Basic Ellipsoid Elements Calculator
Primarily for Planetary Meridian and Orbital Parameter Computations - Exp v1.02

ENTER Ellipsoid Equatorial and Polar (a , b) Parameters in Any Units (ab)


On empty input, default Earth (WGS-84) parameters (a, b), in meters, will be used.

The program will compute the ellipsoid elements from the given (a, b) parameters
using the standard equations following below.
ELLIPSOID PARAMETERS

a  = Equatorial radius    = 6378137.0000000000000000 units
b  = Polar radius         = 6356752.3142450000000000 units

f  = Flattening factor    = 0.0033528106647756233521 = 1/298.2572235604965054

e  = Eccentricity         = 0.0818191908429643023611
e²                        = 0.0066943799901974135468

       Equatorial Quarter = 10018754.1713946215382942 units
       Meridional Quarter = 10001965.7293125819531904 units

Circumference of Equator  = 40075016.6855784861531768 units = Red Equatorial Circle
Circumference of Meridian = 40007862.9172503278127614 units = Cyan Meridional Ellipse
Circumference Difference  = 67153.7683281583404154 units





  • PLANETARY ELLIPSOID PARAMETERS (a, b)
    Known (a, b) Parameters of Planets in Kilometers and Miles
    Source: NASA
    
    The equatorial and meridional circumferences were computed
    from the given (a , b) parameters using the above program.
    __________________________________________________________
    Earth               |
    6378.1 , 6356.8 km  |  Equat C = 40074.8 km  = 24901.3 mi
       a        b       |  Diff    =  1326.0 km  =   824.0 mi
    3963.2 , 3949.9 mi  |  Merid C = 40007.9 km  = 24859.8 mi
    ____________________|_____________________________________
    The Moon            |
    1738.1 , 1736.0 km  |  Equat C = 6785.8 km   = 4216.5 mi
       a        b       |  Diff    =    6.6 km   =    4.1 mi
    1080.0 , 1078.7 mi  |  Merid C = 6781.8 km   = 4214.0 mi
    ____________________|_____________________________________
    Mars                |
    3396.2 , 3376.2 km  |  Equat C = 21339.0 km  = 13259.4 mi
       a        b       |  Diff    =    62.8 km  =    39.0 mi
    2110.3 , 2097.9 mi  |  Merid C = 21276.2 km  = 13220.4 mi
    ____________________|_____________________________________
    Jupiter             |
    71492 , 66854 km    |  Equat C = 449197 km   = 279118 mi
      a       b         |  Diff    =  14449 km   =   8978 mi
    44423 , 41541 mi    |  Merid C = 434749 km   = 270140 mi
    ____________________|_____________________________________
    Saturn              |
    60268 , 54364 km    |  Equat C = 378675 km   = 235298 mi
       a      b         |  Diff    =  18309 km   =  11377 mi
    37449 , 33780 mi    |  Merid C = 360366 km   = 223921 mi
    ____________________|_____________________________________
    Uranus              |
    25559 , 24973 km    |  Equat C = 160592 km   = 99787 mi
      a       b         |  Diff    =   1836 km   =  1141 mi
    15882 , 15518 mi    |  Merid C = 158756 km   = 98647 mi
    ____________________|_____________________________________
    Neptune             |
    24764 , 24341 km    |  Equat C = 155597 km   = 96683 mi
      a       b         |  Diff    =   1326 km   =   824 mi
    15388 , 15125 mi    |  Merid C = 154271 km   = 95859 mi
    
    
References

The Earth Ellipsoid
https://en.wikipedia.org/wiki/Earth_ellipsoid

Complete Elliptic Integral of the Second Kind
https://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_second_kind

Ordinance Survey - A Guide to Coordinate Systems in Great Britain
An introduction to mapping coordinate systems and the use of GNSS datasets with Ordnance Survey mapping
https://www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf

A PHP Science Program by Jay Tanner - Revised: 2019 November 05 Tuesday at 09:44:04 AM GMT