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 |
yˣ |
|
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 |
|