Astronomía
Orbital mechanics, cosmology, planetary science, astrophotography, and space exploration calculators.
Calculadora de Período Orbital
Calculate the orbital period of a body circling a central mass using Kepler's relation T = 2pi * sqrt(a^3 / (G * M)).
Calculadora de Velocidad Orbital
Determine the orbital speed of a body in a circular orbit using v = sqrt(G * M / r).
Calculadora de Velocidad de Escape
Calculate the minimum speed needed to escape a celestial body's gravitational pull using v_esc = sqrt(2 G M / r).
Calculadora de Aceleración Gravitacional
Compute the surface gravitational acceleration of a celestial body from its mass and radius using g = G M / r^2.
Calculadora de la Tercera Ley de Kepler
Relate orbital period and semi-major axis for bodies orbiting the Sun using T^2 = a^3 (years and AU).
Calculadora de Transferencia de Hohmann
Compute the two delta-v burns and transfer time for a Hohmann transfer orbit between two circular orbits.
Calculadora de Delta-V
Compute the delta-v available from a rocket stage using the Tsiolkovsky equation: dv = v_e * ln(m0 / mf).
Calculadora de Energía Orbital Específica
Find the specific mechanical energy of an orbit: epsilon = -G M / (2a).
Calculadora de Esfera de Hill
Estimate the Hill sphere radius within which a body's gravity dominates: r_H = a * (m / (3M))^(1/3).
Calculadora de Límite de Roche
Calculate the Roche limit, the minimum distance at which a self-gravitating satellite can orbit without tidal disruption.
Calculadora de Período Sinódico
Calculate the synodic period between two orbiting bodies: the time between successive conjunctions as seen from one body.
Convertidor de Período Sideral a Sinódico
Convert a planet's sidereal period to its synodic period relative to Earth.
Calculadora de Velocidad de Satélite
Determine the speed and period of a satellite in circular orbit at a given altitude above Earth.
Calculadora de Órbita Geoestacionaria
Compute the geostationary orbit altitude and speed for any planet given its mass and rotation period.
Calculadora de Excentricidad Orbital
Compute the eccentricity of an orbit from its periapsis and apoapsis distances: e = (r_a - r_p) / (r_a + r_p).
Convertidor de Años Luz a Kilómetros
Convert astronomical distances between light-years and kilometres. One light-year is the distance light travels in one Julian year.
Convertidor de Pársec a Año Luz
Convert distances between parsecs and light-years. One parsec is the distance at which 1 AU subtends 1 arcsecond of parallax.
Calculadora de Distancia por Paralaje
Calculate the distance to a star from its parallax angle: d(pc) = 1/p(arcsec).
Convertidor de Unidad Astronómica
Convert between Astronomical Units (AU) and kilometres, miles, and light-minutes.
Calculadora de Velocidad por Corrimiento al Rojo
Estimate a galaxy's recession velocity from its cosmological redshift using the classical approximation v = z * c.
Calculadora de Distancia de Hubble
Estimate the distance to a galaxy from its recession velocity using Hubble's law: d = v / H0.
Calculadora de Tiempo de Retrospección
Estimate the lookback time (how far back in time you are seeing) from distance in megaparsecs, using t = d / c.
Calculadora de Tamaño Angular
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.
Calculadora de Magnitud Aparente
Determine a star's apparent magnitude from its absolute magnitude and distance using the distance modulus: m = M + 5 log10(d/10).
Calculadora de Magnitud Absoluta
Find a star's absolute magnitude from its apparent magnitude and distance: M = m - 5 log10(d/10).
Calculadora de Módulo de Distancia
Calculate the distance to a star from the difference between apparent and absolute magnitudes: d = 10^((m - M + 5) / 5).
Calculadora de Luminosidad
Calculate the luminosity of a star from its flux and distance using L = 4 pi d^2 F.
Calculadora de Flujo Estelar
Calculate the observed flux from a star of known luminosity at a given distance: F = L / (4 pi d^2).
Calculadora de Brillo por Ley del Inverso del Cuadrado
Compare the brightness of an object at two different distances using the inverse square law: F2/F1 = (d1/d2)^2.
Calculadora de Escala de Distancias Cósmicas
Enter a distance in parsecs and see which measurement methods are appropriate at that scale, plus conversions to multiple units.
Calculadora de Luminosidad Estelar
Calculate a star's luminosity from its absolute magnitude: L/L_sun = 10^((M_sun - M_star) / 2.5).
Estimador de Hertzsprung-Russell
Estimate a main-sequence star's luminosity and radius from its effective temperature using empirical scaling relations.
Calculadora de Vida en la Secuencia Principal
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.
Calculadora de Radio de Schwarzschild
Calculate the Schwarzschild radius (event horizon) of a black hole: r_s = 2 G M / c^2.
Calculadora del Límite 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.
Calculadora de Densidad de Estrella de Neutrones
Estimate the average density of a neutron star from its mass and radius: rho = 3M / (4 pi r^3).
Calculadora de Radio de Enana Blanca
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.
Calculadora de Temperatura Estelar
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)).
Calculadora de Longitud de Onda Pico de Wien
Find the peak emission wavelength of a blackbody from its temperature using Wien's displacement law: lambda_max = b / T.
Calculadora de Luminosidad de Stefan-Boltzmann
Calculate a star's luminosity from its radius and surface temperature: L = 4 pi R^2 sigma T^4.
Calculadora de Luminosidad de 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.
Calculadora de Relación Masa-Luminosidad
Estimate a main-sequence star's luminosity from its mass using the empirical relation L/L_sun ~ (M/M_sun)^3.5.
Estimador de Clase Espectral
Estimate which spectral class (O, B, A, F, G, K, M) a star belongs to based on its effective temperature.
Calculadora de Color-Temperatura Estelar
Convert between a star's colour temperature in Kelvin and its peak emission wavelength, plus approximate visible colour description.
Calculadora de Energía de Fusión Nuclear Estelar
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.
Calculadora de Gravedad Planetaria
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.
Calculadora de Peso en Otros Planetas
Find what you would weigh on another planet by scaling your Earth weight by the surface gravity ratio.
Calculadora de Mediodía Solar
Estimate the local solar noon time from your longitude and the standard meridian of your time zone.
Calculadora de Duración del Día
Estimate the number of daylight hours from your latitude and the Sun's declination using the hour-angle formula.
Calculadora de Fase Lunar
Estimate the Moon's illumination fraction and phase from the number of days since the last known new moon.
Calculadora de Magnificación de Telescopio
Calculate the magnification of a telescope from the focal lengths of the objective and eyepiece: M = f_obj / f_eye.
Calculadora de Resolución de Telescopio
Compute the angular resolution (Dawes limit) of a telescope from its aperture: theta = 116 / D (arcseconds, D in mm).
Calculadora de Relación Focal de Telescopio
Calculate the focal ratio (f-number) of a telescope: f/# = focal_length / aperture.
Calculadora de Campo de Visión
Calculate the true field of view of a telescope and eyepiece combination: TFOV = AFOV / Magnification.
Calculadora de Magnitud Límite
Estimate the faintest star visible through a telescope: m_lim = 2 + 5 log10(D) where D is aperture in mm.
Calculadora de Recolección de Luz de Telescopio
Compare the light-gathering power of a telescope to the naked eye: LGP = (D / d_eye)^2.
Calculadora de Pupila de Salida de Binoculares
Calculate the exit pupil of binoculars or a telescope eyepiece: exit_pupil = aperture / magnification.
Calculadora de Regla de Exposición Astronómica
Calculate the maximum untracked exposure time before stars trail using the NPF rule or simplified 500 rule: t = 500 / (focal_length).
Calculadora de Energía de Impacto de Asteroide
Estimate the kinetic energy of an asteroid impact from its diameter, density, and velocity: KE = 0.5 * (pi/6) * d^3 * rho * v^2.
Calculadora de la Ecuación de Drake
Estimate the number of detectable civilisations in the Milky Way using the Drake equation: N = R* * fp * ne * fl * fi * fc * L.
Calculadora de Tasa de Expansión Cósmica
Estimate the recession velocity of a distant galaxy from the Hubble-Lemaitre law v = H0 * d, where H0 is the Hubble constant.
Calculadora de Densidad de Energía Oscura
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).
Calculadora del Parámetro de Densidad de Materia
Calculate the matter density parameter Omega_m = rho_m / rho_crit, indicating what fraction of the critical density is made up of matter.
Calculadora de Densidad Crítica
Compute the critical density of the universe rho_crit = 3 H0^2 / (8 pi G), the density needed for a flat geometry.
Calculadora del Parámetro de Desaceleración
Estimate the deceleration parameter q0 = Omega_m / 2 - Omega_Lambda, which indicates whether the expansion of the universe is accelerating or decelerating.
Calculadora de Distancia Comóvil
Approximate the comoving distance to a galaxy at low redshift using d = c * z / H0, the linearised Hubble relation.
Calculadora de Distancia Propia
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.
Calculadora de Edad del Universo
Estimate the age of the universe as t ≈ 1 / H0 (the Hubble time), providing a rough upper bound for a matter-only universe.
Calculadora de Densidad Bariónica
Compute the baryon (ordinary matter) density parameter Omega_b from the baryon density and the critical density.
Calculadora del Tiempo de Hubble
Calculate the Hubble time t_H = 1/H0, the characteristic timescale of cosmic expansion, in seconds and gigayears.
Calculadora de Período Orbital Planetario
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.
Calculadora de Temperatura Superficial Planetaria
Estimate the effective surface temperature of a planet using Stefan-Boltzmann balance: T = ((L * (1 - A)) / (16 * pi * sigma * d^2))^0.25.
Calculadora de Altura de Escala Atmosférica
Calculate the atmospheric scale height H = k_B * T / (m * g), the altitude over which pressure drops by a factor of e.
Calculadora de Fuerza de Marea
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.
Calculadora de Albedo Planetario
Determine a planet's bond albedo from the reflected and incident flux: A = F_reflected / F_incident.
Calculadora de Temperatura de Equilibrio Planetaria
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).
Calculadora de Intensidad de Campo Magnético Planetario
Estimate a planet's dipole magnetic field strength at the surface using the dipole approximation B = (mu0 / 4pi) * M_dipole / R^3.
Calculadora de Presión Atmosférica por Altitud
Calculate the atmospheric pressure at a given altitude using the barometric formula P = P0 * exp(-h / H), where H is the scale height.
Calculadora de Densidad Planetaria
Calculate the mean bulk density of a planet from its mass and radius: rho = 3 M / (4 pi R^3).
Calculadora de Velocidad de Escape Planetaria
Compute the escape velocity from a planet's surface using v_esc = sqrt(2 G M / R).
Calculadora de Campo de Visión del Sensor
Calculate the field of view of a camera sensor attached to a telescope: FOV = 2 * atan(sensor_size / (2 * focal_length)) converted to degrees.
Calculadora de Escala de Píxel
Determine the angular size each pixel subtends on the sky: pixel_scale = 206.265 * pixel_size / focal_length arcseconds per pixel.
Calculadora de Resolución de Imagen Astronómica
Calculate the angular resolution of a telescope from its aperture using the Dawes limit: theta = 116 / D arcseconds, where D is in mm.
Calculadora de Tiempo de Exposición para Estrellas
Calculate the maximum exposure time before stars trail using the NPF rule: t = (35 * N + 30 * p) / (f * cos(dec)), with declination correction.
Calculadora de Señal-Ruido por Apilamiento
Estimate the signal-to-noise improvement from stacking multiple exposures: SNR_total = SNR_single * sqrt(n).
Calculadora de Impacto de Contaminación Lumínica
Estimate how light pollution reduces contrast by computing the sky-brightness ratio: contrast_loss = sky_brightness / (sky_brightness + object_brightness).
Calculadora de Efecto de Reductor Focal
Calculate the effective focal length and f-ratio after adding a focal reducer: f_eff = f * reduction_factor, N_eff = N * reduction_factor.
Calculadora de Magnificación Barlow
Calculate the effective focal length and f-ratio after adding a Barlow lens: f_eff = f * barlow_factor.
Calculadora de Eficiencia Cuántica CCD
Calculate the number of photoelectrons generated by a CCD sensor: electrons = photon_flux * area * QE * exposure_time.
Calculadora de Tolerancia de Error de Seguimiento
Determine the maximum acceptable periodic error of a mount: PE_max = pixel_scale * acceptable_drift_px, in arcseconds.
Calculadora de Delta-V de Cohete
Calculate the total delta-v a rocket can achieve from the Tsiolkovsky equation: dv = ve * ln(m0 / mf).
Calculadora de la Ecuación de Tsiolkovsky
Compute the required mass ratio for a given delta-v and exhaust velocity: m0/mf = exp(dv / ve).
Calculadora de Impulso Específico
Calculate the specific impulse of a rocket engine: Isp = ve / g0, the exhaust velocity normalised by standard gravity.
Calculadora de Relación Empuje-Peso
Calculate the thrust-to-weight ratio of a rocket: TWR = thrust / (mass * g), determining if it can lift off.
Calculadora de Costo de Maniobra Orbital
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))).
Calculadora de Velocidad por Asistencia Gravitatoria
Estimate the maximum speed change from a gravity assist: dv_max = 2 * v_planet * sin(theta/2), where theta is the bending angle.
Calculadora de Calentamiento de Reentrada
Estimate the stagnation-point heat flux during atmospheric reentry using q = k * sqrt(rho / r_nose) * v^3, the Sutton-Graves correlation.
Calculadora de Aceleración de Vela Solar
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.
Calculadora de Masa de Combustible de Misión
Calculate the fuel mass required for a mission: m_fuel = m_dry * (exp(dv / ve) - 1).
Calculadora de Tiempo de Viaje Interestelar
Estimate the travel time to a star at constant velocity: t = d / v, where d is the distance in light-years.