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Table of Contents
Orbital Mechanics
Manoeuvring In Space
Using Rocket Engines to Change Orbit
Steering in Space
Manoeuvring a vehicle in space is unlike manoeuvring any other kind of vehicle.
Unlike cars, trucks, and bicycles, which can change direction by making contact with the ground, there is no ground in space.
Ships and boats react with the force of moving water over the rudder in order to change direction, and airplanes react to the forces which are caused by the air moving over their control surfaces in order to change direction.
In space there is absolutely nothing against which a spacecraft can react in order to manoeuvre.
Therefore all spacecraft must take something along with them with which they can react should they need to change direction or speed...
and that something is rocket fuel.
Interplanetary Baseball
Every manoeuvre in space is a bit like throwing a baseball. One "throws" rocket fuel in one direction, the spacecraft reacts by launching itself in the opposite direction.
The motion of the spacecraft is fully determined by gravitational forces acting on the spacecraft when the rocket burn is completed.
The only effect of a rocket burn is to change the orbital speed and/or direction of the spacecraft. When the burn is completed the path of the spacecraft is fully determined by gravitational forces acting on the spacecraft.
After the burn any changes in the speed or direction of the spacecraft are beyond the control of the crew. Gravity rules!
The Effect of a Rocket "Burn"
The diagrams below illustrate the initial and final orbital paths taken by a spacecraft which is initially in a circular orbit in the plane of the Earth's equator.
The diagrams are seen looking down on the Earth's North Pole. Scales are exaggerated for purposes of illustration.
The solid lines indicate the initial orbit path, the dashed lines indicate the final orbital configuration attained after the rocket burn indicated.
1. Forward Thrust
When the rocket engines are fired in a direction parallel to the orbital path, the increased energy at first accelerates the spacecraft forward. The laws of orbital mechanics cause the spacecraft to move upwards against the gravitational attraction of the Earth into an elliptical orbit.
To circularize the orbit into a larger orbit, a second rocket burn at the apogee would be needed.
Thrust which accelerates the spacecraft in the direction of its motion increases its orbital radius and results in the speed of the spacecraft becoming slower !
2. Retro (Reverse) Thrust
Firing the rocket engines in a direction parallel to the spacecraft's orbit, but in a direction opposite to its orbital motion causes the spacecraft to slow down and "fall" inwards under the gravitational attraction of the Earth.
The final orbit has a smaller radius than the initial orbit but the spacecraft is actually moving faster!
The apparent contradiction arises as a result of the spacecraft exchanging gravitational potential energy (as it "falls" to a lower orbit), for kinetic energy (causing its speed to increase).
3. Rotating the Orbital Plane
Thrust applied at an angle to the orbital direction has two effects.
The (vector) component of the thrust in the forward (or reverse) direction causes the size of the orbit to change.
The (vector) component of the thrust at right angles to the initial orbital direction causes the plane of the orbit to rotate to a new angle with respect to the initial orbital plane.
For example, in the illustration on the left, a thrust at right angles to the orbital plane would cause the circular orbit to rotate counter-clockwise (looking downwards in the plane of the page).
4. Rotating the Orbital Plane
Similarly, if we wish to rotate the plane of a circular orbit in the opposite sense, we apply a thrust at an angle to the plane of the circular orbit.
The important factor in keeping the same orbital radius (so that only the plane of the orbit changes), is to ensure that its orbital speed does not change. This requires a detailed knowledge of the initial velocity vector (Vi) and the required final velocity vector (Vf).
From these two quantities both the magnitude and the direction of the required velocity change can be calculated so that a circular orbit is maintained and only the orbital plane changes.
NOTE: Compared to changes in orbital radius, changes in the orbital plane require huge amounts of energy (and hence fuel).
5. Radial Thrust "Upwards"
An interesting case occurs involving thrust along a line parallel to the orbital radius.
As one might expect, applying an upward thrust causes the spacecraft to accelerate upwards to a higher orbit. This increases the gravitational potential energy of the spacecraft and it gradually loses its upward speed. At its maximum height it begins to fall back, with an accompanying increase in its kinetic energy, only this time the kinetic energy manifests itself in the forward direction.
The net effect is precisely the same as if the rocket engines had been fired in the forward direction.
6. Radial Thrust "Downwards"
An even more interesting case, (some might even say bizarre), occurs involving thrust along a line parallel to the orbital radius in a downwards direction.
As one might expect, applying a downward thrust causes the spacecraft to accelerate downwards to a lower orbit. This causes gravitational potential energy to be converted into kinetic energy, combined with the increased kinetic energy caused by the rocket thrust.
This large increase in kinetic energy manifests itself as a large velocity increase in the forward direction.
The net effect is precisely the same as if the rocket engines had been fired in the forward direction, causing the spacecraft to move upwards to a large orbit.
