Astronomie
Orbital mechanics, cosmology, planetary science, astrophotography, and space exploration calculators.
Orbital Period Rechner
Calculate the orbital period of a body circling a central mass using Kepler's relation T = 2pi * sqrt(a^3 / (G * M)).
Orbital Geschwindigkeits Rechner
Determine the orbital speed of a body in a circular orbit using v = sqrt(G * M / r).
Escape Geschwindigkeits Rechner
Calculate the minimum speed needed to escape a celestial body's gravitational pull using v_esc = sqrt(2 G M / r).
Gravitational Beschleunigungs Rechner
Compute the surface gravitational acceleration of a celestial body from its mass and radius using g = G M / r^2.
Kepler\
Relate orbital period and semi-major axis for bodies orbiting the Sun using T^2 = a^3 (years and AU).
Hohmann Transfer Rechner
Compute the two delta-v burns and transfer time for a Hohmann transfer orbit between two circular orbits.
Delta-v Rechner
Compute the delta-v available from a rocket stage using the Tsiolkovsky equation: dv = v_e * ln(m0 / mf).
Specific Orbital Energie Rechner
Find the specific mechanical energy of an orbit: epsilon = -G M / (2a).
Hill Sphere Rechner
Estimate the Hill sphere radius within which a body's gravity dominates: r_H = a * (m / (3M))^(1/3).
Roche Limit Rechner
Calculate the Roche limit, the minimum distance at which a self-gravitating satellite can orbit without tidal disruption.
Synodic Period Rechner
Calculate the synodic period between two orbiting bodies: the time between successive conjunctions as seen from one body.
Sidereal-to-Synodic Umrechner
Convert a planet's sidereal period to its synodic period relative to Earth.
Satellite Speed Rechner
Determine the speed and period of a satellite in circular orbit at a given altitude above Earth.
Geostationary Orbit Rechner
Compute the geostationary orbit altitude and speed for any planet given its mass and rotation period.
Orbital Eccentricity Rechner
Compute the eccentricity of an orbit from its periapsis and apoapsis distances: e = (r_a - r_p) / (r_a + r_p).
Licht-Year to Kilometres Umrechner
Convert astronomical distances between light-years and kilometres. One light-year is the distance light travels in one Julian year.
Parsec to Licht-Year Umrechner
Convert distances between parsecs and light-years. One parsec is the distance at which 1 AU subtends 1 arcsecond of parallax.
Parallax Distance Rechner
Calculate the distance to a star from its parallax angle: d(pc) = 1/p(arcsec).
Astronomical Unit Umrechner
Convert between Astronomical Units (AU) and kilometres, miles, and light-minutes.
Redshift Geschwindigkeits Rechner
Estimate a galaxy's recession velocity from its cosmological redshift using the classical approximation v = z * c.
Hubble Distance Rechner
Estimate the distance to a galaxy from its recession velocity using Hubble's law: d = v / H0.
Lookback Time Rechner
Estimate the lookback time (how far back in time you are seeing) from distance in megaparsecs, using t = d / c.
Winkel Size Rechner
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 Rechner
Determine a star's apparent magnitude from its absolute magnitude and distance using the distance modulus: m = M + 5 log10(d/10).
Absolute Magnitude Rechner
Find a star's absolute magnitude from its apparent magnitude and distance: M = m - 5 log10(d/10).
Distance Modulus Rechner
Calculate the distance to a star from the difference between apparent and absolute magnitudes: d = 10^((m - M + 5) / 5).
Luminosity Rechner
Calculate the luminosity of a star from its flux and distance using L = 4 pi d^2 F.
Stellar Flux Rechner
Calculate the observed flux from a star of known luminosity at a given distance: F = L / (4 pi d^2).
Inverse Square Brightness Rechner
Compare the brightness of an object at two different distances using the inverse square law: F2/F1 = (d1/d2)^2.
Cosmic Distance Ladder Rechner
Enter a distance in parsecs and see which measurement methods are appropriate at that scale, plus conversions to multiple units.
Stellar Luminosity Rechner
Calculate a star's luminosity from its absolute magnitude: L/L_sun = 10^((M_sun - M_star) / 2.5).
Hertzsprung-Russell Schätzer
Estimate a main-sequence star's luminosity and radius from its effective temperature using empirical scaling relations.
Main-Sequence Lifetime Rechner
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 Rechner
Calculate the Schwarzschild radius (event horizon) of a black hole: r_s = 2 G M / c^2.
Chandrasekhar Limit Rechner
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 Rechner
Estimate the average density of a neutron star from its mass and radius: rho = 3M / (4 pi r^3).
White Dwarf Radius Rechner
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 Rechner
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 Wellenlänge Rechner
Find the peak emission wavelength of a blackbody from its temperature using Wien's displacement law: lambda_max = b / T.
Stefan-Boltzmann Luminosity Rechner
Calculate a star's luminosity from its radius and surface temperature: L = 4 pi R^2 sigma T^4.
Eddington Luminosity Rechner
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 Rechner
Estimate a main-sequence star's luminosity from its mass using the empirical relation L/L_sun ~ (M/M_sun)^3.5.
Spectral Class Schätzer
Estimate which spectral class (O, B, A, F, G, K, M) a star belongs to based on its effective temperature.
Star Colour-Temperature Rechner
Convert between a star's colour temperature in Kelvin and its peak emission wavelength, plus approximate visible colour description.
Nuclear Fusion Energie Rechner
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 Rechner
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 Gewichts Rechner
Find what you would weigh on another planet by scaling your Earth weight by the surface gravity ratio.
Solar Noon Rechner
Estimate the local solar noon time from your longitude and the standard meridian of your time zone.
Daylight Duration Rechner
Estimate the number of daylight hours from your latitude and the Sun's declination using the hour-angle formula.
Moon Phase Rechner
Estimate the Moon's illumination fraction and phase from the number of days since the last known new moon.
Telescope Magnification Rechner
Calculate the magnification of a telescope from the focal lengths of the objective and eyepiece: M = f_obj / f_eye.
Telescope Resolution Rechner
Compute the angular resolution (Dawes limit) of a telescope from its aperture: theta = 116 / D (arcseconds, D in mm).
Telescope Focal Ratio Rechner
Calculate the focal ratio (f-number) of a telescope: f/# = focal_length / aperture.
Field of View Rechner
Calculate the true field of view of a telescope and eyepiece combination: TFOV = AFOV / Magnification.
Limiting Magnitude Rechner
Estimate the faintest star visible through a telescope: m_lim = 2 + 5 log10(D) where D is aperture in mm.
Telescope Licht Gathering Rechner
Compare the light-gathering power of a telescope to the naked eye: LGP = (D / d_eye)^2.
Binocular Exit Pupil Rechner
Calculate the exit pupil of binoculars or a telescope eyepiece: exit_pupil = aperture / magnification.
Camera Exposure Rule Rechner
Calculate the maximum untracked exposure time before stars trail using the NPF rule or simplified 500 rule: t = 500 / (focal_length).
Asteroid Impact Energie Rechner
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 Rechner
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 Rechner
Estimate the recession velocity of a distant galaxy from the Hubble-Lemaitre law v = H0 * d, where H0 is the Hubble constant.
Dark Energie Density Rechner
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 Rechner
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 Rechner
Compute the critical density of the universe rho_crit = 3 H0^2 / (8 pi G), the density needed for a flat geometry.
Deceleration Parameter Rechner
Estimate the deceleration parameter q0 = Omega_m / 2 - Omega_Lambda, which indicates whether the expansion of the universe is accelerating or decelerating.
Comoving Distance Rechner
Approximate the comoving distance to a galaxy at low redshift using d = c * z / H0, the linearised Hubble relation.
Proper Distance Rechner
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 Rechner
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 Rechner
Compute the baryon (ordinary matter) density parameter Omega_b from the baryon density and the critical density.
Hubble Time Rechner
Calculate the Hubble time t_H = 1/H0, the characteristic timescale of cosmic expansion, in seconds and gigayears.
Planet Orbital Period Rechner
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 Rechner
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 Rechner
Calculate the atmospheric scale height H = k_B * T / (m * g), the altitude over which pressure drops by a factor of e.
Tidal Kraft Rechner
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 Rechner
Determine a planet's bond albedo from the reflected and incident flux: A = F_reflected / F_incident.
Planet Gleichgewichts Temperature Rechner
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 Rechner
Estimate a planet's dipole magnetic field strength at the surface using the dipole approximation B = (mu0 / 4pi) * M_dipole / R^3.
Atmospheric Druck at Altitude Rechner
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 Rechner
Calculate the mean bulk density of a planet from its mass and radius: rho = 3 M / (4 pi R^3).
Planet Escape Geschwindigkeits Rechner
Compute the escape velocity from a planet's surface using v_esc = sqrt(2 G M / R).
Camera Sensor FOV Rechner
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 Rechner
Determine the angular size each pixel subtends on the sky: pixel_scale = 206.265 * pixel_size / focal_length arcseconds per pixel.
Image Resolution Rechner
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 Rechner
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 Rechner
Estimate the signal-to-noise improvement from stacking multiple exposures: SNR_total = SNR_single * sqrt(n).
Licht Pollution Impact Rechner
Estimate how light pollution reduces contrast by computing the sky-brightness ratio: contrast_loss = sky_brightness / (sky_brightness + object_brightness).
Focal Reducer Effect Rechner
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 Rechner
Calculate the effective focal length and f-ratio after adding a Barlow lens: f_eff = f * barlow_factor.
CCD Quantum Efficiency Rechner
Calculate the number of photoelectrons generated by a CCD sensor: electrons = photon_flux * area * QE * exposure_time.
Tracking Error Tolerance Rechner
Determine the maximum acceptable periodic error of a mount: PE_max = pixel_scale * acceptable_drift_px, in arcseconds.
Rocket Delta-V Rechner
Calculate the total delta-v a rocket can achieve from the Tsiolkovsky equation: dv = ve * ln(m0 / mf).
Tsiolkovsky Equation Rechner
Compute the required mass ratio for a given delta-v and exhaust velocity: m0/mf = exp(dv / ve).
Specific Impulse Rechner
Calculate the specific impulse of a rocket engine: Isp = ve / g0, the exhaust velocity normalised by standard gravity.
Thrust-to-Gewichts Ratio Rechner
Calculate the thrust-to-weight ratio of a rocket: TWR = thrust / (mass * g), determining if it can lift off.
Orbital Manoeuvre Cost Rechner
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 Rechner
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 Rechner
Estimate the stagnation-point heat flux during atmospheric reentry using q = k * sqrt(rho / r_nose) * v^3, the Sutton-Graves correlation.
Solar Sail Beschleunigungs Rechner
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 Rechner
Calculate the fuel mass required for a mission: m_fuel = m_dry * (exp(dv / ve) - 1).
Interstellar Travel Time Rechner
Estimate the travel time to a star at constant velocity: t = d / v, where d is the distance in light-years.