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.
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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.
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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.
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:
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