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PostPosted: Sun Nov 24, 2013 4:01 pm 
Broken Crown Panelist
Broken Crown Panelist

Joined: Wed Oct 17, 2012 1:47 pm
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Although the US Space Shuttle is no longer active, most people have a vivid recollection of what it takes to get off of Earth’s surface and out into space. Just as a reminder, this is what it takes to get humans off of Earth:

Image

The largest component, the large red object in the middle attached to the orbiter (the orbiter looks like a plane) is the external tank, containing liquid oxygen and liquid hydrogen, which were used to feed the engines. Filled and ready for takeoff, this tank could weigh about 1.7 million pounds. The two smaller white structures abutting the external tank are the solid rocket boosters. They provide the thrust to lift the shuttle off the launch pad and up to an altitude of about 150,000 feet. Each of the boosters weighs about 1.3 million pounds.

The reason why so much fuel and power is required the launch a shuttle into space is because of Earth’s gravity. Newton’s law of gravitation tells us that two factors are involved in how strongly gravity interacts with an object on a planet’s surface. The key measurement of how hard it is to escape a planet is its escape velocity.

The way to think of escape velocity is to think about what happens if you throw a baseball up. If you throw it straight up, it graduall slows down, stopping instantaneously at the height of its trajectory, and than falls back to Earth. When it gets back to you, it will be travelling at the same speed as when it left your hand, just downwards instead of upwards (this is true in principle if you neglect the effects of air resistance). Below is an illustration of the trajectory of several objects, thrown in the same direction, but at different speeds.

Image

Escape velocity is the speed at which, if you are throw an object straight up, Earth’s gravity is not strong enough to bring it back. The escape velocity on Earth is about 7 miles per second or 25,000 miles per hour! That’s how fast a shuttle has to get to escape Earth’s gravity and make it to outer space. The main factors are:

Mass of the Planet or Body: The more massive an planet, satellite, or other object is, the harder it is to escape its gravity at the surface and get into outer space. It turns out that escape velocity is related to the square root of the velocity needed to escape. So, on a body the same size as Earth, but 4 times as massive, an object would need an escape velocity double that of Earth, or about 50,000 miles per hour!

Size of the Planet: If there are two planets of the same mass, but they are different sizes, it will be harder to escape off of the smaller planet because its gravity is stronger at the surface. This is because an object sitting at the surface of the smaller body is closer to all the mass composing the body, making its gravitational tug stronger. For a body four times the size of another body with the same mass, the escape velocity will only be half as much!

Earth about 13,000,000,000,000,000,000,000,000 (13 septillion!) pounds. It is basically a sphere with a radius of about 4,000 miles from the center of its core to the surface. Titan weighs about 300,000,000,000,000,000,000,000 (300 sextillion) pounds, about one 40th of Earht’s weight. Tian also has a radius of about 1,600 miles, or about 40% that of Earth. This makes the escape velocity of Titan about 1.6 miles per second, that is, a seventh of what is it is on Earth.

Once you’re on Titan, it’s much easier to get off than on Earth. To see a table of escape velocities for some of the more important bodies in the solar system, see the table here: http://en.wikipedia.org/wiki/Escape_velocity#List_of_escape_velocities


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