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## Planetary Satellite Integrator

(PSI) 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, theta is
the angle between the z-axis and the radius vector, and phi is
measured from the x-axis to the projection of the radius vector into
the xy plane (see figure). Valid Ranges: r (must be positive), theta
(0-180 degrees), phi (0-360 degrees).
INITIAL VELOCITY. The initial velocity is specified in a local
coordinate system based on the particle's position. The velocities vr,
vtheta, and vphi are in the directions that would cause r, theta, and
phi 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. Reset form entries to their default values.

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