Jan 082018

Program Demonstrates Orbital Mechanics – Requires CGA. | |||
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File Name | File Size | Zip Size | Zip Type |

ORBIT.COM | 29192 | 18097 | deflated |

ORBIT.DOC | 14060 | 4691 | deflated |

# Download File ORBMECH.ZIP Here

## Contents of the ORBIT.DOC file

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

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

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

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

mixed notation where only large numeric values above 1x10E6 and

very small numbers will be shown in scientific notation.

Option

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 thekey

to get a listing and select item #4 for the earth.

The program will now ask for a diameter, press thekey

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.

January 8, 2018
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