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Text File | 1986-02-17 | 13.7 KB | 274 lines

ORBITAL MECHANICS PROGRAM Version 1.0 2-16-86 By Don Thayer This program will calculate the major orbital parameters associated with two astronomical objects when one orbits around the other. When the program is first started, the GRAVITATIONAL PARAMETER (GP) will be requested. Whenever this parameter is required, you can either enter it directly or press the <CR> key to get a list of possible choices. Selections 1 through 11 are common solar system objects. Selection 12 lets you enter the parameter directly. With selection 13 you can combine any two of the choices from 1 to 11 and selection 14 will show the GPs for black holes. Once the GP is entered, you will be required to enter the object's diameter. Again you can either enter the diameter directly or press the <CR> key to get a listing. If you selected a GP for a black hole, the option 13 will select a diameter equivalent to the EVENT HORIZON diameter. Selecting option 13 when a black hole GP was not chosen will enter a very small value which will force any major astronomical object to simulate a black hole. After initially entering the GP and diameter a menu of input options will be displayed. Before the orbital parameters can be computed, you must select option <2>, <3>, <4>, <5> or <6> to enter final necessary information. Selecting option <2> from this menu will allow you to input the SEMIMAJOR AXIS and the ECCENTRICITY of the orbit. Both of these options can be either entered directly or from a list provided when the <CR> key is pressed in lieu of entering a number. NOTE: Only selections <1> and <2> will give you the option of selecting from a list. Selection numbers <3>, <4>, <5> and <6> will require direct input of the values. Option <7> when available, will give a range that can be used. Selecting option <3> will allow you to input the RADIUS at APOGEE and the RADIUS at PERIGEE. VELOCITY at APOGEE and PERIGEE are the orbital velocities and can be entered from option <4> on the main menu. The PERIOD of ROTATION in option <5> is the time in seconds required for the orbiting object to revolve around the main object. Selecting option <6> will allow you to define an orbit given your PRESENT RADIUS (or distance to the object), your VELOCITY and the ATTACK ANGLE. An angle of 90 degrees will define an orbit at a right angle to your velocity vector and the main object. Selecting an angle of "0" degrees may be disastrous to both you and the program as it will direct you straight at the main object. Choosing too high of a velocity may exceed the escape velocity and a warning will be shown at the bottom of the screen. No orbit can be computed if this happens. If the velocity is too small, your orbit will intersect the object. Option <7> will not be available until after an orbit has been calculated. This option allows you to enter the distance you are from the object (orbital radius) and show data relative to your position on the orbit. Option <X> will toggle between full scientific notation and mixed notation where only large numeric values above 1x10E6 and very small numbers will be shown in scientific notation. Option <Q> quits the program. ---------------------------------------- Once data has been entered by using options <2>, <3>, <4>, <5> or <6>, the orbital data will be displayed and you will be given a chance to print the data on a printer. Type a "Y" or "y" if you want a printout otherwise type "N" or "n" for no printout. A command line will appear at the bottom of the screen that will allow you change any of the input sets of data. You can enter options 1, 2, 3, 4, 5, 6, 7, 8, X, Q which are the same as those on main menu or you can select option "M" to display the main menu again. You can see a graphic representation of the orbit by selecting the "G" option if you have an IBM or equivalent graphics card. If you change the GP & diameter by selection option <1>, the new orbit data will be computed from the existing semimajor axis and eccentricity. When you select options <6> or <7> from either the command line or the main menu, data in addition to the normal orbital statistics will be shown on the screen. THE GRAPHIC SCREEN When you choose then graphic display your orbit will shown. If the eccentricity is near 1.0000, then the orbit will appear as a straight line and if the eccentricity was 0.000, a circle will be displayed as the orbit. Values in between will produce orbits of varying ellipses. A small cross will mark the center of the main object at the focal point of the orbital ellipse. If possible, the relative size of the main object will also be shown as a solid circle about the objects center. This will occur if the relative diameter of the object is more than four pixles across and if it is not greater than size of the screen. If a black hole was selected from the GP & diameter option, it will be shown as broken line orbit if its relative size can be shown on the screen. When options <6> or <7> are selected, the graphic screen will also show your relative position on the orbit in the form of a larger cross. ENTERING NUMBERS Sometimes when a number is entered, the data will be requested again or the computer will beep and display another question mark. When this happens, you have either entered an illegal string of characters such as 3q23 or the value you entered is not acceptable for the input such as trying to enter 0.00 for the semimajor axis. Many times the value you are to enter is very large or very small, for example: 200000000 (2 with eight zeros following it). This number can be entered as 2.0E8 or 2.0E+8 in scientific notation. Very small number such as 0.00000123 should be entered as 1.23E-6 in the scientific format. DEFINITIONS Gravitational Parameter: This is the gravitational attraction between two objects and is the result of the gravitation constant multiplied by the mass of the object and is measured in miles cubed per second squared. Diameter of Object: The diameter of the main object in miles. Event Horizon: The radius of a black hole at which the escape velocity is equal to the speed of light. This is measured in miles. Semimajor Axis: The greatest distance from the center of the orbital ellipse to the orbit and is measured in miles. Eccentricity: A measure of the out of roundness of the orbit. An eccentricity of "0" will produce a perfect circular orbit while a value of 0.9999 will produce a very flattened elliptical orbit. Radius at Apogee: The greatest distance between the orbiting object and the center of the main object as measured in miles. Radius at Perigee: The closest distance between the centers of two objects in miles. Velocity at Apogee: The orbital velocity in miles per second at the furthest distance between the two objects. Velocity at Perigee: The velocity at the nearest point between the objects in miles per second. Period of Rotation: The time in seconds for an object to complete one orbital revolution. Escape Velocity: The minimum velocity for which no orbit will exist at a given orbital position. Gravitational Force: The force in gee's exerted on the orbiting object by the main object. Note: This is also the centrifugal force induced by the orbiting object thus canceling the gravitational force and results in "free fall" if the orbiting object is a space vessel. Tidal Force: The force in gee's at one foot from the orbital path. In normal orbital mechanics this value is too small to bother with, however, if a space vessel should approach a black hole or neutron star, this can become very great. This is how a space vessel too close to such an object can be torn apart. SAMPLE PROBLEM Many objects have been placed in a stationary orbit around the earth in order for them to remain in one relative position above our planet. These satellites are in what is called an earth- synchronous orbit. Since the earth rotates about its axis every 24 hours, this means that a satellite must also make its orbital rotation in 24 hours. To determine a earth-synchronous orbit for a satellite, either start the program or if already started, select option <1> from the main menu. When asked for the Gravitational Parameter, press the <CR> key to get a listing and select item #4 for the earth. The program will now ask for a diameter, press the <CR> key again and select item #4 on that list. Now select option <5> to enter the period of rotation and eccentricity. When the program prompts you for the Period Of Rotation, enter 86400 (24 hrs * 3600 sec/hr). When asked for the eccentricity, enter a small value such as 0.01 since we want the satellite's orbit to nearly round. The program will now show you the orbital statistics for an earth-synchronous orbit. Answer the printout question appro- priately and if you have a graphics board select option "G" for a graphic display of the orbit. Once the data is back on the screen, try experimenting with different orbital parameters or select option <7> and see some of the other orbital data. Another Example: On October 4, 1957 the Soviet Union launched the first artificial satellite. It's orbit ranged between 584 miles and 143.5 miles. Add these values to the radius of the earth to get the approximate values of 4540 miles and 4100 miles respectively. Select the GP and Diameter for the earth if you haven't already done so and then select option <3>. Enter 4540 for the Radius at Apogee and then enter 4100 for the Radius at Perigee. ABOUT THIS PROGRAM The initial idea started out as a mere curiosity when I ran across some interesting equations on black holes. This led to more in-depth studying of orbital mechanics. The first program was written for a Hewlett-Packard 67 programable calculator. When more memory came available in form of an HP-41CV, the program was expanded. Boy, this was really great! A whole 3K of memory. Then came the PC with its free basic and later a compiler to speed things up a bit. This final(?) version has been written with Borland's Turbo Pascal with thanks to Michael Covington for his movable window procedure. The formulas used in this program are mostly basic orbital mechanics methods and cannot possible give exact results. Also in orbital systems, there are many massive objects that also influence the orbit. Our own solar system contains at least 10 major bodies all interacting with each other while this program only deals with the "two-body problem". Every precaution I can think of has been taken to keep this program on-line, however, when dealing with astronomical values, the figures themselves become astronomical and can cause floating point overflow which will abort the program. I wouldn't try determining the data for orbiting galaxies.