'Space' Award for Air Cadets: Investigation of orbital mechanics

The mathematics of orbits is well defined. To hold an object in orbit round another object a force is required that continuously redirects its direction of travel so that it follows the orbital path. In the case of satellites, asteroids, planets and stars the force that maintains orbital motion is gravity. A special case of orbital motion is that of a circular orbits (see Orbital Mechanics page below for more details).

When the orbit is elliptical rather than circular the calculations get a little less simple, so it is helpful to be able to call on a program that solves the equations, conserving energy and angular momentum, for the general case of 2 dimentional orbits. The software used here comes from the University of Colarado's Physics Education Technology group (PhET).

**Orbital investigation tasks**

*Objectives*

*See that gravity provides the necessary force to sustain circular motion at a specific combination of orbital velocity and radius**Perturb circular motion to produce elliptical orbits**Recognise the way orbital speed changes with radius for circular orbits*

*Watch the video tutorial first.*

**Explore**

1. Open the PheT Software and select the Earth-Moon system.

2. Check boxes for path, grid and (orbital) velocity.

3. Use the zoom in-out slider to increase the area you are observing on the page.

4. Start the simulation and check the lunar orbit period – close to 28 d, yes?

**Investigate gravity**

5.
Stop the motion – reset the Earth-Moon system.

See what will happen if you switch off gravity

a) before starting the simulation

b) after the simulation has started.

**Investigate the effect of orbital velocity**

6.
Stop the motion – reset the Earth-Moon system.

Drag the Moon out to 4 squares from the centre of the Earth

Does the initial velocity need to be larger or smaller to escape from orbit?

7. Find the initial velocity for executing a
circular orbit at this radius - you can increase or decrease the initial velocity by dragging the tip of the velocity vector - be sure to keep it directed tangetially if you want to set up a ciircular orbit.

* Now try the test.*

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