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This post is a largely technical note that continues an exploration of the Ideal Rocket Equation in a perturbed Keplerian gravitational field. It is a continuation of an earlier post entitled "A Generalised Ideal Rocket Equation" in the Maths & Physics section of the Orbiter Forum. These notes...

The subject of this post is a generalisation of the well-known ideal rocket equation \Delta V = v_e\,\log\frac{m_i}{m_f} to a Keplerian gravitational field. The resulting equations of motion are relevant to the calculation of optimal launch trajectories (for bodies without atmospheres) and...

In Orbiter, to do anything useful, you need to know the future trajectory of your spacecraft so that you can ensure that you are 'on target'. Usually, the standard Orbiter MFDs of TransX and IMFD's Map program will give you the information that you want to achieve whatever you mission goal you...

This post presents another optimised trajectory for getting from Earth to Jupiter. The trajectory starts at Earth, drops to Venus, then back to Earth, then out to Mars, then back to Earth and finally a transfer out to Jupiter. The total cost of the transfer is 3,630 m/s from LEO to Jupiter...

This post is going to focus on the maths behind performing an Earth Gravity Assist (EGA) manoeuvre. It will finish by setting up a basic, general purpose EGA flight plan. The Earth Gravity Assist manoeuvre is designed to 'kick' a spacecraft from a low energy orbit around the Sun into a higher...

I haven't had much time form Orbiter of late, but I've been musing on how to make use of PyKEP / PyGMO output within Orbiter. PyKEP / PyGMO is a free mission planning tool from the European Space Agency. However, it knows nothing about Orbiter and produces optimal trajectory plans in ways...

As part of development of an Aldrin Cycler trajectory (see http://www.orbiter-forum.com/showthread.php?t=36763), I've cobbled together this simple 'challenge' to illustrate use of an Aldrin Cycler. The scenario is quite simple: The Aldrin Cycler (that looks suspiciously like the ISS) is...

This is just a quick note on the use of a PyKEP / PyGMO to the design of an optimal ballistic transfer from Earth to Mercury with one gravity assist at Venus thrown in as well. PyKEP / PyGMO PyKEP and PyGMO is a trajectory planning modelling suite built by the Advanced Concepts Team of the...

This is a post detailing the design of a low delta-V mission from Earth to Mercury. As many Orbiter users will know, Mercury is a challenging destination because of its orbital location deep inside the Sun's gravitational well. A direct Hohmann transfer from Earth to Venus requires an ejection...

Introduction This is the third in a series of posts aimed at providing tools with which to design transfer manoeuvres that minimise the delta-V requirements for: a. the 'Begin Game' problem - i.e., using gravity assists to boost the spacecraft's kinetic energy so as to reduce the overall...

Introduction This is the second in a series of three (or, possibly, four) posts aimed at providing the theoretical background for designing transfer manoeuvres that are relevant for the reduction of delta-V requirements for both: a. the 'Begin Game' problem - i.e., using gravity assists to...

The purpose of this post is to record a number of equations that are useful in designing transfer manoeuvres that are relevant for the reduction of delta-V requirements for both: a. the 'Begin Game' problem - i.e., using gravity assists to boost the spacecraft's kinetic energy so as to reduce...

Attached is a C code version of the GalSat (Galilean Satellite) routines. The GalSat routines are used by Orbiter 2010 to calculate the position of the Galilean moons - Io, Europa, Ganymede and Callisto. As part of the development of my own 'offline' numerical integrator, I have transcribed...

Introduction Standard Keplerian physics, in which objects orbit around bodies in perfect ellipses or hyperbolas, is the mainstay of Orbiter mission planning. Its utility rests on the assumption that a spacecraft is, for the most part, either close to a planet (in which case the gravity of that...

In this post, I present some general musing about Belbruno & Topputo's "Earth-Mars transfer with ballistic capture" paper. These musings are a consequence of thinking about how to achieve capture by any of the Galilean moons 'on the cheap' with as low a delta-v budget as possible. Much of this...

OK, here's a little challenge that people may find interesting: Using the following QuickSave scenario, take the Delta Glider that has just entered the Jovian SOI enroute from Earth (and which is low on fuel) and enter into a 20 x 20 km parking orbit around Callisto. This sounds simple - but...

For those that have watched David Courtney's Orbiter videos, you will undoubtedly seen his him debate whether or not to take advantage of the Oberth Effect in approaching the Galilean moons - Io, Europa, Ganymede and Callisto. His original premise was that the Oberth Effect was probably a 'good...

In an earlier post, I showed how to build a 2nd order symplectic integrator. To recap, we can think of the symplectic integrator as a small 'machine' that takes one set of 6 numbers \left\{Q_{x,0},Q_{y,0},Q_{z,0},P_{x,0},P_{y,0},P_{z,0}\right\} to a new set of six numbers...

In a recent post, 'meson800' asked: In response I offered to write up some more detailed notes on numerical integrators and how to build them. This post constitutes these notes. In these notes, I'm going to concentrate on symplectic integrators A second-order symplectic integrator First...

In an earlier post, I asked 'martins' a question: "On another issue: in an earlier comment relating to making public integrators you mentioned that "this would come in handy in various places, e.g. for mission planning tools, or for creating our own power series ephemeris solutions for...