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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.

43Formulas

2Subcategories

Updated Oct 2026

All (43) Orbital Mechanics (21) Stellar Physics (22)

Orbital Mechanics

Hour Angle from Local Solar Time

H = 15° * (LST_hours - 12)

Stellar Physics

Cosmological Redshift to Recession Velocity

v ≈ c * z

Stellar Physics

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

Stellar Physics

Telescope Limiting Magnitude

m_lim ≈ 2.7 + 5*log10(D)

Stellar Physics

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

Stellar Physics

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

Stellar Physics

Astrophotography NPF Rule (Simplified)

t_max = (35 * f_number + 30 * pixel_pitch) / focal_length

Stellar Physics

Astrophotography 500 Rule

t_max = 500 / (focal_length * crop_factor)

Stellar Physics

Telescope Exit Pupil

E = D / M

Stellar Physics

Telescope True Field of View

TFOV = AFOV / M

Stellar Physics

Telescope Focal Ratio (f-number)

f/# = f / D

Stellar Physics

Telescope Resolving Power (Dawes' Limit)

R = 116 / D

Stellar Physics

Telescope Magnification

M = f_telescope / f_eyepiece

Stellar Physics

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

Orbital Mechanics

Solar Altitude Angle

sin(a) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H)

Orbital Mechanics

Solar Declination (Approximate)

δ ≈ 23.44° * sin(360°/365 * (N_day - 81))

Orbital Mechanics

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

Orbital Mechanics

Julian Date (Simplified)

JD = 367*Y - INT(7*(Y+INT((M+9)/12))/4) + INT(275*M/9) + D + 1721013.5

Orbital Mechanics

Minimum Orbital Inclination from Launch Latitude

i_min = latitude of launch site

Orbital Mechanics

Kepler's Equation & Orbital Anomaly Calculator

M = E - e*sin(E)

Orbital Mechanics

Orbit Equation (Semi-Latus Rectum Form)

r = p / (1 + e*cos(θ))

Orbital Mechanics

Specific Orbital Angular Momentum

h = r * v * cos(γ)

Orbital Mechanics

Specific Orbital Energy

ε = v^2/2 - μ/r = -μ/(2a)

Orbital Mechanics

Geostationary Orbit Radius

r = (μ * T^2 / (4π^2))^(1/3)

Orbital Mechanics

Hohmann Transfer Time of Flight

t = π * sqrt(a_t^3 / μ)

Orbital Mechanics

Vis-Viva Equation

v = sqrt(μ * (2/r - 1/a))

Orbital Mechanics

Circular Orbital Velocity

v = sqrt(μ / r)

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