Resit astro

come on ur never gonna see this again

Distance ladder

Series of methods one building on the other to measure distances in the universe.

Parallax formula + triangle

\tan\left(p\right)=\frac{s}{d}

for a small p —> small angle formula tan(p) = p. (radians)

Parallax angle

the opening angle relative tto a position

Parallax for AU

d=\frac{1}{p} for 1 AU (distance earth sun). d in PC and p in arcsecons.

Parsec

Distance of an object that has a parallax angle of one arcsecond.

Use of parsec triangle

Luminosity

Total energy emitted per second by a star.

Light is emitted

Isotropically: the same amount in all directions

Flux

Energy per second that an observer on earth measures.

flux equation

f=\frac{L}{4\pi d^2} [w/m²]

Inverse square law

Force of gravity between two objects< is inversely proportional to the square of the distance between them.

Standard candles

star or object with known luminosity, it doesn’t vary with distance.

eg. cephids

Cephids

• supergiant stars

• vary periodically in brightness

• pulsation period and luminosity —> related —> we know the flux

Magnitudes

logarithm based scale for flux

m_1-m_2=-2.5\log_{10}\left(\frac{f_1}{f_2}\right)=-2.5\log_{10}\left(\frac{L_1}{L_2}\right)

lower magnitude - brighter star

Absolute magnitudes

• m = apparent magnitude (depends on distance)

• M = absolute magnitude (apparant magnitude at distance 10 pc)

m-M=5\log_{10}\left(\frac{d}{10psc}\right)

This is called distance modulus

Blackbody

Emits radiation at the same rate it absorbs in thermodynamic equilibrium with surrounding

Doppler effect

Wavelength of the observer depends on the relative motion between source and us

• toards —> blue shifted

• away —> redshifted

Doppler effect equation

\frac{\Delta\lambda}{\lambda}=\frac{\upsilon}{c} where \Delta\lambda=\lambda_{}-\lambda_0

radial velocity

relative speed along the line of sight of source observer

radial velocity equation

Binary star systems

• visual binaries: see 2 stars moving together in space

• close binaries: too close to see separately

• Spectroscopic: 2 stars with doppler shifts in opposite directions

• Eclipsing binaries: very rares

Binaries mass radius equation

m_1r_1=m_2r_2 since the centre of mass between them is 0

Two stars in mutual grav attraction orbiting a common centre of mass

Orbital periods for binary sistem eq

P_1=P_2

\frac{r_1}{v_1}=\frac{r_2}{v_2}

\frac{v_1}{v_2}=\frac{r_1}{r_2}=\frac{m_2}{m_1}

Kepler’s 3rd law

Newton’s law of grav = force that keeps the star in orbit (ma)

\frac{4\pi^2R^3}{G}=\left(m_1+m_2\right)P^2 (SI)

a^3=M_{T}P^2 where it’s AU, years and solar masses

what do wavelength and intenisty of radiation depend on?

Temperature

Planck function

At any wavelength the body at the higher temp will always emit more.

These lines never cross

Wien’s law

\lambda_{\max}T=0.0029mK

balckbody ay constant temp

It must radiate energy at the same rate its absorbs it

Effective temperature

The temoerature that a perfect blackbody would need to have to emit the same amount of energy as the real object/star in question

Color of the star (placks function)

depends on where where most of the rad leans towards

Stefan - Noltzmann law equation

E\left(t\right)=\sigma T^4 (w/m²)

Total energy emitted by the blackbody over all wavelengths

Luminosity stefan boltzmann equation

L=4\pi R^2\sigma T_{ef}^4 (w)

L-R^2T^4

Multicolor photometrey

Used to determine color by measuring mag in regions of spectrum can be used to estimate T

multicolor photoetry equations

B-V=2.5\log_{10}\left(\frac{I\lambda_{V}}{I\lambda_{B}}\right) + constant

B - V < 0

Bright in blue so mb is small

B - V > 0

faint in blue so mb is large

Spectral types from hottest to coldest

O B A F G K M

40000, 20000, 10000, 7500, 5500, 4500, 3000

hot/cold colors

hot —> blue

cool —> red

Dwarf stars

L.-type, T-type, Y-type

HR diagrams + where is the sun

Theory: luminosity and Teff

Observation: Magnitude and color

spectral types in smaller groups

each types is divided into 10 subtypes (O, O1, O2, …, O9

Spectral lines hydrogen

• Balmer: any transition from/to 2nd level - UV

• Lyman: any transition from/to 1st level - Visible

Rydberg equation

\frac{1}{\lambda}=R\left(\frac{1}{n_{l}^2}-\frac{1}{n_{u}^2}\right)

where R is rydberg constant, nl is lower quantum number, nu is upper quantum number

Hot stars spectrum look

• more energy - they ionize

• too much energy to allow molecules to form

types of gas for temperaruers in stars

• hot stars - ionized gas

• medium - more neutral gas: metals, hydrogen

• cool stars - molecule lines: oxide, methane, water

Refractor Teelscopes

• lenses to focus the light

• aren’t build anymore

  • lenses too heavy

focal ration

The focal ratio describes how fast the beam converges to the focal plane.

F=\frac{f}{D} where f = focal length and d D = diameter of lens mirror

Written as F/x

Types of reflectors

Refecltor telescope

Use mirrors (at least one, usually more than one) to focus the light

Aperure of a telescop e

How much light can a telescope collect

smaller/bigger focal ratios

• Smaller: converges quicker, better picture of a faint star

  • wide feild images, small image scale, good for surveys

• larger: better details, takes longer, longer exposure rratio

  • small images, large image scale

Resolving power of a tekescope

How much detail can be seen

Minimum angular separation of two sources on sky

Diffraction limit of telescope

\alpha=\frac{1.22\lambda}{D}\left(rad\right)

where:

D= diameter of aperure

Extinction of telescopes

loss of light via absorption and scattering by molecules in the atmosphere

Airmass

The airmass A is a measure of the path the light has to take through the atmosphere

z = zenith, e = 90 - z

A=\frac{1}{\cos\left(z\right)}

airmass doesn’t change with altitude

Atmospheric trasnmision

T=\frac{F}{F_{o}}=e^{-\tau A}

F = measured flux

Fo = flux above atmosphere

tau = opacity (%)

A = airmass

Ideal telescope location

• above cloud layer

• number of clear nights should be high

• very low rainfall

• light pollution

Spectral resolution

R=\frac{\lambda}{\Delta\lambda}=\frac{v}{c}

R depends upon width of entrance slits, dispersion of grating, seeing, etc.

Problem with x ray teelscopes and solution

lamda is comparable to the distance between atoms, so photons “see” a smooth surface

solution: grazing, use nested mirrors

Problem with infrared telescopes and solution

everything that is warm emits infrared radiation

so the cooling becomes extremly important

xray telescope use

see through hot gases

IR telescope use

used to see through dust and colder objects

radio telescope problem and solution

Problem: At long wavelengths the diffraction limit is very large

The solution is interferometry. In short, interferometers combine the power of multiple telescopes

\theta=\frac{\lambda}{b} where b is the separation

Kirchoff’s laws

there are three types of spectra:

• continuous spectrum (all wavelengths) produced by a hot opaque body - hot, dense, gas

• continuous spectrim with dark absorption lines is produced by a hpt opaque body seen through a trasparent layer of cool gas whuch absorvs some light

• emission line spectrum is produced by hot transparent gas. Here light is only specific wavelengths. This can occur. when clouds of gas are heated by nearby hot stars.

radial velocity

observed as doppler effect

\frac{\Delta\lambda}{\lambda}=\frac{v_{rad}}{c}

proper motion

The proper motion µ is the motion of the star in the plane of the sky

separated into:

t_{a,}t_{\delta}

proper motion equation

\mu=\sqrt{\left(\mu_{a}\cos\left(\delta\right)\right)^2+\mu_{\delta^{^{}}}^{^2}} (arcsec/year)

transverse velocity equation

t = 4.74 mu *d

full space motion

s=\sqrt{v_{r}^2+t^2} +9

solar day

time it takes earth to rotate around its axis

sideral day

time earth takes for axis rotation so that distant stars appear in the same position

equation relation between periods days

\frac{1}{P_{Rot}}=\frac{1}{P_{day}}+\frac{1}{P_{0rb}}

P rot is sideral period

The orbital plane of the earth around the sun

ecliptical

what causes seasons?

The tilt of the Earth’s rotation relative to the ecplitic

Flux winter

since the angle is small, it reduces flux felt by the earth

flux summer

since the angle is large, there’s greater flux of light that hits the earth

Rotation of the earth

The Earth rotates anticlockwise as viewed from above the North Celestial pole So, stars appear to rotate clockwise (rise in East, set in West) around the North celestial pole.

Synchronous rotation of the moon

Same face always towards earth at all points of the rotation

infirior conjugation

E-P-S

Greatest elongation

Maximum separation from the sun 90º angle at planet

superior conjugatiion

other side of the sun

conjunction

E-S-P

Quadrature

90º angle at earth

Opposition

P-E-S

perihelion

closer

d_{per}=a\left(1-e\right)

aphelion

further

d_{aph}=a\left(1+e\right)

Planetary velocity

Fgrav = ma

v=\sqrt{\frac{GM}{r}}

retorgrade motion

appparent motion opposite to that of the direct motions of members of the solar system

Sideral and solar days drawing

Sidereal period

true orbital period measured relative to the stars

Synodic period:

time for planet, Earth and Sun to come back to a particular configuration (planets lap each other)

Equation periods

\frac{1}{P_{syn}}=\frac{1}{P_{i}}-\frac{1}{P_{o}}

where Pi is the inner planet’s period

and Po is the inner planet’s

Relative distances to inner planets

when inner is at max elongation

d=\left(1AU\right)\sin\left(\alpha\right)

Relative distances to outer planets

Copernicu’s method

d=\frac{1}{\cos\left(\beta-\gamma\right)}AU

\beta=\omega_{ear}t ,\gamma=\omega_{planet}t

Calculate planet radii

At oposition:

R=\tan\left(\alpha\right)d

d = distance earth-planet

eclipse equation

f/a = e (eccentricity)

a² = f² +b²

b=a\sqrt{1-e^2}

Kepler’s first law

Planets move in an elliptical orbit around the Sun, with the Sun at one focus of the ellipse.

Kepler’s second law

The straight line drawn from the Sun to a planet sweeps out equal areas during equal intervals of time.

Mercury (5)

• Lots of craters

• Primordial lava flows

• No plate tectonics

• Scarps (cliffs)

• very weak magnetic field

Venus (7)

• very thick cloud coverege in the atmosphere

• young —> nor many craters

• Volcanic plains, lava flows

• No plate tectonics

• High density, sluggish atmosphere

• a lot of greenhouse effect

• no magnetic field