Table of Contents

Orbital Mechanics

Student Activity

Changing Orbital Inclination

Delta "v" problems are most easily solved by using simple scale drawings called vector diagrams.

1. Select an appropriate and convenient scale to represent the speed, such as 2cm = 1km/s

2. Lay out an "arrow" to represent the initial (old) velocity. The "arrow" points in the direction of the velocity.

3. Using a protractor and a ruler lay out a second arrow to indicate the final (new) velocity's direction and speed . Draw the new vector tail-to-tail with the initial velocity vector.

4. Draw in the delta "v" velocity (red in the diagram to the left). Using your speed scale and a protractor, measure this vector to compute the direction and speed change needed to achieve the new velocity.

1. Determine the delta "v" (change in velocity) required to accomplish the following orbital changes.

   • Change the orbital inclination from 51⁰ to zero 0⁰ in low Earth orbit where the orbital speed is 7.8km/s.

   • Change the orbital inclination from 51⁰ to zero 0⁰ in low geosyschronous orbit where the orbital speed is 3.2km/s.

     

     • Assuming no speed change, only a velocity change, the required "delta vee" is approximately 7.5 km/s at 116 degrees away from the current orbital direction.

     • Assuming no speed change, only a velocity change, the required "delta vee" is approximately 2.25 km/s at 116 degrees away from the current orbital direction.

2. Based on your calculations, is it better to change a satellite's orbital plane at it's apogee (highest point), or perigee (lowest point)?

   ANS: Orbital plane changes use the least amount of energy (fuel) at apogee (or apehelion for interplanetary probes).

3. Suppose an asteroid were discovered on a collision course with the Earth. If rockets could be used to nudge the asteroid into a new orbit by changing its orbital plane, when in its orbit would be the best time to try to affect this manoeuvre?

   ANS: The best place would be as far from the Sun as possible. The deeper into space the asteoid is, the less energy (and hence smaller "delta vee") is required to modify the direction of its orbit. This is why the early detection of potentially dangerous earth-impacting asteriods is very important.

4. Comets usually have high orbital inclinations with respect to the Earth's orbital plane. Astronomers would like to send a space probe to visit a comet. To do this they send the space probe as far as possible away from the Sun before applying the change in its orbital plane to match the orbital plane of the comet. Why?

   ANS: It's a matter of energy (and hence cost). The less rocket fuel one needs, the bigger the payload a spacecraft can carry. Changes in the orbital plane of a space probe use less energy the further from the Sun they are.

5. It is very difficult to send a space probe over the polar regions of the Sun, even at the Earth's distance. Why?

   ANS: The Earth is moving at approximately 35km/s in an orbital plane which is close to the equatorial plane of the Sun. The required change in the orbital inclination of a space probe (which is co-moving at 35 km/s with the Earth and in the same plane) by nearly 90o requires a gigantic ”delta vee“.