## 1.1 Stars and Galaxies [[../Assets/Extended summaries booklet.pdf#page=6]] The [[../Glossary/Astronomical Unit]] (AU) is the average distances between the Earth and the Sun (1.496 x $10^8$ km (4 s.f.)) The Solar radius $R_\odot$ = 6.955 x $10^5$ km so 1 *AU* = 215 $R_\odot$ *c* = 2.9979 x $10^5$ km $s^-1$ 1 *lightyear* (ly) = 9.461 x $10^{12}$ km *parsec* (pc) = 3.086 x $10 ^{13}$ km 1 pc = 3.262 ly (4 s.f.) 1 year = 3.156 x $10^7$ seconds ### *Galaxies* A [[../Glossary/galaxy]] is a collection of stars, gas, dust and dark matter which is gravitationally bound together. ## 1.2 Mapping the sky *Galactic coordinates* consists of galactic latitude ( symbol = $b$) and Galactic longitude (symbol = $l$) ![[../Assets/Galactic coordinates.png|350]] *Equatorial coordinates* ![[../Assets/Screenshot 2023-10-03 at 11.28.23.png|300]] The celestial latitude is called declination ( DEC or $\delta$ ). The celestial equivalent of longitude is Right Ascension (RA or $\alpha$ ). The prime meridian for right ascension is not quite as arbitrary as the prime meridian for terrestrial longitude. It is defined to pass through the point at which the Sun crosses the celestial equator at the (Northern Hemisphere) spring equinox. This location is referred to as the first point of Aries. Right ascension is measured eastwards from this point. ## 1.3 Differences in position The angular size or angular separation is the angle between objects whereas the linear size or linear separation is the physical distance. ### *angular separation:* #### cos( $\theta$) = sin($\delta_{1}$)sin($\delta_{2}$) + cos($\delta_{1}$)cos($\delta_{2}$)cos($\alpha_{1}$-$\alpha_{2}$) simpler derivative if within a few degrees: #### $\theta^2$ = ($\alpha_{1}$-$\alpha_{2})$^2$ cos($\delta^2$) + ($\delta_{1}$ - $\delta_{2}$)$^2$ ### *Distance:* #### sin( $\theta$) = $\frac{D}{d}$ ($\theta$ = ang sep, D = linear sep and d = distance in pc) (In small angles the sin of theta is equal to $\theta$ if in radians) ### *Proper motion:* #### in RA: $\mu_{\alpha}$ = ($\alpha_{1}$-$\alpha_{2}$) / $\Delta$ t ) #### in DEC: $\mu_{{\delta}}$ = ($\delta_{1}$ - $\delta_{2}$)$ / $\Delta$ t ) #### Total proper motion: $\mu^2$ = $(\mu_{\alpha})^2$ x cos($\delta^2$) + $(\mu_{\delta})^2$ #### $\mu_{\alpha^*}$ = $\mu_{\alpha}$ x cos ($\delta$) , so $\mu^2$ = $(\mu_{\alpha_{*}})^2$ + $(\mu_{\delta})^2$ ### *Transverse velocity:* #### sin($\mu$) = $\frac{v_{T}}{d}$ {$\mu$ in radians!!, d in pc and V in pc/y!!} [[../Glossary/parsec]] ## 1.4 Star and Galaxy databases databases - http://simbad.cds.unistra.fr/simbad/ - https://ned.ipac.caltech.edu/byname ## References [[Docent/S284 Astronomy]] [[../Supporting info/calculating rules]] [[../Assets/TMA1 questions.pdf]] [[Tutor/constants & formula's|constants & formula's]] Tags #distances #angularseparation