Introduction to Satellite Orbits

Summary

This presentation was developed as a basic introduction to seven parameters, or elements, that define a satellite orbit. It focuses on each element in a simplified, understandable approach with little math and no physics background. For instance, only a geocentric (Earth centered) orbit is considered and gravity is not explained. Seven defining parameters of an orbit are applicable to any satellite orbiting around a single gravitational body. There are several other approaches and refinements to define an orbit but any study of orbits will reference these parameters.

Intro To Orbits Presentation

A set of charts are in both PowerPoint and pdf:

Orbit Intro (pptx) Orbit Intro (pdf)

Summary:

• Brief History of Tycho Brahe and Kepler and hist Astromica Nova
• Seven Orbital Parameters
• The Elllipse and its measurements
• Elliptical Satellite Motion and Orbital Planes
• Perigee and Apogee
• Geocenter Coordinate Reference
• Orbital Inclination
• Ascending Node
• Argument of Perigee
• True Anomaly and Epoch (Date/Time)
• All Seven Orbital Parameters

Physical Orbit Model

It is always helpful to see a physical model to understand new concepts. For an in-person class setting, the design of this model is detailed here for use by any instructor. There are five laser engraved pieces, two for the earth equator and three different orbits. All seven orbital parameters can be demonstrated by moving the engraved orbit plates.

Orbit Parameter Demonstration

There are three elliptical orbit plates for Semi-circular, mid-elliptical, and high-elliptical orbits. The semi-major axis and eccentricity are noted on the plates. The outside of the plates are the orbit of the satellite.

Parts List

Base Ring	{CorelDraw file}
Top Ring	{CorelDraw file}
Semi-circular Orbit	{CorelDraw file}
Mid-Elliptical Orbit	{CorelDraw file}
Elliptical Orbit	{CorelDraw file}
Transparent Circular Protractor	{PowerPoint file}
Earth Hemisphere	{3D Printed}
Post to mount Earth sphere	{3D STL file}
Satellite Clip	{3D STL file}
4 - 6"x1/2" square wood for legs
2 - 180mm x 1/4" Wood Dowels
#8 Flat head brass screws
#4 x 1" screw and nut
Overhead projector transparency sheet

Assembly

The main elliptical orbit plates are made with a laser engraver using 1/8" wood. Alternatives are using a 3D printer if the printing area is large enough. Use this as a guide for your creativity.

• Laser cut and engrave the four CorelDraw files on 1/8" wood
• Use adhesive to attach the bottom ring to the top ring
• Optionally coat the wood parts with a polyurethane
• Drill holes through the top plate and countersink the holes for the flat head screws
• Tap drill the legs and attach to the assembled rings with #8 flat head brass screws
• 3D print the Earth hemisphere, resizing to 20mm diameter (optional: paint or print blue)
• Drill vertical hole in Earth hemisphere for #4 screw
• Cut and sand dowel so that it jam fits the inner diameter of the top ring
• Drill clearance hole centered on dowel for #4 screw
• Drill clearance hole in orbit plates at center of Earth (at distance "c")
• Print transparent protractor, cut out circle, punch hole at center
• Attach orbit plates to dowel with #4 screws with transparent protractor behind circular orbit plate
• Optional: 3D print both halves of Earth hemispheres at 40mm diameter and mount on Earthstand
• Print 3D model of satellite to demonstrate location of satellite on orbit plane for true anomaly

Demonstration

Place the Earth globe, on its stand, in the center of the circular outer rings. Note that the ring aligns with the equator of the earth. All references to orbits with this demo will be considering the earth at the center and the longitude measured related to the earth's equator. The zero point on longitude is measured from the first point of Ares, marked on the ring.

Lay one of the orbital plates attached to the dowel on the model. These seven orbital parameters can be shown:

1. Semi-Major Axis (a)
2. and Eccentricity (e) engraved on the plate
3. Move the dowel horizontally to demonstrate Right Ascension of the Ascending Node (RAAN)
4. Rotate the dowel to show orbit Inclination (i)
5. Turn the orbit plates on dowel to show Argument of Perigee (AP) and measure with transparent protractor from RAAN
6. Pick a place on the orbit and measure True Anomaly (TA) with the transparent protractor. One of the orbit plates can be used by itself with the satellite clip to demonstrate this parameter.
7. Lastly check the time of observation for the Epoch (t)

Additional References:

• Wiki page on Orbital Elements
• JPL page with Orbits and Ephemerides where you can find elements for planets and numerous satellites
• For those who want to take this introduction and do some real rocket science, check out this free mission planning tool used by NASA:
  General Mission Analysis Tool (GMAT) - A space trajectory optimization and mission analysis tool. Also, there are GMAT tutorials from beginner to expert.
• There is also a fun way to learn about space flight. The Kerbal Space Program is a excellenet way to experiment with a spacecraft simulation.

This Orbit Model by Bruce Bream is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. You are free to Share and Adapt this model.
Permissions beyond the scope of this license may be available from tarrow@roadrunner.com