天文学
Orbital mechanics, cosmology, planetary science, astrophotography, and space exploration calculators.
轨道周期计算器
Calculate the orbital period of a body circling a central mass using Kepler's relation T = 2pi * sqrt(a^3 / (G * M)).
轨道速度计算器
Determine the orbital speed of a body in a circular orbit using v = sqrt(G * M / r).
行星逃逸速度计算器
Calculate the minimum speed needed to escape a celestial body's gravitational pull using v_esc = sqrt(2 G M / r).
重力加速度计算器
Compute the surface gravitational acceleration of a celestial body from its mass and radius using g = G M / r^2.
开普勒第三定律计算器
Relate orbital period and semi-major axis for bodies orbiting the Sun using T^2 = a^3 (years and AU).
霍曼转移计算器
Compute the two delta-v burns and transfer time for a Hohmann transfer orbit between two circular orbits.
Δv计算器
Compute the delta-v available from a rocket stage using the Tsiolkovsky equation: dv = v_e * ln(m0 / mf).
比轨道能量计算器
Find the specific mechanical energy of an orbit: epsilon = -G M / (2a).
希尔球计算器
Estimate the Hill sphere radius within which a body's gravity dominates: r_H = a * (m / (3M))^(1/3).
洛希极限计算器
Calculate the Roche limit, the minimum distance at which a self-gravitating satellite can orbit without tidal disruption.
会合周期计算器
Calculate the synodic period between two orbiting bodies: the time between successive conjunctions as seen from one body.
恒星周期转会合周期转换器
Convert a planet's sidereal period to its synodic period relative to Earth.
卫星速度计算器
Determine the speed and period of a satellite in circular orbit at a given altitude above Earth.
地球静止轨道计算器
Compute the geostationary orbit altitude and speed for any planet given its mass and rotation period.
轨道离心率计算器
Compute the eccentricity of an orbit from its periapsis and apoapsis distances: e = (r_a - r_p) / (r_a + r_p).
光年转千米转换器
Convert astronomical distances between light-years and kilometres. One light-year is the distance light travels in one Julian year.
秒差距转光年转换器
Convert distances between parsecs and light-years. One parsec is the distance at which 1 AU subtends 1 arcsecond of parallax.
视差距离计算器
Calculate the distance to a star from its parallax angle: d(pc) = 1/p(arcsec).
天文单位转换器
Convert between Astronomical Units (AU) and kilometres, miles, and light-minutes.
红移速度计算器
Estimate a galaxy's recession velocity from its cosmological redshift using the classical approximation v = z * c.
哈勃距离计算器
Estimate the distance to a galaxy from its recession velocity using Hubble's law: d = v / H0.
回溯时间计算器
Estimate the lookback time (how far back in time you are seeing) from distance in megaparsecs, using t = d / c.
角大小计算器
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.
视星等计算器
Determine a star's apparent magnitude from its absolute magnitude and distance using the distance modulus: m = M + 5 log10(d/10).
绝对星等计算器
Find a star's absolute magnitude from its apparent magnitude and distance: M = m - 5 log10(d/10).
距离模数计算器
Calculate the distance to a star from the difference between apparent and absolute magnitudes: d = 10^((m - M + 5) / 5).
光度计算器
Calculate the luminosity of a star from its flux and distance using L = 4 pi d^2 F.
恒星通量计算器
Calculate the observed flux from a star of known luminosity at a given distance: F = L / (4 pi d^2).
平方反比亮度计算器
Compare the brightness of an object at two different distances using the inverse square law: F2/F1 = (d1/d2)^2.
宇宙距离阶梯计算器
Enter a distance in parsecs and see which measurement methods are appropriate at that scale, plus conversions to multiple units.
恒星光度计算器
Calculate a star's luminosity from its absolute magnitude: L/L_sun = 10^((M_sun - M_star) / 2.5).
赫罗图估算器
Estimate a main-sequence star's luminosity and radius from its effective temperature using empirical scaling relations.
主序星寿命计算器
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.
史瓦西半径计算器
Calculate the Schwarzschild radius (event horizon) of a black hole: r_s = 2 G M / c^2.
钱德拉塞卡极限计算器
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.
中子星密度计算器
Estimate the average density of a neutron star from its mass and radius: rho = 3M / (4 pi r^3).
白矮星半径计算器
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.
恒星温度计算器
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)).
维恩峰值波长计算器
Find the peak emission wavelength of a blackbody from its temperature using Wien's displacement law: lambda_max = b / T.
斯特藩-玻尔兹曼光度计算器
Calculate a star's luminosity from its radius and surface temperature: L = 4 pi R^2 sigma T^4.
爱丁顿光度计算器
Compute the Eddington luminosity, the maximum luminosity a body can achieve when radiation pressure balances gravity: L_Edd = 4 pi G M c / kappa.
质光关系计算器
Estimate a main-sequence star's luminosity from its mass using the empirical relation L/L_sun ~ (M/M_sun)^3.5.
光谱分类估算器
Estimate which spectral class (O, B, A, F, G, K, M) a star belongs to based on its effective temperature.
恒星色温计算器
Convert between a star's colour temperature in Kelvin and its peak emission wavelength, plus approximate visible colour description.
核聚变能量计算器
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.
行星重力计算器
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.
星球体重计算器
Find what you would weigh on another planet by scaling your Earth weight by the surface gravity ratio.
正午太阳计算器
Estimate the local solar noon time from your longitude and the standard meridian of your time zone.
日照时长计算器
Estimate the number of daylight hours from your latitude and the Sun's declination using the hour-angle formula.
月相计算器
Estimate the Moon's illumination fraction and phase from the number of days since the last known new moon.
望远镜放大率计算器
Calculate the magnification of a telescope from the focal lengths of the objective and eyepiece: M = f_obj / f_eye.
望远镜分辨率计算器
Compute the angular resolution (Dawes limit) of a telescope from its aperture: theta = 116 / D (arcseconds, D in mm).
望远镜焦比计算器
Calculate the focal ratio (f-number) of a telescope: f/# = focal_length / aperture.
视场计算器
Calculate the true field of view of a telescope and eyepiece combination: TFOV = AFOV / Magnification.
极限星等计算器
Estimate the faintest star visible through a telescope: m_lim = 2 + 5 log10(D) where D is aperture in mm.
望远镜集光力计算器
Compare the light-gathering power of a telescope to the naked eye: LGP = (D / d_eye)^2.
双筒望远镜出瞳计算器
Calculate the exit pupil of binoculars or a telescope eyepiece: exit_pupil = aperture / magnification.
相机曝光规则计算器
Calculate the maximum untracked exposure time before stars trail using the NPF rule or simplified 500 rule: t = 500 / (focal_length).
小行星撞击能量计算器
Estimate the kinetic energy of an asteroid impact from its diameter, density, and velocity: KE = 0.5 * (pi/6) * d^3 * rho * v^2.
德雷克方程计算器
Estimate the number of detectable civilisations in the Milky Way using the Drake equation: N = R* * fp * ne * fl * fi * fc * L.
宇宙膨胀率计算器
Estimate the recession velocity of a distant galaxy from the Hubble-Lemaitre law v = H0 * d, where H0 is the Hubble constant.
暗能量密度计算器
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).
物质密度参数计算器
Calculate the matter density parameter Omega_m = rho_m / rho_crit, indicating what fraction of the critical density is made up of matter.
临界密度计算器
Compute the critical density of the universe rho_crit = 3 H0^2 / (8 pi G), the density needed for a flat geometry.
减速参数计算器
Estimate the deceleration parameter q0 = Omega_m / 2 - Omega_Lambda, which indicates whether the expansion of the universe is accelerating or decelerating.
共动距离计算器
Approximate the comoving distance to a galaxy at low redshift using d = c * z / H0, the linearised Hubble relation.
固有距离计算器
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.
宇宙年龄计算器
Estimate the age of the universe as t ≈ 1 / H0 (the Hubble time), providing a rough upper bound for a matter-only universe.
重子密度计算器
Compute the baryon (ordinary matter) density parameter Omega_b from the baryon density and the critical density.
哈勃时间计算器
Calculate the Hubble time t_H = 1/H0, the characteristic timescale of cosmic expansion, in seconds and gigayears.
行星轨道周期计算器
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.
行星表面温度计算器
Estimate the effective surface temperature of a planet using Stefan-Boltzmann balance: T = ((L * (1 - A)) / (16 * pi * sigma * d^2))^0.25.
大气标高计算器
Calculate the atmospheric scale height H = k_B * T / (m * g), the altitude over which pressure drops by a factor of e.
潮汐力计算器
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.
行星反照率计算器
Determine a planet's bond albedo from the reflected and incident flux: A = F_reflected / F_incident.
行星平衡温度计算器
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).
行星磁场强度计算器
Estimate a planet's dipole magnetic field strength at the surface using the dipole approximation B = (mu0 / 4pi) * M_dipole / R^3.
海拔大气压力计算器
Calculate the atmospheric pressure at a given altitude using the barometric formula P = P0 * exp(-h / H), where H is the scale height.
行星密度计算器
Calculate the mean bulk density of a planet from its mass and radius: rho = 3 M / (4 pi R^3).
行星逃逸速度计算器
Compute the escape velocity from a planet's surface using v_esc = sqrt(2 G M / R).
相机传感器视场计算器
Calculate the field of view of a camera sensor attached to a telescope: FOV = 2 * atan(sensor_size / (2 * focal_length)) converted to degrees.
像素比例计算器
Determine the angular size each pixel subtends on the sky: pixel_scale = 206.265 * pixel_size / focal_length arcseconds per pixel.
图像分辨率计算器
Calculate the angular resolution of a telescope from its aperture using the Dawes limit: theta = 116 / D arcseconds, where D is in mm.
恒星曝光时间计算器
Calculate the maximum exposure time before stars trail using the NPF rule: t = (35 * N + 30 * p) / (f * cos(dec)), with declination correction.
叠加信噪比计算器
Estimate the signal-to-noise improvement from stacking multiple exposures: SNR_total = SNR_single * sqrt(n).
光污染影响计算器
Estimate how light pollution reduces contrast by computing the sky-brightness ratio: contrast_loss = sky_brightness / (sky_brightness + object_brightness).
减焦镜效果计算器
Calculate the effective focal length and f-ratio after adding a focal reducer: f_eff = f * reduction_factor, N_eff = N * reduction_factor.
巴罗放大计算器
Calculate the effective focal length and f-ratio after adding a Barlow lens: f_eff = f * barlow_factor.
CCD量子效率计算器
Calculate the number of photoelectrons generated by a CCD sensor: electrons = photon_flux * area * QE * exposure_time.
跟踪误差容限计算器
Determine the maximum acceptable periodic error of a mount: PE_max = pixel_scale * acceptable_drift_px, in arcseconds.
火箭速度增量计算器
Calculate the total delta-v a rocket can achieve from the Tsiolkovsky equation: dv = ve * ln(m0 / mf).
齐奥尔科夫斯基方程计算器
Compute the required mass ratio for a given delta-v and exhaust velocity: m0/mf = exp(dv / ve).
比冲计算器
Calculate the specific impulse of a rocket engine: Isp = ve / g0, the exhaust velocity normalised by standard gravity.
推重比计算器
Calculate the thrust-to-weight ratio of a rocket: TWR = thrust / (mass * g), determining if it can lift off.
轨道机动成本计算器
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))).
引力弹弓速度计算器
Estimate the maximum speed change from a gravity assist: dv_max = 2 * v_planet * sin(theta/2), where theta is the bending angle.
再入加热计算器
Estimate the stagnation-point heat flux during atmospheric reentry using q = k * sqrt(rho / r_nose) * v^3, the Sutton-Graves correlation.
太阳帆加速度计算器
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.
任务燃料质量计算器
Calculate the fuel mass required for a mission: m_fuel = m_dry * (exp(dv / ve) - 1).
星际旅行时间计算器
Estimate the travel time to a star at constant velocity: t = d / v, where d is the distance in light-years.