Category
Astronomy & Astrophysics
Astronomy and astrophysics formulas and calculators covering orbital mechanics and stellar physics for studying celestial bodies and space missions. Includes gravitational force, orbital period, and stellar luminosity equations.
34Formulas
2Subcategories
Updated Jul 2026
General
Hour Angle from Local Solar Time
H = 15° * (LST_hours - 12)
Stellar Physics
Cosmological Redshift to Recession Velocity
v ≈ c * z
General
Barlow Lens Combined Focal Length
f_new = f_telescope * Barlow_factor
Orbital Mechanics
Kepler's Third Law (AU-Year Simplified Form)
T² = a³ (T in years, a in AU, orbiting the Sun)
Orbital Mechanics
Precession Period of the Equinoxes
P ≈ 360° / (rate of precession per year)
Orbital Mechanics
Moonrise/Moonset Daily Shift (Approx.)
Δt ≈ 50 minutes/day
General
Telescope Limiting Magnitude
m_lim ≈ 2.7 + 5*log10(D)
General
Angular Diameter of the Moon or Sun
θ = 2 * arctan(R / d)
Stellar Physics
Age of the Universe (Hubble Time, Approx.)
t_H ≈ 1 / H_0
General
Light Travel Time
t = d / c
Orbital Mechanics
Synodic Period (Planetary Opposition Interval)
1/S = |1/T_1 - 1/T_2|
Stellar Physics
Inverse Square Law of Flux (Brightness-Distance)
F = L / (4π d²)
Stellar Physics
Wien's Displacement Law
λ_max = b / T
Stellar Physics
Doppler Redshift (Radial Velocity)
v = c * (λ_observed - λ_rest) / λ_rest
General
Astrophotography NPF Rule (Simplified)
t_max = (35 * f_number + 30 * pixel_pitch) / focal_length
General
Astrophotography 500 Rule
t_max = 500 / (focal_length * crop_factor)
General
Telescope Exit Pupil
E = D / M
General
Telescope True Field of View
TFOV = AFOV / M
General
Telescope Focal Ratio (f-number)
f/# = f / D
General
Telescope Resolving Power (Dawes' Limit)
R = 116 / D
General
Telescope Magnification
M = f_telescope / f_eyepiece
General
Small-Angle Formula (Angular Size)
θ (arcsec) = 206265 * (d / D)
Stellar Physics
Distance Modulus
m - M = 5*log10(d) - 5
Stellar Physics
Parallax Distance (Parsec)
d = 1 / p
General
Solar Altitude Angle
sin(a) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H)
General
Solar Declination (Approximate)
δ ≈ 23.44° * sin(360°/365 * (N_day - 81))
General
Day Length (Daylight Hours)
N = (2/15) * arccos(-tan(φ)*tan(δ))
Stellar Physics
Moon Illumination Fraction
k = (1 + cos(θ)) / 2
Orbital Mechanics
Local Sidereal Time (Approx.)
LST = GST + Longitude/15
General
Julian Date (Simplified)
JD = 367*Y - INT(7*(Y+INT((M+9)/12))/4) + INT(275*M/9) + D + 1721013.5
Stellar Physics
Hubble's Law
v = H₀d
Stellar Physics
Stefan-Boltzmann Law (Luminosity)
L = 4πR²σT⁴
Orbital Mechanics
Escape Velocity
v_esc = √(2GM / r)
Orbital Mechanics
Kepler's Third Law
T² = (4π² / GM) a³