Option E Astrophysics

Bits The solar system is the collection of bodies gravitationally bound to the sun. The 8 planets orbit the sun in elliptical orbits and are the major bodies of the solar system. In order of increasing size: Mercury, Mars, Venus, Earth, Uranus, Neptune, Saturn and Jupiter. In order from the sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. Moons orbit planets and are called natural satellites. Between Mars /Jupiter is the asteroid belt/dwarf planets. Comets are a mix of ice, dust and gas and orbit in parabolic orbits (mostly).

Star Groups A galaxy is a collection of 100 billion stars, dust and gas held together by gravity. The shapes of galaxies: spiral, elliptical or irregular. (Our galaxy is spiral.)

Stars A group of stars in a galaxy closely bound is called a cluster. A globular cluster has 105 stars arranged with some symmetry and densely packed in the centre. An open cluster or moving cluster is irregular and has hundreds of stars. Stars grouped together (at varying distances from Earth) that form patterns are called constellations. The stars appear to move, but really it’s the Earth’s rotation that gives this appearance.

Distances A light year is the distance travelled by light in one year = 9.46 x 1015 m. (1ly = 3x108x365x24x60x60 m) Examples: 1) How long does it take light to travel to us from the moon if it is 370 000 km away? Ans: 1.2 s 2) How far away is the sun in light-minutes if it is 150 000 000 km away? Ans: 8.3 min

Distances Examples: 3) Proxima Centauri is 4.3 light-years away, and the fastest man-made object moves at 150 000 ms-1. How long would it take to travel to PC? Ans: 8600 years! 4) The most distant visible star (to the eye) is Epsilon Aurigi at 5000 ly. How far is this in m? Ans: 5 x 1019 m 5) The most distant galaxy visible to the eye is Andromeda M31 at 2.2 x 106 ly. How far is this in m? Ans: 2.1 x 1022 m

Stellar Radiation Nuclear fusion is the energy source for stars. 2 H-atoms collide at speeds to fuse to He. The energy is released as radiation. The pull of gravity is balanced by the outward pressure from fusion.

Luminosity and Apparent Brightness Luminosity, L, is the total power output of a star in Watts. The sun’s luminosity is Lsun = 3.9 x 1026 W The apparent brightness (b) of a star is the power output per unit area at a certain distance, d, measured in Wm-2. 𝑏= 𝐿 4𝜋 𝑑 2 Ex: If you were 3 m away from a 100W bulb, then b = 100/[4x3.14x32] = 0.9 Wm-2.

Examples 1) What is the apparent brightness of the sun (Lsun = 3.9 x 1026 W) at Earth (1.5 x 1011 m away)? Ans: 1.4 x 103 Wm-2 2) What is the apparent brightness of the sun one light-year away? Ans: 3.5 x 10-7 Wm-2

Stellar Distances Parallax Method: Hold up one finger at arm’s length and observe with each eye – it appears to move! The Earth is used in 2 positions 6 months apart and a nearby star is observed. The star’s position relative to the distant stars appears to change. The angle of parallax, p, is the difference in angular positions as seen from the Earth and the sun, in seconds of arc. The closer the star: the larger the parallax.

Parallax Diagram p d

Parallax Example Alpha Centauri has a parallax of 0.760 arcseconds. Note: One degree is 60 minutes, one minute is 60 seconds, so one arcsecond is 1/3600 of a degree. Tan p = O/A so A = O/tanp d = 1 AU/tan0.76 arc sec = 271 000 AU Convert this distance to m and ly. Ans: 4.1 x 1016 m = 4.3 ly

Parsecs A parsec is the distance where a star has p = 1 arcsecond. The distance, d, in parsecs (pc) is d = 1/p when p is given in arcseconds. Ex: How far away is Alpha Centauri in pc? d = 1/p d = 1/0.760 = 1.3 pc

∴The error is quite large for stars farther away! Parsec examples 1) What is the distance in pc when p = 0.010 arcsec? 0.002 arcsec? Ans: 100 pc, 500 pc 2) If the error in parallax is +/- 0.001 arcsec, what errors are associated with the answers from 1? Ans: +/- 10 pc, +/- 250 pc ∴The error is quite large for stars farther away!

Black Body Radiation A black body is a perfect absorber and a perfect emitter of radiation. Stellar objects like stars are examples. The surface temperature of a black body is an indicator of the amount of various types of radiation. A plot of intensity versus wavelength yields a curve, where the peak is at a shorter wavelength.

Blackbody Curves

Blackbody Curves

Example The sun’s blackbody curve peaks at 500 nm with a temperature of 6000 K. This is a green colour, so our star is green. (The yellow we see is due to a mixture of colours). Betelgeuse peaks at 750 nm (4000 K) and thus is a red star.

Wien’s Law The wavelength at peak intensity for black bodies, is inversely proportional to the surface temperature – Wien’s Displacement Law The constant of proportionality is 0.00290Km 𝜆 𝑚𝑎𝑥 = 0.00290𝐾𝑚 𝑇 This property allows us to classify stars called spectral types: ours is a Class G star http://en.wikipedia.org/wiki/Stellar_classificati on#Spectral_types

Examples 1) Betelgeuse peaks at 700 nm, what is the surface temperature of this star? 𝜆 𝑚𝑎𝑥 = 0.00290𝐾𝑚 𝑇 T = 0.00290 700 nm T = 4100 K 2) Repeat for our sun (5o0 nm). T = 5800 K

Stefan-Boltzmann’s Law Luminosity is proportional to a star’s area. Luminosity is also proportional to the temperature to the power of 4 𝐿= 𝜎𝐴 𝑇 4 L is the luminosity in Watts, T in Kelvin, A in m2. σ is Stefan’s constant = 5.7 x 10-8 Wm-2K-1

Example The sun has a radius of 6.7 x 108 m and a temperature of 6000 K. Determine the power output. 𝐿= 𝜎𝐴 𝑇 4 A = 4(3.14159)(6.7 x 108 m)2 = 5.64 x 1018 m2 L = 5.7 x 10-8(5.64 x 1018)(6000)4 = 4.2 x 1026 W Sirius has a surface temperature of 13 000 K and has a radius of 1.3 x 109 m. Determine it’s power output. Answer: 3.5 x 1028 W

Olber’s Paradox Newton believed the Universe to be static but infinite. If this were true: any direction we look we should see stars (if there was a star in each direction, the sky should be uniformly bright). The night sky is black – so Newton’s model was wrong (Olber’s Paradox). The Big Bang helps solve this: the Universe may be infinite but there are not infinite stars. The red-shift of receding stars also reduces the sky’s brightness. Some star light has yet to reach us!