Configure Object Wizards

Since there are three different types of objects, i.e. stars, planets, and observers, the configuration dialogs are slightly different for each of the objects types. The links on the left lead to the respective tutorials.

But before you go there you ought to familiarize yourself with the following concepts that are employed by Space Explorer 1.0

• The global coordinate system used for setting up solar systems
• The local coordinate system used by the observer
• The method used for configuring orbiting objects

Lets treat them one by one.

The user interfaces of Space Explorer 1.0 employ a particular form of spherical coordinates that are also widely used in astronomy. The location of an object is described by the distance the object has from the origin of the coordinate system R and the two angles

• Right Ascension (abbreviated RA) and
• Declination (abbreviated Dec)
  

RA measures rotation about the vertical y-axis while Dec takes account of rotation about a horizontal axis in the (x, z)-plane. Mapped onto the surface of earth, RA would correspond to longitude and Dec to latitude. RA is expressed in hours from 0 to 24h. Dec is measured in degrees from -90° (south) to 90° (north). The third coordinate R is, of course, measured in km. For more information on the astronomical aspects have a look at the links.

The following picture illustrates these relationships where the location of object P in space is given by the coordinates (RA_P, Dec_P, R_P). Also shown are the corresponding cartesian coordinates (x, y, z).

Click to enlarge

Space Explorer 1.0 uses two coordinate systems of this kind for different purposes. The relationship between those two systems is shown in the next figure. The figure shows RA (left) and Dec (right) for a system consisting of three objects (sun, earth, and ship). The global system (in black, coordinates with superscript cfg) is used for configuring a solar system. The local system (in red, coordinates with superscript obs) is used for the heads-up display of the observer. The observer object, called 'ship' in the figure, is always located at the origin of the local coordinate system.

Click to enlarge

In general, even though it is not necessary, the gravitational center of the system will be placed at the origin of the global coordinate system

       ( RA_Sun^cfg, Dec_Sun^cfg, R_Sun^cfg )   =   ( 0, 0, 0 )

Now that it is clear how the Space Explorer 1.0 setup coordinates work, we can go ahead and discuss the configuration of orbiting objects.

When setting up an orbiting object you need to specify two orbital positions: the first or initial position and the second position (see for example the dialog for configuring a planet). Using this information, Space Explorer 1.0 will calculate the velocity of the orbiting object as an initial value for the subsequent simulation such that a stable circular orbit is achieved.

The following picture illustrates this for a simple system consisting of a star, a planet, and a moon. The moon is supposed to orbit the planet. In the following it will be shown how this can be achieved.

Click to enlarge

The two positions determining the orbit must be expressed with respect to the global coordinate system. Any two positions that are not aligned which each other will do the job. However, the easiest choice is the one depicted in the figure where both positions are perpendicular to each other. When the displacement is selected as shown in the figure, the moon will orbit counter clockwise around the planet. In order to have it orbiting clockwise, both positions must be interchanged.

The superscript cfg is dropped because it is clear that from now on everything takes place in the global coordiante system. For simplicity, the declination of all objects is assumed to be zero, i.e.

       Dec_Star  =   Dec_Planet  =   Dec_Moon  =   0

Now all that remains to be done is to express the coordinates

       ( RA_Moon1, 0, R_Moon1 )   and   ( RA_Moon2, 0, R_Moon2 )

in terms of the known quantities

       ( RA_Planet, 0, R_Planet )   and   R_Orbit.

Provided that   R_Orbit  <<   R_Planet, this is what we get for a counter clockwise orbit as shown in the figure

       RA_Moon1  =   RA_Planet
       R_Moon1     =   R_Planet   +   R_Orbit

       RA_Moon2  =   RA_Planet   +   3.82 R_Orbit/R_Planet
       R_Moon2     =   R_Planet

For a clockwise orbit the equations become

       RA_Moon1  =   RA_Planet   -   3.82 R_Orbit/R_Planet
       R_Moon1     =   R_Planet

       RA_Moon2  =   RA_Planet
       R_Moon2     =   R_Planet   +   R_Orbit

Using these equations, it is straightforward to compute the coordinates needed to complete the first sheet of the 'configure object wizards' for orbiting objects, thus enabling Space Explorer 1.0 to calculate the velocity necessary for the orbiting object to assume a stable circular orbit.