Chapter 5 Circular Motion; Gravitation

1. Use Newton's second law of motion, the universal law of gravitation, and the concept of centripetal acceleration to solve problems involving the orbital motion of satellites. 2. Explain the "apparent" weightlessness of an astronaut in orbit. Objectives

5-8 Satellites and “Weightlessness” Satellites are routinely put into orbit around the Earth. The tangential speed must be high enough so that the satellite does not return to Earth, but not so high that it escapes Earth’s gravity altogether.

5-8 Satellites and “Weightlessness” The satellite is kept in orbit by its speed – it is continually falling, but the Earth curves from underneath it.

5-8 Satellites and “Weightlessness” Objects in orbit are said to experience weightlessness. They do have a gravitational force acting on them, though! The satellite and all its contents are in free fall, so there is no normal force. This is what leads to the experience of weightlessness.

5-8 Satellites and “Weightlessness” More properly, this effect is called apparent weightlessness, because the gravitational force still exists. It can be experienced on Earth as well, but only briefly:

The velocity of a satellite keeps it in orbit Even when moving, the satellite is actually accelerating toward the Earth (this is what keeps it in its circular path) Its acceleration results in a curved path which is the same as the curve of the Earth Gravity is providing the centripetal force

Perception of Weightlessness There is still gravity acting in a satellite (about 8.9 m/s 2 ), so why do we feel weightless? In an free falling elevator, if the F A is equal to the F G, there is no F N No force is felt feel weightless – called apparent weightlessness

Weightlessness that you feel in a satellite is like the weightlessness in an elevator The satellite and everything on it are all accelerating toward the earth at the same rate

Practice Problem # 1 Calculate the force of gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1400 kg.

Practice Problem #2 At the surface of a certain planet, the gravitational acceleration g has a magnitude of 12.0 m/s 2. A 2.10 kg brass ball is transported to this planet. What is: –The mass of the brass ball on the Earth and on the planet? –The weight of the brass all on the Earth and on the planet?

Practice Problem #3 A satellite moves in a circular orbit around Earth at a speed of 5,000 m/s. (a) Determine the satellite's altitude above the surface of Earth. (b) Determine the period of the satellite's orbit. R E = 6378 km and M E = 5.98 x kg

Practice Problem #4 A 600-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth’s mean radius. Find (a) the satellite’s orbital speed, (b) the period of its revolution, and (c) the gravitational force acting on it.

Homework Problems in Chapter 5 #43, 45, 48, 50, 60