Orbit and Escape Velocity. Throw a ball straight up in the air and it falls back down. Have your strongest friend throw the ball and it might take a fraction.

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Presentation transcript:

Orbit and Escape Velocity

Throw a ball straight up in the air and it falls back down. Have your strongest friend throw the ball and it might take a fraction longer to return to Earth. Orbit is a path described by one body in its revolution around another. Orbit does not depend on vertical velocity, but on horizontal velocity. Orbital Basics

Fire a cannon, and the ball travels some distance sideways before hitting the ground. Fire the ball faster, and it will travel further before hitting the ground. If we put a stupidly powerful cannon on top of a really tall mountain, the ball might have so much horizontal velocity that the rate it fell towards the Earth’s surface equaled the rate at which the Earth’s surface curved away beneath it. The ball would be in orbit around the Earth. Orbital basics

Isaac Newton’s idea

International Space Station (ISS) orbits at ~350km above the surface. If the Earth were the size of a basketball, the ISS would be 12.8mm above the surface. Because it’s not particularly high, the ISS has to have a huge horizontal velocity, and orbits Earth every 90 minutes. a path described by one body in its revolution about another Outer Space

Escape Velocity

Escape Velocity - Earth

To escape Earth’s gravity and not just fall in an endless circle, you need to go even faster: either 11.2km/s from the surface, or 10.9km/s from LEO. The drag of the atmosphere would make it very dangerous to accelerate a rocket to 11.2km/s at low altitude, so NASA puts probes into LEO first and then gives them a little shove. By ‘little shove’, of course, I mean a huge shove to go from 8km/s to 10.9km/s. Launch Economics

To enter low-Earth orbit (LEO), a rocket has to reach a velocity of 8km/s (28,800km/h). It costs ~$10,000 to put 1 kg into LEO. Cost hasn’t changed much since the 1950s, because we’re still using the same technology – chemical rockets. Launch Economics

You have to time your launch carefully. Earth revolves around the Sun every 365 days, Mars takes 687 days. So about every 2.1 years we make a close approach to Mars. Brahe knew that, and after last week’s lab, so do you. Geometry of the journey