increases the mass of the black hole, changes its spin or charge, but otherwise loses its identity
What is a black hole?
Object whose gravity is so powerful that not even light can escape it Some massive star supernovae can make a black hole if enough mass (>3 Msol) falls onto the core
What is the escape velocity of the Earth?
Radius of Earth - 6,378,000 m Mass of Earth - 6.0 x 10^24 kg G- 6.6 x 10^-11 Nm^2kg^-2 Using 2nd equation: v(esc) = 11.2 m/s
Observational evidence for black holes
Spectroscopic observations can reveal a binary with an unseen companion (i.e. only one set of lines that moves back and forth) If unseen companion is >3 Msol, it must be a black hole
How do stars form?
Stars form in dark clouds of dusty gas in interstellar space The gas between the stars is called the interstellar medium
What is the final stage of evolution for a 15 solar mass star?
Supernova, then neutron star
"Surface" of a black hole
The surface of a black hole is the radius at which the escape velocity equals the speed of light This spherical surface is known as the event horizon The radius of the event horizon is known as the Schwarzschild radius
Escape velocity
You can escape from the surface of an astrophysical object (e.g. planet, star) only if you can reach a speed such that your kinetic energy is equal to or exceeds your initial gravitational potential energy
Gravitational lensing
bending of background light by foreground, massive object
What happens to the escape velocity from an object if you keep its mass the same, but shrink its size?
it increases
Surface of a black hole equation
r(s) = 2GM/c^2
