Universal Gravitation, Satellites and Cosmic Velocities
One law explains a falling apple, the Moon's orbit and every spacecraft ever launched.
Big Idea: Every pair of masses in the Universe attracts each other with a force that grows with the masses and falls off as the square of the distance between them. The same force that pulls a dropped stone to the ground keeps the Moon circling the Earth and satellites circling the planet. Give a body enough sideways speed and its constant fall never reaches the ground — it orbits. Give it even more, and it escapes into space.
By the end you will be able to:
- state and use the law of universal gravitation, F = G·m1m2 / r2;
- explain what the gravitational constant G is and how it was measured;
- connect gravity at a planet's surface to g = GM / R2;
- show why an artificial satellite needs a precise speed, and derive the first cosmic velocity;
- derive the second cosmic velocity (escape velocity) and relate it to the first;
- weigh the benefits and costs of space exploration.