Degeneracy
Roughly what is the size of a 1 solar mass white dwarf?
Approximately 5*106 m. About the size of the Earth (a little smaller).
What is the Tolman-Oppenheimer-Volkoff Limit for neutron stars?
It is the mass that is stable for a neutron star. The “Chandrasekhar Limit” for NS. It is approximately 3 M_Sun.
Roughly how distorted is space time near the Earth?
Time runs about 6.9 parts in 10^10 slower than in deep space (0.69 ns per second or 21 Milliseconds per year).
What is the virial theorem and how did we apply it to contracting clouds?
The Virial Theorem states that in a self-gravitating system in equilibrium, the time -average kinetic energy (K) is related to the time-averaged potential energy (U) as 2K=-U. [Here, the d2I/dt2=0]
Represent as Ω =-2U.
What is the Goldilocks zone?
It is the zone where the surface temperature (conditions) is theoretically right for habitability, with water as a liquid on the surface of a planet. Depends on star’s luminosity and separation, and somewhat on planet size. Optimal distance from star where liquid water can exist.
What is the Fermi energy for a degenerate gas?
The Fermi energy is given by εN. Fermi energy is the highest energy of a particle in the ground state in a degenerate gas.
Why are binary pulsars so good at measuring small effects like gravitational radiation?
Because they are two “exquisite clocks” that orbit each other. Variable Doppler shifts give us incredibly precise information about the systems.
Why can’t matter produce dipole gravitational radiation?
Matter cannot produce dipole gravitational radiation since all matter is attractive.
Why is Io so volcanically active, while its sister moons are dead, or near so?
Tidal heating. Io’s orbit allows it to be squished and stretched as it orbits Jupiter. (Very elliptical orbit because of orbital resonances).
What are the four techniques that have found exoplanets?
Doppler/Radial Velocity Method
Eclipse/Transit Method
Gravitational Microlensing
Direct Imaging
Why does the Chandrasekhar limit exist?
This is the mass limit for a White Dwarf. If a WD surpasses 1.4M_sun then its EDP will lose to gravity. In these conditions, the DP can no longer increase fast enough to counteract gravity.
Who was Mr. Clock and how did he confirm both special and general relativity?
Mr. Clock was Joseph Hafele. He, along with Richard Keating, conducted the Hafele-Keating experiment in 1971 where they flew two atomic clocks around the world on different commercial flights in different directions. Afterwards, they compared the clocks to the one in the U.S. Naval Observatory. This leads to the confirmation/postulate that altitude causes gravitational time dilation, but speed causes special relativistic time dilation.
How would Einstein think of an orbiting object compared to in Newton’s Universe?
In a Newtonian Universe, planets simply orbit around the planet in an ellipse being pulled by the force of gravity. In Einstein’s view, timespace gets curved by massive objects so the planets orbiting are actually circling around the curved path of the space that the massive object is distorting (the object is following the straightest possible path (geodesic) in curved spacetime).
What is tidal locking?
Tidal Locking is when a celestial body’s orbital period around another body matches that of its rotational period, causing the same side to always face the other. Net effect is to slow rotation and force bulge to align with tidal source. (Since tidal forces are proportional to mass of perturber, the Earth long ago locked the Moon to us).
What is the Roche limit and how does it apply to the formation and location of Planetary rings?
The distance from a celestial body within which a satellite (or any object held together by its own gravity) will disintegrate due to the larger body’s tidal forces exceeding the satellite’s Self-gravity. Represented as d<1.26R∛(ρprimary/ρsatellite). Typical safe distance is 2.44R_primary. ALL planetary rings are within this radius.
What is phase space and how much “volume” must a particle occupy in this space?
Phase space is a 6-dimensional space with the 3 spatial coordinates (x, y, z) and then an additional 3 momentum coordinates (p_x, p_y, p_z). With volume a particle must occupy, H.U.P. tells us that there is a limit to a particle’s phase space parameters. Basically an uncertainty distribution, however the P.E.P. states no two identical fermions can occupy the same phase space. Cannot be localized in a phase space smaller than h^3.
How can accretion of material onto neutron stars and black holes be more efficient than Nuclear fusion in releasing energy?
his is due to the friction in the accretion disk turning kinetic energy into thermal energy. This converts 10%-40% of E=mc2 into radiation. L~(0.1-0.4)Mc^2 Compared to nuclear fusion which is only 0.007Mc^2.
How close to forming a black hole is a neutron star?
The Schwarzchild radius of a NS is just about inside its own radius, so not a BH. Slight further compression with the same mass could cause its Schwarzchild radius to be outside its radius, creating an event horizon, therefore a BH. So it is about 50%-70% there. (If it surpasses the TOV Limit 3.0 M_sun).
What are the spring and the neap tides here on Earth?
Spring tides are higher than normal high tides and lower than normal low tides. This occurs when the Earth, Moon, and Sun are in alignment, either during a new moon or a full moon. Neap tides are the opposite of spring tides. They are lower high tides and higher low tides, occurring when the Moon is at a right angle to the Earth-Sun line (i.e., during the first quarter and third quarter phases of the Moon).
How are variations in a distant stars brightness used to find background planets through microlensing?
With the right geometry, the background star is “lensed” by gravity and becomes much brighter. This can even work for planets. If a planet crosses a very bright star, the brightness of the planet crossing will get lensed then dissipate after it passes, suggesting something was there.
Why are white dwarfs supported by electron degeneracy pressure and not a similar pressure from the other particles in the star?
A White Dwarf had already undergone/exhausted its ability for fusion, it underwent gravitational collapse and is supported by EDP. This is due to the Pauli Exclusion Principle. Protons are too massive. If it surpassed the Chandrasekhar limit then another particle, it would be Neutron Degeneracy Pressure, and thus it would be a neutron star.
Cygnus X-1 was the first solid black hole candidate. Its mass is much higher than we think neutron stars can reach based on the orbit with its companion. How do we also know that Cygnus X-1 is very compact?
It was in a binary system with a luminous (18 M_sun) star and unseen companion (~10-15 M_sun) surrounded by a hot accretion disk emitting in X-rays. Orbit each other every 5.6 days. Using the binary system, we can “weigh” both the bright star and the unseen companion surrounded by the accretion disk. Use variability to establish that the companion is very compact (NS or BH).
For gases, how did we estimate the mean free path and mean time between collisions?
We assumed that a particle hits another if its center lies within a cylinder of radius equal to the diameter of the particle. Eventually with a mean correction we found l=(√2*𝛑nD^2)^-1. Where n is number density, D is the diameter of the particle.
Where does the internal heat of the Earth come from?
The internal heat of the Earth comes from a number of reasons:
-Radioactive decay of elements
-Impact heating due to asteroids/meteorites that internally heat the Earth
-Earth’s gravitational contraction released energy, which is the main contributor to the Earth’s
Internal core and mantle heat, essentially due to its Binding Energy.
-Lastly, due to differentiation.
How are the variations in radial velocity in a star used to determine the mass and orbital period of an exoplanet?
The Radial Velocity Method can detect exoplanets by measuring small shifts in a star’s
spectrum caused by the gravitational “tug” (pull) by that of the orbiting planet. The shifts can
Reveal important properties of the planet such as the orbital period and minimum mass.
Using the Doppler Effect, the star also moves slightly due to the counteracting orbit of the
Planet. This motion causes Doppler shifts in the star’s spectral lines:
Towards Earth-> Blueshift (shorter wavelengths)
Away from Earth->Redshift (longer wavelengths)
Orbital Period: The star’s radial velocity varies periodically which matches the planet’s orbital motion. The time between peaks in the velocity curve yields the planet’s orbital period (P).