Astronomy Calculators
Orbital mechanics, cosmology, planetary science, astrophotography, and space exploration calculators.
Orbital Period Calculator
Calculate the orbital period of a body circling a central mass using Kepler's relation T = 2pi * sqrt(a^3 / (G * M)).
Orbital Velocity Calculator
Determine the orbital speed of a body in a circular orbit using v = sqrt(G * M / r).
Escape Velocity Calculator
Calculate the minimum speed needed to escape a celestial body's gravitational pull using v_esc = sqrt(2 G M / r).
Gravitational Acceleration Calculator
Compute the surface gravitational acceleration of a celestial body from its mass and radius using g = G M / r^2.
Kepler's Third Law Calculator
Relate orbital period and semi-major axis for bodies orbiting the Sun using T^2 = a^3 (years and AU).
Hohmann Transfer Calculator
Compute the two delta-v burns and transfer time for a Hohmann transfer orbit between two circular orbits.
Delta-v Calculator
Compute the delta-v available from a rocket stage using the Tsiolkovsky equation: dv = v_e * ln(m0 / mf).
Specific Orbital Energy Calculator
Find the specific mechanical energy of an orbit: epsilon = -G M / (2a).
Hill Sphere Calculator
Estimate the Hill sphere radius within which a body's gravity dominates: r_H = a * (m / (3M))^(1/3).
Roche Limit Calculator
Calculate the Roche limit, the minimum distance at which a self-gravitating satellite can orbit without tidal disruption.
Synodic Period Calculator
Calculate the synodic period between two orbiting bodies: the time between successive conjunctions as seen from one body.
Sidereal-to-Synodic Converter
Convert a planet's sidereal period to its synodic period relative to Earth.
Satellite Speed Calculator
Determine the speed and period of a satellite in circular orbit at a given altitude above Earth.
Geostationary Orbit Calculator
Compute the geostationary orbit altitude and speed for any planet given its mass and rotation period.
Orbital Eccentricity Calculator
Compute the eccentricity of an orbit from its periapsis and apoapsis distances: e = (r_a - r_p) / (r_a + r_p).
Light-Year to Kilometres Converter
Convert astronomical distances between light-years and kilometres. One light-year is the distance light travels in one Julian year.
Parsec to Light-Year Converter
Convert distances between parsecs and light-years. One parsec is the distance at which 1 AU subtends 1 arcsecond of parallax.
Parallax Distance Calculator
Calculate the distance to a star from its parallax angle: d(pc) = 1/p(arcsec).
Astronomical Unit Converter
Convert between Astronomical Units (AU) and kilometres, miles, and light-minutes.
Redshift Velocity Calculator
Estimate a galaxy's recession velocity from its cosmological redshift using the classical approximation v = z * c.
Hubble Distance Calculator
Estimate the distance to a galaxy from its recession velocity using Hubble's law: d = v / H0.
Lookback Time Calculator
Estimate the lookback time (how far back in time you are seeing) from distance in megaparsecs, using t = d / c.
Angular Size Calculator
Compute the angular size of an object from its physical diameter and distance: theta = 2 arctan(d / (2D)), approximated as theta = d / D (radians) for small angles.
Apparent Magnitude Calculator
Determine a star's apparent magnitude from its absolute magnitude and distance using the distance modulus: m = M + 5 log10(d/10).
Absolute Magnitude Calculator
Find a star's absolute magnitude from its apparent magnitude and distance: M = m - 5 log10(d/10).
Distance Modulus Calculator
Calculate the distance to a star from the difference between apparent and absolute magnitudes: d = 10^((m - M + 5) / 5).
Luminosity Calculator
Calculate the luminosity of a star from its flux and distance using L = 4 pi d^2 F.
Stellar Flux Calculator
Calculate the observed flux from a star of known luminosity at a given distance: F = L / (4 pi d^2).
Inverse Square Brightness Calculator
Compare the brightness of an object at two different distances using the inverse square law: F2/F1 = (d1/d2)^2.
Cosmic Distance Ladder Calculator
Enter a distance in parsecs and see which measurement methods are appropriate at that scale, plus conversions to multiple units.
Stellar Luminosity Calculator
Calculate a star's luminosity from its absolute magnitude: L/L_sun = 10^((M_sun - M_star) / 2.5).
Hertzsprung-Russell Estimator
Estimate a main-sequence star's luminosity and radius from its effective temperature using empirical scaling relations.
Main-Sequence Lifetime Calculator
Estimate how long a star spends on the main sequence: t = t_sun * (M/M_sun) / (L/L_sun), approximated as t ≈ 10^10 * (M/M_sun)^(-2.5) years.
Schwarzschild Radius Calculator
Calculate the Schwarzschild radius (event horizon) of a black hole: r_s = 2 G M / c^2.
Chandrasekhar Limit Calculator
Compute the Chandrasekhar mass limit for a white dwarf with a given mean molecular weight per electron: M_Ch = 5.83 / mu_e^2 solar masses.
Neutron Star Density Calculator
Estimate the average density of a neutron star from its mass and radius: rho = 3M / (4 pi r^3).
White Dwarf Radius Calculator
Estimate the radius of a white dwarf using the mass-radius relation: R/R_sun ~ 0.0126 * (M/M_sun)^(-1/3) for non-relativistic degeneracy.
Stellar Temperature Calculator
Estimate a star's surface temperature from its B-V colour index using the Ballesteros formula: T = 4600 * (1/(0.92*(B-V)+1.7) + 1/(0.92*(B-V)+0.62)).
Wien Peak Wavelength Calculator
Find the peak emission wavelength of a blackbody from its temperature using Wien's displacement law: lambda_max = b / T.
Stefan-Boltzmann Luminosity Calculator
Calculate a star's luminosity from its radius and surface temperature: L = 4 pi R^2 sigma T^4.
Eddington Luminosity Calculator
Compute the Eddington luminosity, the maximum luminosity a body can achieve when radiation pressure balances gravity: L_Edd = 4 pi G M c / kappa.
Mass-Luminosity Relation Calculator
Estimate a main-sequence star's luminosity from its mass using the empirical relation L/L_sun ~ (M/M_sun)^3.5.
Spectral Class Estimator
Estimate which spectral class (O, B, A, F, G, K, M) a star belongs to based on its effective temperature.
Star Colour-Temperature Calculator
Convert between a star's colour temperature in Kelvin and its peak emission wavelength, plus approximate visible colour description.
Nuclear Fusion Energy Calculator
Calculate the energy released by converting a given mass of hydrogen to helium via stellar fusion (0.7% mass-energy conversion): E = 0.007 m c^2.
Planet Gravity Calculator
Calculate the surface gravity of a planet relative to Earth from its mass and radius ratios: g = g_Earth * (M/M_Earth) / (R/R_Earth)^2.
Planet Weight Calculator
Find what you would weigh on another planet by scaling your Earth weight by the surface gravity ratio.
Solar Noon Calculator
Estimate the local solar noon time from your longitude and the standard meridian of your time zone.
Daylight Duration Calculator
Estimate the number of daylight hours from your latitude and the Sun's declination using the hour-angle formula.
Moon Phase Calculator
Estimate the Moon's illumination fraction and phase from the number of days since the last known new moon.
Telescope Magnification Calculator
Calculate the magnification of a telescope from the focal lengths of the objective and eyepiece: M = f_obj / f_eye.
Telescope Resolution Calculator
Compute the angular resolution (Dawes limit) of a telescope from its aperture: theta = 116 / D (arcseconds, D in mm).
Telescope Focal Ratio Calculator
Calculate the focal ratio (f-number) of a telescope: f/# = focal_length / aperture.
Field of View Calculator
Calculate the true field of view of a telescope and eyepiece combination: TFOV = AFOV / Magnification.
Limiting Magnitude Calculator
Estimate the faintest star visible through a telescope: m_lim = 2 + 5 log10(D) where D is aperture in mm.
Telescope Light Gathering Calculator
Compare the light-gathering power of a telescope to the naked eye: LGP = (D / d_eye)^2.
Binocular Exit Pupil Calculator
Calculate the exit pupil of binoculars or a telescope eyepiece: exit_pupil = aperture / magnification.
Camera Exposure Rule Calculator
Calculate the maximum untracked exposure time before stars trail using the NPF rule or simplified 500 rule: t = 500 / (focal_length).
Asteroid Impact Energy Calculator
Estimate the kinetic energy of an asteroid impact from its diameter, density, and velocity: KE = 0.5 * (pi/6) * d^3 * rho * v^2.
Drake Equation Calculator
Estimate the number of detectable civilisations in the Milky Way using the Drake equation: N = R* * fp * ne * fl * fi * fc * L.
Cosmic Expansion Rate Calculator
Estimate the recession velocity of a distant galaxy from the Hubble-Lemaitre law v = H0 * d, where H0 is the Hubble constant.
Dark Energy Density Calculator
Compute the dark-energy density of the universe from the cosmological constant and the speed of light using rho_Lambda = Lambda * c^2 / (8 * pi * G).
Matter Density Parameter Calculator
Calculate the matter density parameter Omega_m = rho_m / rho_crit, indicating what fraction of the critical density is made up of matter.
Critical Density Calculator
Compute the critical density of the universe rho_crit = 3 H0^2 / (8 pi G), the density needed for a flat geometry.
Deceleration Parameter Calculator
Estimate the deceleration parameter q0 = Omega_m / 2 - Omega_Lambda, which indicates whether the expansion of the universe is accelerating or decelerating.
Comoving Distance Calculator
Approximate the comoving distance to a galaxy at low redshift using d = c * z / H0, the linearised Hubble relation.
Proper Distance Calculator
Convert comoving distance to the physical (proper) distance at a given epoch using d_proper = a(t) * d_comoving, where a is the scale factor.
Cosmic Age Calculator
Estimate the age of the universe as t ≈ 1 / H0 (the Hubble time), providing a rough upper bound for a matter-only universe.
Baryon Density Calculator
Compute the baryon (ordinary matter) density parameter Omega_b from the baryon density and the critical density.
Hubble Time Calculator
Calculate the Hubble time t_H = 1/H0, the characteristic timescale of cosmic expansion, in seconds and gigayears.
Planet Orbital Period Calculator
Find the orbital period of a planet using Kepler's third law in a simplified form: T = sqrt(a^3) years, where a is the semi-major axis in AU.
Planet Surface Temperature Calculator
Estimate the effective surface temperature of a planet using Stefan-Boltzmann balance: T = ((L * (1 - A)) / (16 * pi * sigma * d^2))^0.25.
Atmospheric Scale Height Calculator
Calculate the atmospheric scale height H = k_B * T / (m * g), the altitude over which pressure drops by a factor of e.
Tidal Force Calculator
Compute the differential tidal acceleration across an object of size dr due to a mass M at distance d: a_tidal = 2 G M dr / d^3.
Planet Albedo Calculator
Determine a planet's bond albedo from the reflected and incident flux: A = F_reflected / F_incident.
Planet Equilibrium Temperature Calculator
Compute the radiative equilibrium temperature of a planet from stellar properties and albedo: T_eq = T_star * sqrt(R_star / (2 * d)) * pow(1 - A, 0.25).
Planetary Magnetic Field Strength Calculator
Estimate a planet's dipole magnetic field strength at the surface using the dipole approximation B = (mu0 / 4pi) * M_dipole / R^3.
Atmospheric Pressure at Altitude Calculator
Calculate the atmospheric pressure at a given altitude using the barometric formula P = P0 * exp(-h / H), where H is the scale height.
Planet Density Calculator
Calculate the mean bulk density of a planet from its mass and radius: rho = 3 M / (4 pi R^3).
Planet Escape Velocity Calculator
Compute the escape velocity from a planet's surface using v_esc = sqrt(2 G M / R).
Camera Sensor FOV Calculator
Calculate the field of view of a camera sensor attached to a telescope: FOV = 2 * atan(sensor_size / (2 * focal_length)) converted to degrees.
Pixel Scale Calculator
Determine the angular size each pixel subtends on the sky: pixel_scale = 206.265 * pixel_size / focal_length arcseconds per pixel.
Image Resolution Calculator
Calculate the angular resolution of a telescope from its aperture using the Dawes limit: theta = 116 / D arcseconds, where D is in mm.
Exposure Time for Stars Calculator
Calculate the maximum exposure time before stars trail using the NPF rule: t = (35 * N + 30 * p) / (f * cos(dec)), with declination correction.
Stacking Signal-to-Noise Calculator
Estimate the signal-to-noise improvement from stacking multiple exposures: SNR_total = SNR_single * sqrt(n).
Light Pollution Impact Calculator
Estimate how light pollution reduces contrast by computing the sky-brightness ratio: contrast_loss = sky_brightness / (sky_brightness + object_brightness).
Focal Reducer Effect Calculator
Calculate the effective focal length and f-ratio after adding a focal reducer: f_eff = f * reduction_factor, N_eff = N * reduction_factor.
Barlow Magnification Calculator
Calculate the effective focal length and f-ratio after adding a Barlow lens: f_eff = f * barlow_factor.
CCD Quantum Efficiency Calculator
Calculate the number of photoelectrons generated by a CCD sensor: electrons = photon_flux * area * QE * exposure_time.
Tracking Error Tolerance Calculator
Determine the maximum acceptable periodic error of a mount: PE_max = pixel_scale * acceptable_drift_px, in arcseconds.
Rocket Delta-V Calculator
Calculate the total delta-v a rocket can achieve from the Tsiolkovsky equation: dv = ve * ln(m0 / mf).
Tsiolkovsky Equation Calculator
Compute the required mass ratio for a given delta-v and exhaust velocity: m0/mf = exp(dv / ve).
Specific Impulse Calculator
Calculate the specific impulse of a rocket engine: Isp = ve / g0, the exhaust velocity normalised by standard gravity.
Thrust-to-Weight Ratio Calculator
Calculate the thrust-to-weight ratio of a rocket: TWR = thrust / (mass * g), determining if it can lift off.
Orbital Manoeuvre Cost Calculator
Calculate the delta-v for a Hohmann transfer between two circular orbits: dv = sqrt(GM/r1) * (sqrt(2r2/(r1+r2)) - 1) + sqrt(GM/r2) * (1 - sqrt(2r1/(r1+r2))).
Gravity Assist Speed Calculator
Estimate the maximum speed change from a gravity assist: dv_max = 2 * v_planet * sin(theta/2), where theta is the bending angle.
Reentry Heating Calculator
Estimate the stagnation-point heat flux during atmospheric reentry using q = k * sqrt(rho / r_nose) * v^3, the Sutton-Graves correlation.
Solar Sail Acceleration Calculator
Calculate the acceleration of a solar sail from radiation pressure: a = 2 * S * A_sail / (c * m * d^2), where S is solar flux at 1 AU.
Mission Fuel Mass Calculator
Calculate the fuel mass required for a mission: m_fuel = m_dry * (exp(dv / ve) - 1).
Interstellar Travel Time Calculator
Estimate the travel time to a star at constant velocity: t = d / v, where d is the distance in light-years.