Scales of reference:

⚖️ Masses:

• $M_{planets}\approx10^{25} \text{kg}$
• $M_{galaxies}\approx10^{40} \text{kg}$

↕️ Distances:

• $d_{earth-sun}\approx1.5*10^{11}\text{m}$
• $d_{proximaCentauri}\approx4*10^{16}\text{m}$
• $d_{andromeda}\approx2*10^{22}\text{m}$

🗜️ Density:

• $\rho_{univ}=\frac{M_{univ}}{V_{univ}}=\frac{M_{univ}}{(4\pi/3)R_{univ}^3}$

• Composition of the universe:

• $M_{stars}\approx10^{30} \text{kg}$

• $M_{universe}\approx10^{52} \text{kg}$

• $d_{earth-pluto}\approx6*10^{12}\text{m}$

• $d_{galacticCenter}\approx2*10^{20}\text{m}$

• $d_{edgeUniverse}\approx10^{26}\text{m}$

= $2.4*10^{-27}\text{kgm}^{-3}$

H 90%; He: 10%; Rest: 0.01%

Units used:

Solar Mass: $M_0=1.989*10^{30}\text{kg}$

Astronomical Unit: $1\text{AU}=1.5*10^{11}\text{m}$

Parsec: $1\text{pc}=3.1*10^{16}\text{m}$

$$ \text{Kilo}=10^3 \text{ ; Mega}=10^6 \text{ ; Giga}=10^{12} \text{ ; Tera}=10^{15} $$

$$ 1^{\text{o }}\text{degree}=60^{\text{o }}\text{arcmin ; }1^{\text{o }}\text{arcmin}=60^{\text{o }}\text{arcsec ; }1^{\text{o }}\text{rad}=57.3^{\text{o }}\text{degree} $$

Accuracy:

• numbers = 10-20%

• never give more than 3 significant digits

Coordinates:

⬆️ Declination: from -90 to +90

➡️ Right ascension: from 0 to 24h

📐 Solid angle(surface area):

• Unit: steradian = 1 radian squared
• total area of the sky = $4\pi$ sterad
• surface area: $\Omega_{galaxy}=\frac{\pi}{4}\theta^2$

($\theta$ is the diameter of the galaxy)

Definitions:

⌛ Parallax: change in position due to earth in arcsec

🌍 Proper motion: change in position($\mu$) due to star velocity(v) in the plane of the sky

• $v\text{[km}\cdot\text{s}^{-1}]=\mu\text{[arcsec}\cdot\text{yr}^{-1}]4.74r[\text{pc}]$
• in R