Table of Contents

Orbital Mechanics

Gravitational and Rotational Assist

Sling Shots in Space

The image to the left is looking down on the Earth's North Pole. The Earth rotates eastward (counter-clockwise) in this view. The Earth also orbits the Sun in an eastward (counter-clockwise) direction as shown.

Since the Earth is a solid body which rotates on its axis once every twenty-four hours, everything on its surface rotates with it. An object on the Earth's equator must travel around in a circle 40 000 km in circumference each day. This means its speed is about 0.46km/s.

Closer to the poles the circumference of the circle an object must travel each day gets smaller. At the latitude of Winnipeg, for example, the rotation speed is only about 0.20km/s.

At the North Pole the rotational speed of an object on the Earth's surface is zero.

By launching satellites at very low latitudes, as close to the Equator as possible, one can capitalize on the rotational speed of the Earth to give the spacecraft a "boost" into orbit.

This results in a very considerable saving in rocket fuel and the related costs that the extra fuel would incur in added mass and expense.

Gravitational Assist - The Good Guys

It is possible to use the orbital motion of a planet to give a spacecraft a gravitational "boost".

The diagram to the left shows a spacecraft in a transfer ellipse from 1 to 2 along a trajectory labelled a.

If the orbit is well timed, the spacecraft approaches the planet 2 from slightly behind and begins to free-fall towards the planet, drawn by the planet's gravitational field.

The trajectory of the spacecraft is designed so that it is swung slightly around the planet and with its increased kinetic energy it is inserted into a large transfer ellipse towards an outer planet along the trajectory labelled b.

It is clear that precise and accurate timing is required for this manoeuvre to be successful.

Gravitational Assist - The Bad Guys

Changes in an object's kinetic energy due to the effects of gravitational assist can also be a very bad thing. Consider the computer simulation shown in the frame to the left.

It shows the effect of a wandering star converging on the inner solar system. In this simulation the Sun is taken to be at the focus of all orbital motion.

As the star is "captured" into an elliptical orbit around our Sun its gravitational effect causes the ejection of Mars and the Earth from the inner solar system.

The orbit of Mercury (red) is relatively unchanged.

Venus is captured into an orbit around the intruder star and in this simulation it eventually crashes into the Sun.

As with asteroid collisions, this would certainly be considered a close encounter of the worst kind.