Atmospheric Refraction: Geometric and Apparent Solar Altitude
Calculate apparent solar altitude with a stated NOAA model. Explore unit conversion, inverse calculations, disk compression and why sunrise corrections vary.
॥ असतो मा सद्गमय ॥
Study Jyotish and Hindu tradition
Thoughtful guides to charts, planets, sacred texts and Hindu traditions. Begin with one subject and go one step at a time.
Panchang and sacred days
55–72 / 72Ecliptic Longitude, Right Ascension and Declination Explained
Convert ecliptic directions to right ascension and declination with a worked rotation, original graph, latitude examples and clear degree-versus-hour units.
Hour Angle to Altitude and Azimuth: A Worked Local-Sky Guide
Turn right ascension and sidereal time into local altitude and azimuth, with a checked graph, east/north/up vectors, longitude signs and zenith examples.
Angular Separation: Calculate the True Gap Between Sky Directions
Calculate great-circle separation from RA and declination, with a checked graph, wraparound examples, unit vectors and clear limits on conjunction claims.
Position Angle in the Sky: North, East and Spherical Calculations
Calculate position angle from right ascension and declination. Explore worked bearings, a 20-degree offset chart, reverse directions and undefined cases.
Parallactic Angle: Calculate the Turning Vertical and Field Rotation
Calculate parallactic angle from latitude, hour angle and declination. Compare three sky tracks, near-zenith sensitivity, meridian cases and field-rotation limits.
Airmass and Altitude: The Secant Rule, Spherical Geometry and Horizon Limits
Derive airmass from altitude, compare the secant rule with two spherical teaching models, read an original chart and calculate illustrative observing limits.
Stellar Magnitudes: Flux Ratios and the Combined Brightness of Stars
Convert stellar magnitude differences to flux ratios, add the light of multiple sources, check detector examples and read an original companion-brightness chart.
Stellar Parallax: Parsecs, Distance Calculations and Unequal Uncertainty
Convert stellar parallax to parsecs, avoid the factor-of-two baseline error, explore asymmetric distance changes and distinguish simple geometry from inference.
Stellar Proper Motion: Components, Tangential Velocity and Worked Calculations
Convert stellar proper motion to transverse speed with the 4.74047 factor, correct RA components, parallax examples, uncertainty and epoch calculations.
Doppler Shift and Radial Velocity: Redshift, Blueshift and Worked Calculations
Calculate redshift and radial velocity from spectral lines, compare optical, radio and relativistic conventions, and check units, uncertainty and frames.
Wien's Law and Stellar Temperature: Blackbody Peaks, Units and Worked Examples
Calculate blackbody temperature from a wavelength peak, compare wavelength and frequency spectra, and understand normalized curves, uncertainty and stellar limits.
Stellar Luminosity and Radius: Stefan–Boltzmann Law with Worked Examples
Calculate stellar luminosity, radius and received flux with units, solar conversion constants, an original plot, inverse examples and uncertainty checks.
Distance Modulus and Extinction: Calculate Stellar Distance with Worked Examples
Calculate stellar distance from apparent and absolute magnitude, correct for extinction, propagate uncertainty, check parallax and avoid unresolved-binary bias.
Telescope Angular Resolution: Rayleigh Limit, Airy Disks and Camera Sampling
Calculate the Rayleigh limit with aperture and wavelength tables, Airy-radius examples, pixel scale, Nyquist sampling and clear limits from seeing and contrast.
Kepler's Third Law: Orbital Period, Total Mass and the Correct Semimajor Axis
Calculate two-body orbital periods with full units, distinguish relative and barycentric axes, infer total mass and test eccentricity and uncertainty examples.
Vis-Viva Equation: Orbital Speed, Escape Velocity and Energy Explained
Calculate orbital speed from distance and semimajor axis, compare circular and escape speeds, distinguish altitude from radius and check energy and delta-v examples.
Hohmann Transfer Calculation: Two Burns, Delta-v and Travel Time
Calculate both Hohmann transfer burns and the coast time with a complete 7000-to-14000 km example, normalized curves, inward transfers and rendezvous limitations.