Cosmology (inc. Special Relativity) Flashcards
Einstein’s SR Postulates
- Physical laws have the same form in all inertial (non-accelerating) frames of reference.
- The speed of light in free space is invariant.
Luminosity, L
Luminous flux, F
L: Total energy irradiated by a star or other ‘hot’ object per second. …. A measure of the absolute brightness of an object ….. Watts
- F: Power per unit area … i.e. L per unit area.
L and F equation
For a spherical emitter of radius R:
F = L/4πR^2
Standard candle definition/ use.
Types of stars or galaxies for which the luminosity L can be determined directly from observations.
Used to find distances to galaxies/ objects that are too far away to use parallax.
- Find the absolute brightness from the observed period of the pulsation of the star/ galaxy.
- Compare this with the brightness the object appears to have from Earth.
Then use F=L/4πR^2, where L is the known absolute luminosity and F is the power per unit area received on Earth.
Hence calculate R, the distance to the star/ galaxy.
Wien’s displacement law
λ max ∝ 1/T,
where T is absolute temperature of the object.
NB: Wien’s constant = 2.9 * 10^-3 metres * kelvin
Stefan-Boltzmann law
F=σT^4, where F = luminous flux, T = absolute temp and σ is the Stefan-Boltzmann constant.
F=L/A, so L=Aσt^4 = 4πr^2T^4, where r is the radius of the star.
❗ ❗ ❗ ‘r’ here is the RADIUS of the star, NOTNOTNOTNOTNOTNOT the distance ‘R’ from earth to the star/ galaxy as in F=L/4πR^2.
Light year
Distance travelled by light in a vacuum in 1 year.
9.46 * 10^15 m
Astronomical unit, Au
Average radius of orbit of the Earth around the Sun.
1.50 * 10^11 m.
Parsec (parallax second)
The distance which results in a parallax shift of 1 arcsecond over a 3 month period (i.e. after Earth has travelled 1 Au).
❗ 1 Au/ 1 Parsec = tan( 1 arcsecond)
THEN Small angle approximation of tan(theta) = theta …
→ 1 Au/ 1 Parsec = 1 arcsecond.
(works because length/ length = dimensionless, which an angle is).
3.09 * 10^16 m.
