Download Option: Astrophysics Objects in the Universe: Asteroid: a small rocky

Option: Astrophysics
Objects in the Universe:

Asteroid: a small rocky body

Meteorites: Pieces of a meteor that land on the Earth

Comet: mixture of rock and ice that has an elliptical orbit

Any model of the solar system must explain three things:
1. All the orbits of the planets are prograde
a. Rotates counterclockwise if viewed from the North Pole of the sun
2. All planets have orbital planes that are inclined by less than 6°
3. Terrestrial planets are dense, rocky and small; Jovian planets are gaseous and
large
Jovian Planets
Oort Cloud
Kuiper Belt
Solar System:
Asteroid Belt

Terrestrial Planet

Stars
o A massive body of plasma held together be gravity with fusion going at its center
giving off electromagnetic radiation. In hydrostatic equilibrium.
o Formation

Nebulae condenses and potential energy is converted to kinetic energy

If the temperature becomes high enough, then ignition happens and
hydrogen begins to fuse to form He
o Nuclear Fusion


4 11𝑝 → 42𝐻𝑒 + 2 01𝑒 + + 2𝜈
Clusters: gravitationally bound system of galaxies or stars
o Stellar cluster: group of stars held together by gravitation in the same region of
space, created roughly at the same time from the same nebulae
o Open Cluster: Up to several hundred stars that are 10 billion years old or less.
May still contain gas and dust
o Globular Cluster: Cluster of many old stars containing little to no gas or dust

Constellation: a pattern formed by stars that are in the same general direction when
viewed from the Earth

Nebulae: intergalactic regions of dust and gas
Astronomical Distances and Stellar Parallax:

Astronomical Unit (AU): average distance between the Sun and the Earth
o 1 AU = 1.50 x 1011 m ≈ 8 light minutes

Parsec (pc): most commonly used distance in astrophysics
o Found using the parallax method
o When pc can be used


Distances between nearby stars can be measured in pc

Distant stars in the same galaxy measured in kpcxxxxxxxx

Distance between galaxies is Mpc or Gpc
The parallax method:
o Relies on the apparent movement of the nearby star against the background of
further stars as the Earth orbits the Sun
o Most direct way to measure the distance to stars
o
o tan 𝑝 =
𝑆𝑢𝑛−𝐸𝑎𝑟𝑡ℎ 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑆𝑢𝑛−𝑆𝑡𝑎𝑟 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
=
1 𝐴𝑈
𝑑
1 𝐴𝑈

For small angles: sin 𝑝 ≈ tan 𝑝 ≈ 𝑝, so 𝑑 =

p is measured in terms of arc seconds. 1 arc second is equivalent to 648000.

𝑑=

1 𝑝𝑐 = 3.09 × 1016 𝑚

1 pc is a distance corresponding to a parallax of one arc second
𝑝
𝜋
1 𝐴𝑈
𝑝
=
1.5×1011
𝜋
648000
=
648000×1.5×1011
𝜋
= 3.09 × 1016 𝑚
o Limits:

100 pc is the max distance that can be calculated accurately from the
Earth’s surface

100,000 pc is the max distance that can be calculated accurately from
Gaia, the best satellite currently
Luminosity and Apparent Brightness of Stars:

Luminosity: total power radiated by a star
o L=AσT4=4πr2σT4

Apparent Brightness: power received per unit area
𝐿
o 𝑏 = 4𝜋𝑑2

Black body: a theoretical object that absorbs 100% of the radiation that incident upon it
o Can also be a blackbody if it emits 100% of the electromagnetic spectrum
o Emit energy according to Planck’s and Wein’s Law

Planck’s Law predicts the radiation of a black body at different temperatures
o Gives intensity of radiation as a function of wavelength
o The hotter the black body, the more energy emitted per unit area for all
wavelengths

Wein’s Law gives the wavelength of a black body at a given temperature
o 𝜆𝑚𝑎𝑥 =
2.9×10−3
𝑇
Cepheid Variables:

Stars with regular variation in luminosity caused by periodic expansion and contraction
of outer surface
o Expansion caused by the balance between nuclear and gravitational pressures
o Known as standard candles because they can be used to calculate distances to
galaxies
o
1. Hydrostatic equilibrium is lost and the surface of the star is pulled inward by
gravity
2. The layer becomes compressed and less transparent to radiation.
3. The temperature in the core increases, causing the pressure to increase
4. Surface is pushed outwards
5. Surface expands, cools, becomes less dense
6. The layer becomes more transparent
H-R Diagrams:

Scatter gram of stars showing relation between the stars’ luminosities versus surface
temperature
o Main sequence stars

90% of stars

H → He

Progression depends on mass
o Red Giants

Cooler than the Sun

Larger than main sequence stars but emit less energy
o White dwarves

Remnants of old stars

No longer produce energy

Very small, hot very dense stars

Relatively low luminosity
o Supergiant Stars

106 power of the Sun
o L ∝ M3.5
Stellar Evolution:

Formation
o Gravity pulls together H nuclei
o PE converts to KE and temperature increases, creating a protostar
o At high enough temperature and pressure, Hydrogen can undergo nuclear fusion
and a star forms
o
1. If the star is 1 to 4 solar masses
a. Core temperature will not be high enough to fuse carbon
b. Core shrinks while emitting radiation causing the surface to blow
away
2. If the white dwarf of the star is 1.4 solar masses
a. The Chandrasekhar Limit defines the maximum mass of a white
dwarf
b. At 1.4 solar masses a white dwarf becomes a neutron star
c. Neutron degeneracy prevents further compression
3. If the neutron star is 1.5 to 3 solar masses
a. The Oppenheimer-Volkoff limit defines the maximum mass of a
neutron star
b. At 1.5 to 3 solar masses a neutron star has so much gravitational
force that it overcomes neutron degeneracy and a black hole forms
Olber’s Paradox:

Paradox provides evidence that the universe is expanding or has a finite beginning
o This means there is a limit to the universe or the universe had a beginning

Doppler’s Redshift
o Hubble: Stars further away from us have a recession velocity

Cosmological Redshift:
o Space itself is being stretched expansion, so electromagnetic waves are also
stretched

The universe is of a finite age
o 14 billion years old
Hubble:

In 1920, Hubble realized that all galaxies are demonstrating red shift
o ∆𝜆 = 𝜆 − 𝜆0
o 𝑧=
∆𝜆
𝜆
𝑣
=𝑐
o Recessional velocity of distant galaxies are proportional to their d from Earth

v= H0d
1
o 𝑇=𝐻
0
o H0 = 70 kms-1Mpc-1

1
72 × 103 𝑚𝑠 −1 𝑀𝑝𝑐 −1
1
→ 7.2×104 𝑚𝑠−1 × 106 𝑝𝑐 × 3.09 × 1016 𝑚 = 4.29 ×
1017 𝑠 = 13.6 × 109 𝑦𝑒𝑎𝑟𝑠

CMB
o Smoking gun of the Big Bang
o Uniform, equal radiation of about 3K