Title: InkPhysics / Astrophysics
On every note of this deck, unless a note says otherwise:
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Front: DEFINITION
Define: Red shift.
Back: The fractional increase in the wavelength of light from a receding source: z = Δλ/λ.

Front: DEFINITION
Define: Angular magnification.
Back: The angle subtended by the final image at the eye divided by the angle subtended by the object at the unaided eye.

Front: DEFINITION
Define: Quasar.
Back: The active nucleus of a distant galaxy, powered by a supermassive black hole: galaxy-scale power from a volume the size of the solar system.

Front: CHECK YOURSELF
A quasar's brightness varies noticeably over about two days. Explain what this says about its size, and why that observation, combined with its red shift, forces an extraordinary power source.
Show a hint
Nothing can synchronise a change faster than light can cross the object.
Back: A source cannot brighten as a whole faster than light can cross it, so its diameter is at most about two light-days, roughly 5 × 10^13 m: solar-system sized, not galaxy sized.
The large red shift places the quasar billions of parsecs away by Hubble's law, and to be visible at all from there it must radiate more power than a whole galaxy.
Galaxy-scale power from a solar-system-scale volume rules out ordinary starlight; only matter heating violently as it falls towards a supermassive black hole fits both facts at once.

Front: DEFINITION
Define: Parsec.
Back: The distance at which one astronomical unit subtends an angle of one arcsecond: about 3.26 light years.

Front: DEFINITION
Define: Absolute magnitude.
Back: The apparent magnitude a star would have at a distance of 10 parsecs.

Front: CHECK YOURSELF
A telescope has an objective of focal length 900 mm and an eye lens of focal length 15 mm. Jupiter subtends 2.4 × 10^−4 rad to the naked eye. Find the magnification and the angle Jupiter subtends through the telescope, and state what normal adjustment means.
Show a hint
The ratio of focal lengths first; then remember what a telescope multiplies.
Back: M = f_o/f_e = 900 / 15 = 60: millimetres are fine as long as both lengths use them.
Through the eyepiece Jupiter subtends 60 × 2.4 × 10^−4 = 1.4 × 10^−2 rad, half as big again as the Moon appears unaided.
Normal adjustment: the two focal planes coincide, so the final image sits at infinity and a relaxed eye views it.

Front: CHECK YOURSELF
A white dwarf has surface temperature 25 000 K and radiates 9.5 × 10^24 W. Find its peak wavelength and its radius, and comment on the size.
Show a hint
Wien for the peak; rearrange Stefan for area, then radius from A = 4πr².
Back: λ_max = 2.9 × 10^−3 / 25 000 = 1.2 × 10^−7 m, deep in the ultraviolet.
A = P/σT^4 = 9.5 × 10^24 / (5.67 × 10^−8 × 25 000^4) = 4.3 × 10^14 m^2, so r = √A/4π = 5.8 × 10^6 m.
That is about the radius of the Earth: a star's worth of matter, hotter than the Sun's surface, packed into a planet's volume.

Front: DEFINITION
Define: Black body.
Back: A body that absorbs all radiation falling on it and is therefore the best possible emitter, with a spectrum that depends only on its temperature.

Front: CHECK YOURSELF
Vega has apparent magnitude 0.0 at a distance of 7.68 pc. Find its absolute magnitude. Then state which appears brighter from Earth, Sirius at m = −1.5 or Polaris at m = +2.0, and by what brightness factor.
Show a hint
Vega is nearer than the 10 pc shelf, so decide first whether M should be bigger or smaller than m.
Back: M = 0.0 − 5 log(0.768) = 0.0 + 0.57 = +0.6: moved out to 10 pc, Vega would look slightly dimmer than it does now, as expected for a star nearer than 10 pc.
Sirius appears brighter: −1.5 is smaller than +2.0.
The gap is 3.5 magnitudes, so the ratio is 2.51^3.5 ≈ 25 times.

Front: CHECK YOURSELF
What diameter would a radio telescope observing at 0.21 m need to match the resolving power of a 10 cm optical telescope working at 5.0 × 10^−7 m? Comment on the answer.
Show a hint
Find the optical telescope's θ first; then ask what D gives the radio dish the same θ.
Back: Optical: θ ≈ λ/D = 5.0 × 10^−7 / 0.10 = 5.0 × 10^−6 rad.
Radio: D = λ/θ = 0.21 / 5.0 × 10^−6 = 4.2 × 10^4 m.
A single dish 42 km across is not buildable, which is the point of the comment: matching a small optical telescope at radio wavelengths takes networks of dishes spread across the countryside, acting together as one giant aperture.

Front: DEFINITION
Define: Hertzsprung–Russell diagram.
Back: A plot of stellar luminosity or absolute magnitude against temperature or spectral class, with temperature decreasing to the right.

Front: DEFINITION
Define: Apparent magnitude.
Back: A star's brightness as seen from Earth, on the backwards scale where each step of 1 is a factor of 2.51 and smaller numbers are brighter.

Front: DEFINITION
Define: Cosmic microwave background.
Back: Black-body radiation at 2.7 K arriving uniformly from every direction: the cooled, red-shifted afterglow of the hot early universe.

Front: DEFINITION
Define: Transit method.
Back: Detecting an exoplanet from the periodic dip in a star's brightness as the planet crosses its face.

Front: CHECK YOURSELF
A quasar shows z = 0.15. Estimate its recession speed and its distance for H = 65 km s^−1 Mpc^−1, and explain one reason the answer is only an estimate.
Show a hint
v = zc first; then keep v in km per second so H's units do the conversion.
Back: v = zc = 0.15 × 3.0 × 10^8 = 4.5 × 10^7 m s^−1, or 45 000 km s^−1.
d = v/H = 45 000 / 65 = 690 Mpc.
At fifteen per cent of light speed the small-shift approximation z = v/c is beginning to strain, and H itself is only known roughly; both make the distance an estimate rather than a measurement.

Front: CHECK YOURSELF
Describe the future of the Sun as a track on the HR diagram, naming each stage, and explain in one sentence each why the Sun will not become a supernova and why type 1a supernovae can be used to measure distance.
Show a hint
Three stages on the diagram; then mass for the first sentence, fixed peak brightness for the second.
Back: The Sun sits on the main sequence now; when core hydrogen runs low it swells and cools, moving up and to the right as a red giant; after shedding its outer layers the remnant drops down-left as a white dwarf, then cools and fades.
No supernova: the Sun's mass is far below what core collapse requires, so its endpoint is the white dwarf.
Type 1a supernovae all detonate at the same trigger mass and so peak at the same absolute magnitude, about −19.3; comparing that with the measured apparent magnitude gives the distance through the distance modulus.

Front: EQUATION — NOT ON THE DATA SHEET
Collecting power and dish diameter:
collecting power ∝ ?
Back: collecting power ∝D^2

Front: DEFINITION
Define: Radial velocity method.
Back: Detecting an exoplanet from the periodic Doppler shift of its star's spectral lines as star and planet orbit their common centre of mass.