Stars Distance Getting distances to stars 1 Geometry

Stars

Distance

Getting distances to stars: 1. Geometry: ‘Stellar Parallax’ > Only direct method! 2. Inverse-Square Law * Measure F * Know (or guess!) L Find d

Stellar Parallax Triangulation: d p x Baseline q x and q (or x and p) d

For getting distances to stars, we want longest possible baseline: x d p Earth p parallax angle d distance x = 1 AU; measure p d

As a practical matter, how do we get p? B d p A Star appears to shift position against background – the parallax effect. A B Shift proportional to 2 p

Clearly, as d increases, p decreases. Astronomers find: p: arcseconds (1 arcsec = 1/3600 o) If p = 1 arcsec, 1 parsec = 3. 26 light year = 206, 265 AU

Nearest star: Proxima Centauri p = 0. 772 arcsec d = 1. 295 pc = 4. 22 ly

Inverse-Square Law Luminosity: total amount of energy radiated per second (“wattage”) Watt? 50 W 100 W Twice the luminosity

Star Luminosity Sun 1 Proxima Centauri 0. 00082 Alpha Centauri 1. 77 Sirius 26. 1 Betelgeuse 15, 000 Rigel 70, 000

These stars would appear to be about equally “bright. ” Does this mean they’re equally luminous?

(Apparent) Brightness Luminosity 2 stars – differ in luminosity – may appear equally bright!

On the other hand. . . two stars that differ in brightness need not differ in luminosity.

Brighter Dimmer How much dimmer? How much brighter?

Sphere, radius = d d L 1 m 2 Flux (F) amt. of light energy flowing per second through 1 m 2

All of star’s light must pass through sphere. . . So the energy is spread over the sphere’s surface. Amt. of energy per sec through 1 m 2 = Total energy per second flowing Total number of sq meters Inverse-square law of light!

For a given star (i. e. , specified luminosity): d d (ly) F (watt/m 2) 1 100 2 25 5 4 10 1

Flux & distance Luminosity Sun’s flux at Earth: F = 1370 W/m 2 d = 1 AU = 1. 5 x 1011 m L = 4 (1. 5 x 1011)2 x 1370 = 3. 9 x 1026 Watt (!)