translunar injection from a circular Earth park orbit

[cdeaglejr]

This HP Prime program can be used to estimate the delta-v required to reach the moon. The algorithm assumes the translunar injection occurs impulsively from a circular Earth orbit.

The user provides an initial departure calendar date according to

// departure calendar date

month := 9;

day := 1;

year := 2013;

The park orbit semimajor axis and orbital inclination are also required; for example

/////////////////////
// initial park orbit
/////////////////////

// semimajor axis (kilometers)

oev_po(1) := req + 185.32;

// orbital eccentricity (non-dimensional)

oev_po(2) := 0.0;

// orbital inclination (degrees)

oev_po(3) := 28.5 * dtr;

Finally, the software requires the user to define the transfer time from Earth to the moon in hours.

// time-of-flight in hours

tof_hours := 84.0;

The PDF document included with the zip archive explains the assumptions and algorithms used to solve this classic orbital transfer problem.

[Steve Simpkin]

While not directly related, this reminds me of a HP-25 program by Paul Lutus that "performs that calculations required to describe how an object (spacecraft) would move about in relation to two bodies (planets) of chosen sizes".

The program that Paul Lutus submitted to Popular Electronics magazine (Space Flight) really fired my imagination with what could be done with a programmable calculator. I had been saving for almost two years and was already planning to buying my HP-25 in June 1977 on my 16th birthday. This article in Popular Electronics (which came out in May) just added to the fever. After I bought my HP-25 I ended up playing with Paul's program for hours plotting the orbits around various sized planets.

https://www.hpmuseum.org/forum/thread-4710.html