'Standard Orbit, Mr Sulu'

It's a pretty good bet that you've seen the Enterprise orbiting a planet in the Star Trek standard orbit. Of course, we can only really speculate why such an orbit was standard in Star Trek. Perhaps it's a good orbit for scanning planets, or avoiding being attacked by things on the surface. What we can be sure of is that Captain Kirk's standard orbit isn't actually a very good orbit from a navigation point of view. It's circular, but it's neither close to the planet nor far away. It's actually not the best orbit for doing anything.

So what are the standard orbits for Orbiter? I'd say there were five standards. Why five? The reason is that different orbits are good for different things. Things that are easy in one orbit can be incredibly expensive in fuel in another. So doing the right thing in the right orbit can make the all the difference.

The Low Orbit

When you take off from any planet, including Earth, the first stable orbit you will (hopefully) come to is a low circular orbit - rather like the one on the right. Unlike Captain Kirk's standard orbit, this orbit is actually the best orbit for some things.

For a start, it's the lowest energy stable orbit. Gravitational energy, by convention, is negative. Even with all the kinetic energy tied up in the high speed movement of your craft, your overall energy is still very negative.

Low Earth orbit is sometimes described as being 'halfway to anywhere'. The reason is that in Low Earth orbit, your overall energy is about half as negative as it is sitting on the surface. Add the same energy again, and you reach escape velocity.

Understanding energy is a big part of good navigation in Orbiter. Here are three principles to remember

Kinetic energy is proportional to velocity squared.

At 14 kilometres per second, you have FOUR TIMES as much kinetic energy as you do at 7. If you double the energy of a low orbit, you will escape from the planet. This therefore happens at sqrt(2) x the speed in low Earth orbit.

Increase in energy per second = thrust x velocity

The faster you are going, the more energy you can gain by opening the throttle.

Overall energy in any orbit is a constant

Your gravitational energy and your kinetic energy equal a constant in any orbit. The closer you get to a planet in a given orbit, the lower your gravitational energy, and the more of your energy will show up as velocity - you will move faster.

It is these principles that lead to the standard orbits, and their advantages.

Advantages of a low orbit

So what are the advantages of a low circular orbit?

• It has the lowest energy of any stable orbit. This means it's the first stopping-off point after taking off.
• It's an orbit from which you can efficiently gain further orbital energy. There's a general principle at work here. You gain energy from thrust most efficiently when you're moving fast, because energy increase = thrust x velocity . And you're moving fast because you are close to the planet, and as much as possible of your orbital energy is in the form of velocity
• You can choose to launch into almost any orbital orientation you want from the surface. Although launching is expensive, the orientation of the orbit comes at a very low additional energy cost
• You can transition easily to an ellipse with the semi-major axis on any point of the orbit. The semi-major axis of an ellipse is the long axis. Just by applying thrust prograde at any point, you instantly get an ellipse with a semi-major axis right there.

Disadvantages of a low orbit

• It's expensive to change the orbital plane. Even small changes are expensive. Large ones are prohibitively profligate of fuel and energy - consider a highly elliptical orbit instead

The Highly Elliptical Orbit

This orbit has its Periapsis low - just as low as the low orbit. But the Apoapsis is high - a long way above the planet. For Earth, I often use an orbit with a period of a few days.

Advantages of the highly elliptical orbit

• It's still efficient if you want to gain further orbital energy. You can do this by thrusting at Periapsis, when you are travelling fast. On Earth, you can easily reach 10k per second at the low part of the orbit.
• The BIG advantage of this orbit is that it overcomes the fault of the low orbit. It can be cheap to change the orbital plane. You do this by adjusting the orbit when you are far away from the planet. It's most efficient at Apoapsis, but it's reasonably efficient at any point on the orbit that's a half-decent distance from the planet.
• If the planet below has an atmosphere, you can cheaply get back to a circular orbit again by lowering Periapsis slightly into the atmosphere below. Aerobraking will then lower apoapsis on every orbit.
• It's easy to raise and lower Periasis if you want to, by thrusting at Apoapsis.

Disadvantages of the highly elliptical orbit

• It can be difficult to change the orientation of the semi-major axis. Small changes aren't too bad, but large changes are best made by transitioning to a high circular orbit. It's best to ensure that the semi-major axis is in the right place in the first instance when creating the orbit.

The low hyerbolic orbit

This orbit still has a low Periapsis - just as low as the low orbit. But now there IS no Apoapsis.

Advantages of the low hyperbolic orbit

• When you're still some distance from the planet, it's cheap to change the orbital plane in all the same sorts of ways as you can with a highly elliptical orbit
• Because it goes low, the craft moves fast relative to the planet. And because it goes fast, it's efficient to either add or remove orbital energy at Periapsis.
• You get quite a lot of speed at infinity for almost no extra thrust at Periapsis. Let's take Earth as an example. The table shows that what you get - it's as close to getting something for nothing as you're ever likely to see, and its a classic example of the importance of understanding how kinetic energy works

• This effect is most intense when Periapsis is as low as possible. It can equally be employed in reverse. If you are approaching a planet at speed, the most efficient way to stop is to dive close to the planet before applying full reverse thrust at Periapsis.
• In the same way as with the highly elliptical orbit, it's not too hard to change the plane of your orbit when at a large distance from the central planet.
• The bigger and heavier the planet, the higher the speed at periapsis, and the more powerful this effect becomes.

Disadvantages of the low hyperbolic orbit

• Just as with the highly elliptical orbit, it's difficult to change the semimajor axis cheaply.
• As it's hyperbolic, you only get one chance to get it right!

The high circular orbit

This orbit is a circle a long way above the planet. In fact, the further the better, as long as the orbit is stable. Overall, this is the least useful of the standard orbits

Advantages of the high circular orbit

• The main advantage is total flexibility. Changing the orbital plane is reasonably cheap, because your craft is moving pretty slowly. But its best use is in moving between two highly elliptical orbits, when there's a need to change the semimajor axis.

Disadvantages of the high circular orbit

• One disadvantage is that, in many cases, it still isn't that cheap to get into a high circular orbit from a highly elliptical one. In order to make it cheap, it needs to be VERY high.
• The main disadvantage is that it can take AGES to get anywhere. Your craft moves slowly, and the orbit is large. Expect to use some significant time acceleration

The Hohmann transfer orbit

This orbit is an ellipse just touching the two orbits of two planets. This is what you tend to create with the transfer MFD to go from Earth to Mars. It's the most efficient way to go between most sets of orbits. An orbit which is very close to a Hohmann transfer is shown in yellow between the two green planetary orbits.

Advantage of the Hohmann transfer orbit

• The main advantage of this orbit is that minimises the acceleration required at both ends of the orbit to match speed with the target object. It's worthwhile getting a slight overlap with the target orbit just to make sure that you DO get there. But large overlaps can be bad news - particularly in the inner solar system. You can end up encountering the target planet at very high speeds.

Disadvantage of the Hohmann transfer

• It's slow. Sometimes this doesn't matter decisively when compared to the advantage above. But when going to Neptune, it's just too slow. A Hohmann transfer to Saturn takes around four years.
• For the pure Hohmann transfer, it's often impossible to align the orbital planes using the cheap speed you can gain leaving a planet with a low hyperbolic orbit. This can be addressed by using a shorter and more eccentric transfer. For more on this method of flying, see my second Mars tutorial.