Basic Oblate Spheroid / Ellipse Elements Calculator
A high-precision numerical solution to the complete elliptic integral of the second kind.
Designed originally for oblate spheroid meridian and elliptical orbit length computations.

ENTER Oblate Spheroid Polar and Equatorial Radii (r , R) in Any Units (r ≤ R)

On empty input, default Earth (WGS-84/GPS) parameters (r , R), in kilometers, will be used.

This program will compute the oblate spheroid or ellipse elements from
the given (r , R) parameters using the standard equations given below.

Circumference of Circle, Ellipse or Oblate Spheroid Meridian

Double-Click to Select ALL Text

Here is the summation equation solved by the function to numerically evaluate the
circumference (C) followed by the PHP source code upon which this program is based.

Circumference of Circle, Ellipse or Oblate Spheroid Meridian

`\$C = Ellipse_Circum (\$r, \$R);`

Double-Click to Select ALL Code
• PLANETARY OBLATE SPHEROIDAL PARAMETERS (R, r)
```Known (R, r) Parameters of Planets in Kilometers and Miles
Computational Data Source: NASA

The equatorial and meridional circumferences were computed
from the given (R, r) parameters using the above function.

R ≥ r

Equat C = Equatorial Circumference
Diff  C = (Equat C) − (Polar C)
Polar C = Polar Circumference

__________________________________________________________
Earth               |
6378.1 , 6356.8 km  |  Equat C = 40074.8 km  = 24901.3 mi
R        r       |  Diff  C =  1326.0 km  =   824.0 mi
3963.2 , 3949.9 mi  |  Merid C = 40007.9 km  = 24859.8 mi
____________________|_____________________________________
The Moon (Luna)     |
1738.1 , 1736.0 km  |  Equat C = 10920.8 km  = 6785.8 mi
R        r       |  Diff  C =     6.6 km  =    4.0 mi
1080.0 , 1078.7 mi  |  Merid C = 10914.2 km  = 6781.8 mi
____________________|_____________________________________
Mars                |
3396.2 , 3376.2 km  |  Equat C = 21339.0 km  = 13259.4 mi
R        r       |  Diff  C =    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
R       r         |  Diff  C =  14449 km   =   8978 mi
44423 , 41541 mi    |  Merid C = 434749 km   = 270140 mi
____________________|_____________________________________
Saturn              |
60268 , 54364 km    |  Equat C = 378675 km   = 235298 mi
R      r         |  Diff  C =  18309 km   =  11377 mi
37449 , 33780 mi    |  Merid C = 360366 km   = 223921 mi
____________________|_____________________________________
Uranus              |
25559 , 24973 km    |  Equat C = 160592 km   = 99787 mi
R       r         |  Diff  C =   1836 km   =  1141 mi
15882 , 15518 mi    |  Merid C = 158756 km   = 98647 mi
____________________|_____________________________________
Neptune             |
24764 , 24341 km    |  Equat C = 155597 km   = 96683 mi
R       r         |  Diff  C =   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

A PHP Science Program by Jay Tanner - Revised: 2022 August 03 Wednesday at 10:42:32 PM GMT