Astronomie
Orbital mechanics, cosmology, planetary science, astrophotography, and space exploration calculators.
Calculateur de Période Orbitale
Calculate the orbital period of a body circling a central mass using Kepler's relation T = 2pi * sqrt(a^3 / (G * M)).
Calculateur de Vitesse Orbitale
Determine the orbital speed of a body in a circular orbit using v = sqrt(G * M / r).
Calculateur de Vitesse de Libération
Calculate the minimum speed needed to escape a celestial body's gravitational pull using v_esc = sqrt(2 G M / r).
Calculateur d'Accélération Gravitationnelle
Compute the surface gravitational acceleration of a celestial body from its mass and radius using g = G M / r^2.
Calculateur de la Troisième Loi de Kepler
Relate orbital period and semi-major axis for bodies orbiting the Sun using T^2 = a^3 (years and AU).
Calculateur de Transfert de Hohmann
Compute the two delta-v burns and transfer time for a Hohmann transfer orbit between two circular orbits.
Calculateur de Delta-v
Compute the delta-v available from a rocket stage using the Tsiolkovsky equation: dv = v_e * ln(m0 / mf).
Calculateur d'Énergie Orbitale Spécifique
Find the specific mechanical energy of an orbit: epsilon = -G M / (2a).
Calculateur de Sphère de Hill
Estimate the Hill sphere radius within which a body's gravity dominates: r_H = a * (m / (3M))^(1/3).
Calculateur de Limite de Roche
Calculate the Roche limit, the minimum distance at which a self-gravitating satellite can orbit without tidal disruption.
Calculateur de Période Synodique
Calculate the synodic period between two orbiting bodies: the time between successive conjunctions as seen from one body.
Convertisseur Sidéral en Synodique
Convert a planet's sidereal period to its synodic period relative to Earth.
Calculateur de Vitesse de Satellite
Determine the speed and period of a satellite in circular orbit at a given altitude above Earth.
Calculateur d'Orbite Géostationnaire
Compute the geostationary orbit altitude and speed for any planet given its mass and rotation period.
Calculateur d'Excentricité Orbitale
Compute the eccentricity of an orbit from its periapsis and apoapsis distances: e = (r_a - r_p) / (r_a + r_p).
Convertisseur Année-Lumière en Kilomètres
Convert astronomical distances between light-years and kilometres. One light-year is the distance light travels in one Julian year.
Convertisseur Parsec en Année-Lumière
Convert distances between parsecs and light-years. One parsec is the distance at which 1 AU subtends 1 arcsecond of parallax.
Calculateur de Distance par Parallaxe
Calculate the distance to a star from its parallax angle: d(pc) = 1/p(arcsec).
Convertisseur d'Unité Astronomique
Convert between Astronomical Units (AU) and kilometres, miles, and light-minutes.
Calculateur de Vitesse de Décalage vers le Rouge
Estimate a galaxy's recession velocity from its cosmological redshift using the classical approximation v = z * c.
Calculateur de Distance de Hubble
Estimate the distance to a galaxy from its recession velocity using Hubble's law: d = v / H0.
Calculateur de Temps de Rétrospection
Estimate the lookback time (how far back in time you are seeing) from distance in megaparsecs, using t = d / c.
Calculateur de Taille Angulaire
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.
Calculateur de Magnitude Apparente
Determine a star's apparent magnitude from its absolute magnitude and distance using the distance modulus: m = M + 5 log10(d/10).
Calculateur de Magnitude Absolue
Find a star's absolute magnitude from its apparent magnitude and distance: M = m - 5 log10(d/10).
Calculateur de Module de Distance
Calculate the distance to a star from the difference between apparent and absolute magnitudes: d = 10^((m - M + 5) / 5).
Calculateur de Luminosité
Calculate the luminosity of a star from its flux and distance using L = 4 pi d^2 F.
Calculateur de Flux Stellaire
Calculate the observed flux from a star of known luminosity at a given distance: F = L / (4 pi d^2).
Calculateur de Luminosité en Carré Inverse
Compare the brightness of an object at two different distances using the inverse square law: F2/F1 = (d1/d2)^2.
Calculateur d'Échelle des Distances Cosmiques
Enter a distance in parsecs and see which measurement methods are appropriate at that scale, plus conversions to multiple units.
Calculateur de Luminosité Stellaire
Calculate a star's luminosity from its absolute magnitude: L/L_sun = 10^((M_sun - M_star) / 2.5).
Estimateur Hertzsprung-Russell
Estimate a main-sequence star's luminosity and radius from its effective temperature using empirical scaling relations.
Calculateur de Durée de Vie sur la Séquence Principale
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.
Calculateur du Rayon de Schwarzschild
Calculate the Schwarzschild radius (event horizon) of a black hole: r_s = 2 G M / c^2.
Calculateur de Limite de Chandrasekhar
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.
Calculateur de Densité d'Étoile à Neutrons
Estimate the average density of a neutron star from its mass and radius: rho = 3M / (4 pi r^3).
Calculateur de Rayon de Naine Blanche
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.
Calculateur de Température Stellaire
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)).
Calculateur de Longueur d'Onde de Wien
Find the peak emission wavelength of a blackbody from its temperature using Wien's displacement law: lambda_max = b / T.
Calculateur de Luminosité Stefan-Boltzmann
Calculate a star's luminosity from its radius and surface temperature: L = 4 pi R^2 sigma T^4.
Calculateur de Luminosité d'Eddington
Compute the Eddington luminosity, the maximum luminosity a body can achieve when radiation pressure balances gravity: L_Edd = 4 pi G M c / kappa.
Calculateur de Relation Masse-Luminosité
Estimate a main-sequence star's luminosity from its mass using the empirical relation L/L_sun ~ (M/M_sun)^3.5.
Estimateur de Classe Spectrale
Estimate which spectral class (O, B, A, F, G, K, M) a star belongs to based on its effective temperature.
Calculateur de Couleur-Température Stellaire
Convert between a star's colour temperature in Kelvin and its peak emission wavelength, plus approximate visible colour description.
Calculateur d'Énergie de Fusion Nucléaire
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.
Calculateur de Gravité Planétaire
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.
Calculateur de Poids sur les Planètes
Find what you would weigh on another planet by scaling your Earth weight by the surface gravity ratio.
Calculateur de Midi Solaire
Estimate the local solar noon time from your longitude and the standard meridian of your time zone.
Calculateur de Durée du Jour
Estimate the number of daylight hours from your latitude and the Sun's declination using the hour-angle formula.
Calculateur de Phase Lunaire
Estimate the Moon's illumination fraction and phase from the number of days since the last known new moon.
Calculateur de Grossissement de Télescope
Calculate the magnification of a telescope from the focal lengths of the objective and eyepiece: M = f_obj / f_eye.
Calculateur de Résolution de Télescope
Compute the angular resolution (Dawes limit) of a telescope from its aperture: theta = 116 / D (arcseconds, D in mm).
Calculateur de Rapport Focal de Télescope
Calculate the focal ratio (f-number) of a telescope: f/# = focal_length / aperture.
Calculateur de Champ de Vision
Calculate the true field of view of a telescope and eyepiece combination: TFOV = AFOV / Magnification.
Calculateur de Magnitude Limite
Estimate the faintest star visible through a telescope: m_lim = 2 + 5 log10(D) where D is aperture in mm.
Calculateur de Collecte de Lumière de Télescope
Compare the light-gathering power of a telescope to the naked eye: LGP = (D / d_eye)^2.
Calculateur de Pupille de Sortie de Jumelles
Calculate the exit pupil of binoculars or a telescope eyepiece: exit_pupil = aperture / magnification.
Calculateur de Règle d'Exposition Photographique
Calculate the maximum untracked exposure time before stars trail using the NPF rule or simplified 500 rule: t = 500 / (focal_length).
Calculateur d'Énergie d'Impact d'Astéroïde
Estimate the kinetic energy of an asteroid impact from its diameter, density, and velocity: KE = 0.5 * (pi/6) * d^3 * rho * v^2.
Calculateur de l'Équation de Drake
Estimate the number of detectable civilisations in the Milky Way using the Drake equation: N = R* * fp * ne * fl * fi * fc * L.
Calculateur de Taux d'Expansion Cosmique
Estimate the recession velocity of a distant galaxy from the Hubble-Lemaitre law v = H0 * d, where H0 is the Hubble constant.
Calculateur de Densité d'Énergie Noire
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).
Calculateur de Paramètre de Densité de Matière
Calculate the matter density parameter Omega_m = rho_m / rho_crit, indicating what fraction of the critical density is made up of matter.
Calculateur de Densité Critique
Compute the critical density of the universe rho_crit = 3 H0^2 / (8 pi G), the density needed for a flat geometry.
Calculateur de Paramètre de Décélération
Estimate the deceleration parameter q0 = Omega_m / 2 - Omega_Lambda, which indicates whether the expansion of the universe is accelerating or decelerating.
Calculateur de Distance Comobile
Approximate the comoving distance to a galaxy at low redshift using d = c * z / H0, the linearised Hubble relation.
Calculateur de Distance Propre
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.
Calculateur de l'Âge Cosmique
Estimate the age of the universe as t ≈ 1 / H0 (the Hubble time), providing a rough upper bound for a matter-only universe.
Calculateur de Densité Baryonique
Compute the baryon (ordinary matter) density parameter Omega_b from the baryon density and the critical density.
Calculateur de Temps de Hubble
Calculate the Hubble time t_H = 1/H0, the characteristic timescale of cosmic expansion, in seconds and gigayears.
Calculateur de Période Orbitale Planétaire
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.
Calculateur de Température de Surface Planétaire
Estimate the effective surface temperature of a planet using Stefan-Boltzmann balance: T = ((L * (1 - A)) / (16 * pi * sigma * d^2))^0.25.
Calculateur de Hauteur d'Échelle Atmosphérique
Calculate the atmospheric scale height H = k_B * T / (m * g), the altitude over which pressure drops by a factor of e.
Calculateur de Force de Marée
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.
Calculateur d'Albédo Planétaire
Determine a planet's bond albedo from the reflected and incident flux: A = F_reflected / F_incident.
Calculateur de Température d'Équilibre Planétaire
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).
Calculateur d'Intensité du Champ Magnétique Planétaire
Estimate a planet's dipole magnetic field strength at the surface using the dipole approximation B = (mu0 / 4pi) * M_dipole / R^3.
Calculateur de Pression Atmosphérique en Altitude
Calculate the atmospheric pressure at a given altitude using the barometric formula P = P0 * exp(-h / H), where H is the scale height.
Calculateur de Densité Planétaire
Calculate the mean bulk density of a planet from its mass and radius: rho = 3 M / (4 pi R^3).
Calculateur de Vitesse de Libération Planétaire
Compute the escape velocity from a planet's surface using v_esc = sqrt(2 G M / R).
Calculateur de Champ de Vision du Capteur
Calculate the field of view of a camera sensor attached to a telescope: FOV = 2 * atan(sensor_size / (2 * focal_length)) converted to degrees.
Calculateur d'Échelle de Pixel
Determine the angular size each pixel subtends on the sky: pixel_scale = 206.265 * pixel_size / focal_length arcseconds per pixel.
Calculateur de Résolution d'Image
Calculate the angular resolution of a telescope from its aperture using the Dawes limit: theta = 116 / D arcseconds, where D is in mm.
Calculateur de Temps d'Exposition pour les Étoiles
Calculate the maximum exposure time before stars trail using the NPF rule: t = (35 * N + 30 * p) / (f * cos(dec)), with declination correction.
Calculateur de Signal sur Bruit par Empilement
Estimate the signal-to-noise improvement from stacking multiple exposures: SNR_total = SNR_single * sqrt(n).
Calculateur d'Impact de Pollution Lumineuse
Estimate how light pollution reduces contrast by computing the sky-brightness ratio: contrast_loss = sky_brightness / (sky_brightness + object_brightness).
Calculateur d'Effet de Réducteur Focal
Calculate the effective focal length and f-ratio after adding a focal reducer: f_eff = f * reduction_factor, N_eff = N * reduction_factor.
Calculateur de Grossissement de Barlow
Calculate the effective focal length and f-ratio after adding a Barlow lens: f_eff = f * barlow_factor.
Calculateur d'Efficacité Quantique CCD
Calculate the number of photoelectrons generated by a CCD sensor: electrons = photon_flux * area * QE * exposure_time.
Calculateur de Tolérance d'Erreur de Suivi
Determine the maximum acceptable periodic error of a mount: PE_max = pixel_scale * acceptable_drift_px, in arcseconds.
Calculateur de Delta-V de Fusée
Calculate the total delta-v a rocket can achieve from the Tsiolkovsky equation: dv = ve * ln(m0 / mf).
Calculateur de l'Équation de Tsiolkovski
Compute the required mass ratio for a given delta-v and exhaust velocity: m0/mf = exp(dv / ve).
Calculateur d'Impulsion Spécifique
Calculate the specific impulse of a rocket engine: Isp = ve / g0, the exhaust velocity normalised by standard gravity.
Calculateur de Rapport Poussée/Poids
Calculate the thrust-to-weight ratio of a rocket: TWR = thrust / (mass * g), determining if it can lift off.
Calculateur de Coût de Manœuvre Orbitale
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))).
Calculateur de Vitesse d'Assistance Gravitationnelle
Estimate the maximum speed change from a gravity assist: dv_max = 2 * v_planet * sin(theta/2), where theta is the bending angle.
Calculateur de Chauffage de Rentrée
Estimate the stagnation-point heat flux during atmospheric reentry using q = k * sqrt(rho / r_nose) * v^3, the Sutton-Graves correlation.
Calculateur d'Accélération de Voile Solaire
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.
Calculateur de Masse de Carburant de Mission
Calculate the fuel mass required for a mission: m_fuel = m_dry * (exp(dv / ve) - 1).
Calculateur de Temps de Voyage Interstellaire
Estimate the travel time to a star at constant velocity: t = d / v, where d is the distance in light-years.