Barker’s Equation

Description

by Dr. D.G. Simpson, http://www.pgccphy.net/1030/software.html

Given the constant K = √(GM /2q3) /(t - Tp), this program solves Barker’s equation
tan(f/2) + 1/3·tan3(f/2) = √(GM/2q3)·(t - Tp)

to find the true anomaly f.
To run the program, enter the dimensionless number
K = √(GM/2q3)·(t - Tp)

as K f A

The program returns the anomaly f. The program will work in either Degrees or Radians mode.

Example:
Let K = 19.38 and set the calculator’s angle mode to degrees. Enter the above program, then type:

19.38 f A

The program returns f = 149:0847°.

Program Resources

Labels

Name Description
 A Barker's Equation

Storage Registers

Name Description
.0 Stores the inital value

Program

Line Display Key Sequence Line Display Key Sequence
000 017 14
001 42,21,11 f LBL A 018 36 ENTER
002 44 .0 STO . 0 019 36 ENTER
003 43 16 g ABS 020 20 ×
004 1 1 021 1 1
005 48 . 022 30
006 5 5 023 34 x↔y
007 20 × 024 10 ÷
008 36 ENTER 025 45 .0 RCL . 0
009 36 ENTER 026 36 ENTER
010 20 × 027 43 16 g ABS
011 1 1 028 10 ÷
012 40 + 029 20 ×
013 11 √x̅ 030 43 25 g TAN⁻¹
014 40 + 031 2 2
015 3 3 032 20 ×
016 15 1/x 033 43 32 g RTN