Category: Orbital Mechanics

Distant Retrograde Orbits

A “distant-retrograde orbit” (DRO) is a periodic orbit in the circular restricted three-body problem (CR3BP) that, in the rotating frame, looks like a large quasi-elliptical retrograde orbit around the secondary body. Moon-centered DRO’s in the Earth-Moon system were considered as a

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Earth-Mars Free Return

Let’s try using the Fortran Astrodynamics Toolkit and Pikaia to solve a real-world orbital mechanics problem. In this case, computing the optimal Earth-Mars free return trajectory in the year 2018. This is a trajectory that departs Earth, and then with

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IAU Rotation Models

The IAU Working Group on Cartographic Coordinates and Rotational Elements (WGCCRE) is the keeper of official models that describe the cartographic coordinates and rotational elements of planetary bodies (such as the Earth, satellites, minor planets, and comets).  Periodically, they release a report containing the coefficients

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The Standards of Fundamental Astronomy (SOFA) library is a very nice collection of routines that implement various IAU algorithms for fundamental astronomy computations. Versions are available in Fortran and C.  Unfortunately, the Fortran version is written to be of maximum use to astronomers who

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Speeding up SPICE

The SPICE Toolkit software is an excellent package of very well-written and well-documented routines for a variety of astrodynamics applications.  It is produced by NASA’s Navigation and Ancillary Information Facility (NAIF).  Versions are available for Fortran 77, C, IDL, and Matlab. To speed up

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Rocket Equation

The rocket equation describes the basic principles of a rocket in the absence of external forces.  Various forms of this equation relate the following fundamental parameters: engine thrust (), the engine specific impulse (), the engine exhaust velocity (), the initial mass

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Porkchop Plots

A porkchop plot is a data visualization tool used in interplanetary mission design which displays contours of various quantities as a function of departure and arrival date.  Example pork chop plots for 2016 Earth-Mars transfers are shown here.  The x-axis is the Earth departure

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Lambert’s Problem

Lambert’s problem is to solve for the orbit transfer that connects two position vectors in a given time of flight.  It is one of the basic problems of orbital mechanics, and was solved by Swiss mathematician Johann Heinrich Lambert. A standard

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Fortran Astrodynamics Toolkit

I’m starting a new project on GitHub: the Fortran Astrodynamics Toolkit. Hardly anyone is developing open source orbital mechanics software for modern Fortran, so the time has come. Most of the code from this blog will eventually find its way

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