Formula Sheet ESCI 179

1 μm = 10^-6 m     1 nm = 10^-9 m     1 A = 10^-10 m     1 pc = 3.26 ly     1 pc = 206265 au

1 au = 150,000,000 km      1 kpc = 1000 pc    1 Mpc = 1,000,000 pc

Angular diameter = linear diameter
206265                     distance

C= f λ             C = 300,000 km/sec = 3 X 10⁸ m/s

λ_max = 0.29 cm / T(K)

Apparent wavelength = 1 + recession velocity
True wavelength                     speed of light

L = R² T⁴                                     R = √L / T²

E α f

Angular resolution (arc sec) = 0.25 wavelength (μm)             = 5/d(inches)
                                                    Mirror diameter (m)

Mag = f_o / f_e

LGP_a = (D_a)²
LGP_b    (D_b)²

Parallax (") = 1/distance (pc)             V_s² = V_r² + V_t²                     V_t = 4.75 μ (“/yr) D_pc

m = M + 5log (D/10 pc)

D = 10 pc X 10^(m-M)/5

Luminosity = (mass)⁴

Lifetime = 1 / (mass)³

(M₁ + M₂) P² = a³          a = a₁ + a₂

R_sch = 3 km per solar mass

V = cz = c X (Δλ/λ_true )

V = Hd

T = 1   X 10¹² years (open)
      H

T = 2     X 10¹² years (flat)
      3H