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## Orbit Averaged Integrator

(OAI) Help File

## General Information

HELP. Displays this help screen. To exit, click one of the Exit Help buttons located at the
top and bottom of this screen.
PLANET. Selects the planet that your satellite will orbit. This
option sets the correct mass, spin rate, equatorial bulge, planet-Sun
distance, and additional data appropriate for the planet you select.

## Integration Parameters

ACCURACY. This number specifies the accuracy of the
integration. More accurate integrations take longer and are more prone
to run into numerical problems. Accordingly, you want the lowest
number which gives an accurate plot. Experiment by following the same
orbit at different accuracies and seeing if the output plots are
similar.
INTEGRATION TIME. Here you specify how many years into the future
the orbit should be followed. Be careful in choosing this parameter as
it is directly correlated to how long you will wait before seeing a
plot! A good strategy is to try a short integration time first to get
an idea of how fast the program is.
FREQUENCY. This number determines how often a point along the
orbit is saved to disk. A larger number yields a more accurately drawn
orbit at the expense of plotting time and disk space. You want to
choose the largest number that yields a reasonably accurate
orbit. Experiment!
INTEGRATION LIMITS. These upper and lower limits on the
planet-satellite distance allow you to stop the integration once the
satellite has wandered into an uninteresting regime. Less than 1.0
planetary radii corresponds to a collision, while greater than several
hundred to several thousand radii correspond to a satellite which
escapes the planet.

## Forces and Effects to Include

SOLAR GRAVITY. Choose to either include, approximate, or exclude
the Sun's gravity. Here, as in all selections in this section,
including an effect increases the run time of the simulation.
PLANETARY SHAPE. A planet's shape determines its gravity
field. Here you choose whether to approximate the planet by a sphere
or by an oblate ellipsoid (a slightly squashed sphere) which is closer
to reality.
PLANET'S TILT. Here you set the tilt of the planet's spin axis to
be zero or its actual value. This option is only important if solar
gravity is included in the simulation.
SHAPE OF PLANET'S ORBIT. Use a planet's true orbital shape or
approximate it by a circular orbit? This option affects the strength
of solar gravity and hence is only important if solar gravity is included.
SEASON. This number determines how the planet's spin axis is initially
oriented. A value of 90 means that the spin axis is pointed as close to
the Sun as possible (summer in the northern hemisphere).
This value is only important if the planet's spin axis is tilted.
TRUE ANOMALY. This parameter specifies the angle between
pericenter (the place along the planet's orbit where the planet-Sun
distance is smallest) and the starting position of the planet along
its orbit. Valid range is 0 to 360 degrees. This value is only
important if the planet is on an eccentric orbit.

## Initial Conditions

INITIAL POSITION. The initial position needs to be specified in
spherical coordinates where r is length of the radius vector, θ is
the angle between the z-axis and the radius vector, and φ is
measured from the x-axis to the projection of the radius vector into
the xy plane (see figure). Valid Ranges: r > 0, 0 ≤ &theta ≤ 180 degrees,
-180 ≤ φ ≤ 360 degrees.
INITIAL VELOCITY. The initial velocity is specified in a local
coordinate system based on the particle's position. The velocities
v_{r}, v_{θ}, and v_{φ} are in the
directions that would cause r, θ, and φ to increase (see
figure). Since the velocities are normalized to the circular velocity,
when the total speed is 1.0, the satellite starts on an initially
circular orbit around the planet. The total velocity squared is the
sum of the squares of the three velocity components.

SUBMIT FORM. Send the parameters that you have chosen to the
orbital integration program!
LOAD DEFAULTS. Set all parameters back to their default values.

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