Glom

2003-Feb-24, 07:08 PM

Been reading Fundamentals of Astrodynamics by R R Bate, D D Muellar and J E White.

I finally managed to work through the section on the prediction problem. I even managed to write a program on my graphics calculator that would do the job. I tested it on the EXAMPLE PROBLEM on page 210 and got more or less the right answer (they said they were using slide rules whereas I was using a modern graphics calculator that can operate up to fifteen decimal places so I don't mind being a few tenths of a percent off from their answer).

I had a problem with Exercise 4.5 on page 223.

A radar ship at 150° W on the equator picks up an object directly overhead. Returns indicate a position and velocity of:

r<sub>0</sub> = 1.2I DU

v<sub>0</sub> = .1I + J DU TU<sup>-1</sup>

Four hours later another ship at 120° W on the equator spots the same object directly overhead. Find the values of f, g, f(dot) and g(dot) that could be used to calculate position and velocity at the second sighting.

(Partial Ans. f(dot) = -.625)

Just for reference, f, g, f(dot) and g(dot) are scalars that satisfy the equns:

r = fr<sub>0</sub> + gv<sub>0</sub>

v = f(dot)r<sub>0</sub> + g(dot)v<sub>0</sub>

In the book, we derived equations for f, g, f(dot) and g(dot) in terms of the universal variable x. x must be obtained by use in the Newton iteration. The problem is that when I entered all the data into my program the iteration refused to converge. I checked it manually and the values just seemed to rise at pretty much a constant rate.

There is also the issue of the coordinates of the observing ships. They seem a bit like a red herring because for this method all you need is r<sub>0</sub>, v<sub>0</sub> and t.

Has anyone, who's read the book, tried and succeeded at this question?

I finally managed to work through the section on the prediction problem. I even managed to write a program on my graphics calculator that would do the job. I tested it on the EXAMPLE PROBLEM on page 210 and got more or less the right answer (they said they were using slide rules whereas I was using a modern graphics calculator that can operate up to fifteen decimal places so I don't mind being a few tenths of a percent off from their answer).

I had a problem with Exercise 4.5 on page 223.

A radar ship at 150° W on the equator picks up an object directly overhead. Returns indicate a position and velocity of:

r<sub>0</sub> = 1.2I DU

v<sub>0</sub> = .1I + J DU TU<sup>-1</sup>

Four hours later another ship at 120° W on the equator spots the same object directly overhead. Find the values of f, g, f(dot) and g(dot) that could be used to calculate position and velocity at the second sighting.

(Partial Ans. f(dot) = -.625)

Just for reference, f, g, f(dot) and g(dot) are scalars that satisfy the equns:

r = fr<sub>0</sub> + gv<sub>0</sub>

v = f(dot)r<sub>0</sub> + g(dot)v<sub>0</sub>

In the book, we derived equations for f, g, f(dot) and g(dot) in terms of the universal variable x. x must be obtained by use in the Newton iteration. The problem is that when I entered all the data into my program the iteration refused to converge. I checked it manually and the values just seemed to rise at pretty much a constant rate.

There is also the issue of the coordinates of the observing ships. They seem a bit like a red herring because for this method all you need is r<sub>0</sub>, v<sub>0</sub> and t.

Has anyone, who's read the book, tried and succeeded at this question?