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Some Basic Concepts about Orbits

This page shows how an orbit works in general, defines two important terms, apoapsis and periapsis, and then explains how apoapsis and periapsis altitudes can be changed. These concepts are basic for understanding how Cosmos-1 will operate as a solar sailing spacecraft. Text and images are adapted from the Basics of Space Flight, courtesy NASA/JPL.

How Orbits Work

These drawings simplify the physics of orbital mechanics, making it easy to grasp the basic concepts. We see Earth with a huge, ridiculously tall mountain rising from it. The mountain, as Isaac Newton first described, has a cannon at its summit.

1. When the cannon is fired, the cannonball follows its ballistic arc, falling as a result of Earth's gravity, and of course it hits Earth some distance away from the mountain.

2. If we put more gunpowder in the cannon, the next time it's fired, the cannonball goes faster and farther away from the mountain, meanwhile falling to Earth at the same rate as it did before. The result is that it has gone halfway around the cartoon planet before it hits the ground.

In order to make their point these cartoons ignore lots of facts, of course, such as the impossibility of there being such a high mountain on Earth, the drag exerted by the Earth's atmosphere on the cannonball, and the power cannons can achieve... not to mention how hard it would be for the mountain climbers to carry a heavy cannon, and all that gunpowder, up such a high mountain! Nevertheless the orbital mechanics they illustrate (in the absence of details like atmosphere) are valid.

3. Packing still MORE gunpowder into the capable cannon, the cannonball goes much faster, and so much farther that it just never has a chance to touch down. All the while it would be falling to Earth at the same rate as it did in the previous cartoons. This time it falls completely around Earth! We can say it has achieved orbit.




That cannonball would skim past the south pole, and climb right back up to the same altitude from which it was fired, just like the cartoon shows. Its orbit is an ellipse.

This is basically how a spacecraft achieves orbit. It gets an initial boost from a rocket, and then simply falls for the rest of its orbital life. Modern spacecraft are more capable than cannonballs, and they have rocket thrusters that permit the occasional adjustment in its orbit, as described below. But it's usually just falling. Later, we'll see how solar sails change this picture slightly.

Periapsis and Apoapsis

In the third cartoon, you'll see that part of the orbit comes closer to Earth's surface that the rest of it does. This is called the periapsis of the orbit. The mountain represents the highest point in the orbit. That's called the apoapsis. The altitude affects the time an orbit takes, called the orbit period. The period of the space shuttle's orbit, at say 200 kilometers, is about 90 minutes.

The Key to Space Flight

Basically all of space flight involves the following concept, whether orbiting a planet or travelling among them.

As you watch the third cartoon's animation, imagine that the cannon has been packed with still more gunpowder, sending the cannonball out a little faster. With this extra energy, the cannonball would miss Earth's surface at periapsis by a greater margin, right?

Right. By applying more energy at apoapsis, you have raised the periapsis altitude.

A spacecraft's periapsis altitude can be raised by increasing the spacecraft's energy at apoapsis. This can be accomplished by firing on-board rocket thrusters when at apoapsis.

And of course, as seen in these cartoons, the opposite is true: if you decrease energy when you're at apoapsis, you'll lower the periapsis altitude. In the cartoon, that's less gunpowder, where the middle graphic shows periapsis low enough to impact the surface.

(JPL's Basics of Space Flight goes on to show how these keys enable flight from one planet to another.)

Now suppose you increase speed when you're at periapsis, by firing an onboard rocket. What would happen to the cannonball in the third cartoon?

Just as you suspect, it will cause the apoapsis altitude to increase. The cannonball would climb to a higher altitude and clear that annoying mountain at apoapsis.

A spacecraft's apoapsis altitude can be raised by increasing the spacecraft's energy at periapsis. This can be accomplished by firing on-board rocket thrusters when at periapsis.

And its opposite is true, too: decreasing energy at periapsis will lower the apoapsis altitude. Imagine the cannonball skimming through the tops of some trees as it flys through periapsis. This slowing effect would rob energy from the cannonball, and it could not continue to climb to quite as high an apoapsis altitude as before.

Orbiting a Real Planet

Isaac Newton's cannonball is really a pretty good analogy. It makes it clear that to get a spacecraft into orbit, you need to raise it up and accelerate it until it is going so fast that as it falls, it falls completely around the planet.

In practical terms, you don't generally want to be less than about 150 kilometers above surface of Earth. At that altitude, the atmosphere is so thin that it doesn't present much frictional drag to slow you down. You need your rocket to speed the spacecraft to the neighborhood of 30,000 km/hr (about 19,000 mph). Once you've done that, your spacecraft will continue falling around Earth. No more propulsion is necessary, except for occasional minor adjustments. It can remain in orbit for months or years before the presence of the thin upper atmosphere causes the orbit to degrade. These same mechanical concepts (but different numbers for altitude and speed) apply whether you're talking about orbiting Earth, Venus, Mars, the Moon, the sun, or anything. Saturnian orbit

A Periapsis by Any Other Name...

Periapsis and apoapsis are generic terms. The prefixes "peri-" and "ap-" are commonly applied to the Greek or Roman names of the bodies which are being orbited. For example, look for perigee and apogee at Earth, perijove and apojove at Jupiter, periselene and apselene or perilune and apolune in lunar orbit, perichron and apochron if you're orbiting Saturn, and perihelion and aphelion if you're orbiting the sun, and so on.

Finally: the Solar Sail!

Instead of just applying a burst of energy at one point in an orbit, a solar-sailing spacecraft benefits from long periods of "thrust" from the Sun. You'll read more on this topic later on this site. But before we get there, let's see how the Sun provides "thrust" to the solar sails:

On to the Next Topic...


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