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Orbital Mechanics

 

Lesson Objectives

In this tutorial you will learn the basics of orbital mechanics. A brief review of Keplerian orbits will be give as well as Classical Orbital Elements. These form the bases of orbital mechanics, this tutorial is not meant to be a compressive guide but is merely an introduction to the topic. There are several good books that can be check out at your local library for an in-depth discourse on the subject. This introduction will be tied into how to interpret the navigation systems on the Delta Glider and how to use this information along with the associated performance charts to plan your own space flight. It is also suggested that you read and thoroughly understand the information in the Orbiter Space Flight Simulator Manual.

  1. Introduction

  2. Circular Orbits

  3. Elliptical Orbits

  4. Hyperbolic Orbits

  5. Classic Orbital Elements

  6. Displaying Orbital Maps on the Multifunction Displays (MFDs)

Section 1: Introduction

There are essential three types of Keplerian Orbits: Circular, Elliptical, and Hyperbolic orbits. These orbits are the fundamental flight paths that a space craft will follow. They will be applied to launching from a planet surface, orbiting, and interplanetary travel.

Section 2: Circular Orbits

A Circular Orbit, Figure2, is one in which a space craft follows a near perfectly circular path around a planet. It is the ideal path of an orbit that would be follow by a spacecraft. In realty most orbits are not perfect circles there is always some eccentricity in the orbit. Eccentricity tell us how out-of-round, or non-circular,  a particular orbit is.  Circular orbits have an eccentricity equal to zero. The velocity of a space craft as it travels around a circular path will be constant. This is not true for elliptical, and hyperbolic orbits the velocity of the space craft for these orbits will change depending on its position in the orbit. It is recommended that when you first start to launch into orbit, de-orbit, or interplanetary trajectory to start with or end with a near circular orbit. Elliptical and hyperbolic orbits are used when transitioning from one circular orbit to another circular orbit, or when leaving the gravitational influence of a central body.

Figure2 Circular Orbit

 

 

Section 3: Elliptical Orbits

Elliptical Orbits are the most common type of orbit that a space craft will follow when transferring from one circular orbit to another. Figure 3 show what a typical elliptical orbit will look like.  Elliptical orbits will always have an eccentric that is greater then zero and less then  one. Several parameters are used to define an elliptical orbit.

Figure 3 Elliptical Orbit

  1. a, semi-major axis

  2. b, semi-minor axis

  3. c, distance from geometric center to focus F, or F'

  4. F, primary focus (this is the geometric center of a planetary body about which  satellite will orbit)

  5. F', secondary focus

  6. Apogee, this is maximum distance a spacecraft will have from focus or when it will be at it's highest altitude relative to a planets surface

  7. Perigee, this is the minimum distance  a spacecraft will  be from the primary focus or when it will be at it's lowest altitude relative to a planets surface

  8. ra, apoapsis distance from focus

  9. rp, perigee distance from focus

  10. r, radial distance from focus

Section 4: Hyperbolic Orbits

Hyperbolic orbits, Figure 4, are ones in which the space craft has enough kinetic energy to leave the gravitational influence of a particular planet. These are typically comets or asteroids that may enter or leave our solar system with out ever getting capture into a closed orbit. Hyperbolic orbits are used to gravitational assist a space craft orbits to a higher velocity allowing it to escape the solar system.

Figure 4 Hyperbolic Orbit

  1. a, semi-major axis

  2. F, primary focus (this is the geometric center of a planetary body about which  satellite will orbit)

  3. rp, perigee distance from focus

  4. r, radial distance from focus

Section 5: Classical Orbital Elements

 Six independent quantities called "orbital elements" are used to describe the position of a satellite around a planetary body. These orbital elements completely describe the size, shape, orientation and position of a satellite in a particular orbit. Figure 5 shows an orbit around a planetary body each of these elements are labeled.

Figure 5 Classical Orbital Elements

  1. a, semi-major axis

  2. e, eccentricity

  3. i, inclination

  4. Ω, right ascension of the ascending node

  5. ω, argument of perigee

  6. M, mean anomaly

Section 6: Displaying Orbital Maps on the Multifunction Displays (MFDs)

It is important to understand the orbital elements mention above because they tell you what your position is in an orbit. These orbital elements are graphically and textual depicted on the MFDs displays, Figure 6.1, and 6.2. Study the pictures and thoroughly familiarize your self with their representations, and abbreviations.

Figure 6.1 MFD Orbital Depiction1

Figure 6.2  MFD Numerical Depiction2

 

Orbital Element

Symbol

Abbreviation on MFDs

Semi-major Axis a SMa
Semi-minor Axis b SMi
Periapsis Distance rp PeR
Apoapsis Distance ra ApR
Radial Distance r Rad
Eccentricity e Ecc
Orbital Period T T
Time to Periapsis Passage   PeT
Time to Apoapsis Passage   ApT
Velocity v Vel
Inclination i Inc
Longitude of Ascending Node Ω LAN
Longitude of Periapsis   LPe
Argument of Periapsis ω AgP
True Anomaly   TrA
True Longitude   TrL
Mean Anomaly M MnA
Mean Longitude   MnL

Citations:

Pictures:

1-Orbiter Space Flight Simulator, 2006 Edition User Manual, Martin Schweiger, pg 54

2-Orbiter Space Flight Simulator, 2006 Edition User Manual, Martin Schweiger, pg 54

 

 

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Last modified: 02/07/11