Main Index
Some Basic PHP Math, Science and Astronomy Calculators, Tools and Tables
By Jay Tanner
  

Items marked with an asterisk (*) below are programs, tables or images that can be freely downloaded or copied and pasted for customized use and modification under the provisions of the Creative Commons Attribution-ShareAlike 4.0 International license. 

All the programs come with full source code and related data and graphics files and are ready to run with no extensive setups required other than customizing the program folder names.

Tables are in plain-text format and may be easily copied/pasted in whole or in part as needed.

 
Date and Time ToolsGeneral Description
* JD Number Table CalculatorComputes a table of Julian Day numbers and Julian Dates for every day of any given year from 4713 BC to 10000 AD on both the old Julian and modern Gregorian calendars.
* Julian Date and JD Number CalculatorComputes the Julian Date and JD Number for any given date, time and time zone.
* Inverse Julian Date and JD Number CalculatorGiven any Julian Date (JD) or JD Number (Julian Day Number), this program computes the corresponding calendar date and time on both the old Julian and modern Gregorian calendars.
* Difference Between Dates and TimesThis program computes the difference between any two dates and optional times on either the old Julian or modern Gregorian calendar. The program automatically takes all leap years into acount.
* U.S.A. Holiday Calendar CalculatorComputes a calendar of the major U.S. holidays and other special dates for any given year from 1971 onwards.
* U.S.A. Daylight Saving Time CalculatorDisplays the U.S.A. Daylight Saving Time schedule for any year from 1975 onward.  Various federal laws were enacted since 1975, changing the rules for Daylight Saving Time.  The program takes these rules into account to compute the correct Daylight Saving Time schedule for any given year since then.
* E.U. Summer Time CalculatorDisplays the E.U. Summer Time schedule for any year from 2002 onward.
 
 
Astronomy Tools and TablesGeneral Description
* Basic Astronomical Ephemeris CalculatorA basic geocentric solar system ephemeris calculator spanning the 426-year period from 1600 to 2025.
* Obliquity of the Ecliptic CalculatorComputes the obliquity of the ecliptic and the latitudes of the Earth's arctic and antarctic circles at any given moment for 10,000 years.  Based on a scientific paper by J. Laskar, provided by NASA Astrophysics Data System.
* Earth Perihelion and Aphelion CalculatorComputes the dates and times of Earth's perihelions, aphelions and the intervals between them over the 600-year period from 1600 to 2200.
* Equinoxes and Solstices CalculatorComputes the dates and times of the seasonal equinoxes and solstices for any year within the 600-year period from 1600 to 2200.
* Stellar Magnitude of Sun CalculatorComputes the stellar magnitude of the sun at any given distance in astronomical units, light years or parsecs.
* Basic Lunar Ephemeris CalculatorA basic geocentric lunar ephemeris and phase calculator spanning the 426-year period from 1600 to 2025.
* Basic Lunar Events Synopsis CalculatorA basic lunar events calculator calculator spanning the 600-year period from 1600 to 2200.  The program computes the dates and times of the basic lunar phases and lunar perigees, apogees and eclipses over the 600-year period from 1600 to 2200 based on the NASA/JPL DE405 ephemeris model.
* Lunar Near Side Phase Explorer HDIntended for larger HD displays, this program acts as a virtual telescope allowing you to view the current phase of the moon or as illuminated from any given phase angle.  The phase images are 1500x1500-pixel images in PNG (Portable Network Graphic) format, rendered against a transparent background using POV-Ray 3D ray-tracing software.
* Lunar Far Side Phase Explorer HDSimilar to the Near Side phase explorer above, this program acts as a virtual telescope allowing you to view the current far-side phase of the moon as viewed from behind looking back or as illuminated from any given phase angle.  The phase images are 1500x1500-pixel images in PNG (Portable Network Graphic) format, rendered against a transparent background using POV-Ray 3D ray-tracing software.
* Table of Lunar Phase Images at 1-Degree IntervalsDisplays a sequential table of small lunar phase images (sans librations), rendered at 1-degree intervals, for quick reference.  The phases are rendered with 3D shaded relief for a natural illumination appearance.
* Lunar Phase Image Sets at 1-Degree IntervalsLunar phase image sets (sans librations), rendered at 1-degree intervals.  The phases are rendered with 3D shaded relief for a natural illumination appearance.  The image sets are provided in several sizes from tiny thumbnail size (80x80-pixels) to large images for HD (1024x1024-pixels) and were rendered using POV-Ray 3D ray-tracing software.
Table of Earth Perihelions 1600 to 2200Table of all Earth perihelions, when Earth is closest to the sun, their coordinates and distances, spanning the period from 1600 to 2200
Table of Earth Aphelions 1600 to 2200Table of all Earth aphelions, when Earth is farthest from the sun, their coordinates and distances, spanning the period from 1600 to 2200
Table of Earth Apsides and Intervals From 1600 to 2200Table of all Earth perihelions and aphelions (apsides events), intervals between them and apparent geocentric coordinates and distances at the times of the events, spanning the period from 1600 to 2200.
Table of Earth Perihelions and Intervals From 1600 to 2200Table of all Earth perihelions, when Earth is closest the sun, intervals between them and apparent geocentric coordinates and distances at the times of the events, spanning the period from 1600 to 2200.
Table of Earth Aphelions and Intervals From 1600 to 2200Table of all Earth aphelions, when Earth is farthest from the sun, intervals between them and apparent astronomical coordinates and distances at the times of the events, spanning the period from 1600 to 2200.
Table of Earth Aphelions by Distance From 1600 to 2200Table of all Earth aphelions ordered by increasing distance and spanning the period from 1600 to 2200
Table of Earth Aphelions by Date From 1600 to 2200Table of all Earth aphelions ordered by date and spanning the period from 1600 to 2200
 
 
Metric ToolsGeneral Description
* Temperature Scale InterconverterComputes the equivalents of any given temperature on the F, C, K and R (Fahrenheit, Celsius, Kelvin and Rankine) scales.
* Metric Length Equivalents Table CalculatorComputes equivalents of any given length or distance in 17 different units.
 
 
Special Math ToolsGeneral Description
* Sphere Properties CalculatorComputes all the related properties of a sphere (Radius, Circumference, Surface Area and Volume) given any single known parameter.
* Sphere Distance to Horizon CalculatorComputes the straight line-of-sight distance and corresponding surface traveling distance to the visible horizon of a spherical body.
* Sphere Angular Diameter CalculatorComputes the apparent angular diameter of a sphere at any given distance from its center or surface, taking 3D perspective into account.
* Sphere Visible Fraction of Surface CalculatorComputes the fraction of a sphere visible or illuminated by a point-light source at any given distance, taking into account the 3D perspective in space.

Given the radius of a sphere and distance from its center or surface, this program solves the following equations:
and
* GPS Ellipsoid 3D XYZ CalculatorThis program computes the rectangular 3D XYZ-coordinates corresponding to any given latitude, longitude coordinates and elevation on the GPS/GRS-80/WGS-84 ellipsoid model.

Given the GPS ellipsoid parameters, the program solves
the following equations, where:
* Geodetic Distance CalculatorComputes the geodetic surface distance between two points on Earth given their respective latitudes and longitudes.  It is based on the Andoyer Algorithm and theoretically accurate to the nearest 0.1 km.
* Variance and Standard Deviation CalculatorGiven a set of numerical data, such as a table of measurements, this program computes the variance and standard deviation.

It solves the following equations for a given sample or population:
 and 
* N-Point Lagrangian Interpolation CalculatorPerforms N-point Lagrangian interpolation within a user-defined set of tabulated dual-column (X  vs.  Y) numerical data.  Given any X-value, this program will interpolate the corresponding Y-value based on the given paired numerical data elements.

Given N data pairs arranged as a 2-column matching X vs. Y data table, and an (x) value,
the program solves the following interpolation equation for the corresponding value of (y):
* Combinations CalculatorThis program computes the exact number all possible random combinations of (R) distinct items from a total of pool of (N) items altogether. In combinations, only which items are in the selected group matters, the sequential order in which the items are selected does not matter.  It uses arbitrary-precision arithmetic, so it can handle very large numbers hundreds or even thousands of digits long.

Given any values of (N, R), this program exactly solves the equation:
Factorial CalculatorThis program computes the exact factorial of any positive integer from 0 up to 9999.  Since the numerical values of factorials increase very rapidly, some arguments could result in factorial values hundreds or even thousands of digits long.

Given any positive integer value of (n), the program exactly solves the equation:

Permutations Calculator This program computes the exact number all possible random permutations of (R) distinct items from a total of pool of (N) items altogether. In permutations, the sequential order in which the items are selected is important.  Since the numerical values of permutations increase very rapidly, some arguments could result in permutation values hundreds or even thousands of digits long.

Given any positive integer value of (n), the program exactly solves the equation:

* Integer Base InterconverterThis program converts any given integer expressed in one base into its exact equivalent in another base, where the base can be any value from 2 to 36.  Arbitrary-precision arithmetic is used, so it can handle numbers hundreds or even thousands of digits long for experimental purposes.
* Kepler's Third Law CalculatorThis program is an interactive calculator for Kepler's third law.  Given any three known variables, it solves the equation
to compute the remaining unknown variable.
* Distance Between Two Stars or PlanetsGiven the right ascension, declination coordinates and distances of two stars or planets in space, this program computes the corresponding 3D rectangular XYZ-coordinates and the spatial distance between the bodies.
 
 
Special Custom FunctionsGeneral Description
* Ellipse Circumference FunctionThis web page contains a special PHP function (code) to compute the circumference or perimeter of an ellipse, spheroid, circle or sphere by evaluating the complete elliptic integral of the second kind using an infinite power series summation based on Legendre polynomials.

Given the ellipse parameters (R, r), the function solves the equation:
POV-Ray Lunar ExplorerThis program is a lunar ray-tracing script written for POV-Ray v3.7.0

It allows the user to render customized lunar surface scenes, maps and diagrams with photo-realistic shaded 3D relief.  The script comes with several lunar surface texture maps including altimetry and gravity maps and some maps with grids.