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Kepler

Build Status

A ruby gem for working with two-body Keplerian Orbits.

Installation

Release pending, but you can source it in your Gemfile from Github for now.

Gemfile

gem "kepler", github: "jordanstephens/kepler"

Usage

Defining an Orbit

The easiest way to define an orbit is with common orbital elements.

qzss = Kepler::Orbit.from_params({
  semimajor_axis: 42164, # km
  eccentricity: 0.075,
  inclination: 43, # deg
  right_ascension: 195, # deg
  argument_of_periapsis: 270 # deg
})

QZSS orbital parameters from Wikipedia.

You can also use more colloquial elements like perigee and apogee instead of semimajor_axis and eccentricity.

iss = Kepler::Orbit.from_params({
  apogee: 426.9, # km
  perigee: 416.2, # km
  inclination: 51.65, # deg
  right_ascension: 304.1, # deg
  argument_of_periapsis: 117.8 # deg
})

ISS orbital parameters from Wolfram Alpha.

Or you can use position (r) and velocity (v) vectors.

r = Vector[-6045, -3490, 2500]
v = Vector[-3.457, 6.618, 2.533]
orbit = Kepler::Orbit.new(r, v)

Orbital Attributes

Defining an orbit gives you access to the object's current position (r) and velocity (v) vectors along with many other attributes, including:

  • semimajor_axis
  • semilatus_rectum
  • apoapsis
  • periapsis
  • eccentricity
  • angular_momentum
  • radial_velocity
  • inclination
  • right_ascension
  • argument_of_periapsis
  • true_anomaly
  • period

Updating an Orbit After dt

Once you have an initial orbit defined, you can get updated position (r) and velocity (v) vectors after a period of time (in seconds) has passed.

iss.r # => Vector[4427.6294614883145, 662.2433879237291, 5103.355851378229]
iss.v # => Vector[-3.000020372892516, 6.843005359324254, 1.7091866273043546]

# Update vectors after 45 minutes have passed
iss.update!(60 * 45)

iss.r # => Vector[-4662.9620885090435, -88.56494596532605, -4943.141439770972]
iss.v # => Vector[2.5073027532818064, -6.876096362825007, -2.248327189819066]

Caveats

  • Only point objects are considered in a two-body environment.
  • Perturbations due to atmospheric drag, solar radiation, etc are not considered.
  • Nodal precession is not considered.
  • Ruby 2.1.3 or greater is required because of a bug in STL Vector#cross_product which was present before that release.

Specs

Specs can be run with

$ rspec spec

Most of the specs contain values used in examples found in Orbital Mechanics for Engineering Students.