A calculator can display many decimal places and still mislead if its inputs, model or valid date range are unclear. Astronomy Times therefore separates defined constants, catalogue data, educational approximations and precision ephemerides.
NASA/JPL Solar System Dynamics
The Night Observation Planner uses the approximate planetary-position method published by NASA’s Jet Propulsion Laboratory Solar System Dynamics group. JPL provides Keplerian elements and rates that can be propagated with lower-accuracy formulae when a full integrated ephemeris is unnecessary.
JPL describes these approximate positions as useful for applications including observation scheduling while documenting expected errors and valid time ranges. Astronomy Times uses the 1800-2050 element set and labels the resulting planet visibility as approximate.
JPL: Approximate Positions of the Planets
JPL: Planetary Orbits and Ephemerides
JPL Horizons for precision work
JPL Horizons is the appropriate reference when an observer needs substantially higher-precision Solar System positions, topocentric ephemerides, spacecraft data or professional-grade predictions. Astronomy Times does not present its browser-based approximation as a substitute for Horizons.
NASA HEASARC Messier catalogue
The Deep-Sky Object Explorer uses a curated local dataset derived from the Messier catalogue documentation maintained by NASA’s High Energy Astrophysics Science Archive Research Center. The catalogue provides Messier designations, equatorial coordinates, constellation codes, angular dimensions, visual magnitudes and object classifications.
Astronomy Times rounds catalogue values for browsing and planning. Extended nebulae and galaxies do not have perfectly sharp visible edges, so a quoted angular dimension should be treated as a representative extent rather than a guaranteed visual boundary.
NASA HEASARC: Messier Nebulae catalogue
NOAA Solar Calculator methodology
Sunset and twilight timing in the Night Observation Planner follow the solar-declination, equation-of-time and solar-zenith approach documented by NOAA’s Global Monitoring Laboratory Solar Calculator resources.
Twilight boundaries use the conventional solar-altitude definitions: civil twilight near -6°, nautical twilight near -12° and astronomical twilight near -18°. Terrain, atmospheric refraction and weather can alter the visual experience around those calculated times.
NOAA Global Monitoring Laboratory: Solar Calculator
U.S. Naval Observatory
The coordinate and sidereal-time tools follow astronomical coordinate definitions described by the U.S. Naval Observatory. The RA/Dec converter uses local sidereal time and the standard spherical transformation from equatorial coordinates to altitude and azimuth.
USNO: Sidereal Time
USNO: Computing Altitude and Azimuth
NASA and JPL planetary reference values
The shared planetary dataset used by the Solar System Explorer and comparison tools is based on NASA and JPL planetary reference information. Values such as radius, mass, orbital period and rotation period can differ slightly between sources because definitions, reference levels and measurement updates differ.
For giant planets, a value described as surface gravity is a reference gravity rather than gravity on a solid surface. Jupiter, Saturn, Uranus and Neptune do not have a solid surface comparable with Earth.
JPL: Planetary Physical Parameters
Defined units and physical constants
The speed of light in vacuum is exactly 299,792,458 metres per second in SI. The astronomical unit is exactly 149,597,870,700 metres by IAU definition. The Julian year is defined as 365.25 days. The light-year follows from the speed of light multiplied by a Julian year.
Measured constants such as the gravitational constant carry experimental uncertainty. The Astronomy Constants Reference distinguishes defined values from measured or derived quantities so users can choose appropriate precision.
Moon phase model
The Moon tools use a mean synodic month and a reference new-Moon epoch to estimate lunar age and illuminated fraction. The model is intended for education and ordinary phase planning. It does not reproduce the perturbations and topocentric corrections available from a precision lunar ephemeris.
Optics calculations
Telescope magnification, focal ratio and exit pupil use direct optical relationships. Field-of-view tools use apparent field divided by magnification as a planning approximation. When an eyepiece manufacturer publishes a physical field-stop diameter, a field-stop calculation can provide a more accurate true field.
Dawes’ limit is displayed as a theoretical double-star resolution estimate. Real observing performance also depends on diffraction, atmospheric seeing, optical quality, collimation, focus and the observer.
Astrophotography calculations
The pixel-scale calculator uses the standard small-angle relation of approximately 206.265 × pixel size in micrometres divided by focal length in millimetres. Its comparison with atmospheric seeing is presented as planning context rather than a universal pass/fail judgement.
Corrections and verification
If a source changes, a calculation appears inconsistent with an authoritative ephemeris, or a value needs correction, use the contact page. Reports that include the tool URL, entered values, expected result and an authoritative reference are the easiest to reproduce and verify.