Chapter 3 Orbits and Gravity
3.5 Motions of Satellites and Spacecraft – Escape Velocity
Learning Objectives
By the end of this section, you will be able to:
- Explain how an object (such as a satellite) can be put into orbit around Earth
- Explain how an object (such as a planetary probe) can escape from orbit
Newton’s universal law of gravitation and Kepler’s laws describe the motions of Earth satellites and interplanetary spacecraft as well as the planets. Sputnik, the first artificial Earth satellite, was launched by what was then called the Soviet Union on October 4, 1957. Since that time, thousands of satellites have been placed into orbit around Earth, and spacecraft have also orbited the Moon, Venus, Mars, Jupiter, Saturn, and a number of asteroids and comets.
Once an artificial satellite is in orbit, its behaviour is no different from that of a natural satellite, such as our Moon. If the satellite is high enough to be free of atmospheric friction, it will remain in orbit forever. However, although there is no difficulty in maintaining a satellite once it is in orbit, a great deal of energy is required to lift the spacecraft off Earth and accelerate it to orbital speed.
To illustrate how a satellite is launched, imagine a gun firing a bullet horizontally from the top of a high mountain, as shown below, which has been adapted from a similar diagram by Newton. Imagine, further, that the friction of the air could be removed and that nothing gets in the bullet’s way. Then the only force that acts on the bullet after it leaves the muzzle is the gravitational force between the bullet and Earth.
If the bullet is fired with a velocity we can call va, the gravitational force acting upon it pulls it downward toward Earth, where it strikes the ground at point a. However, if it is given a higher muzzle velocity, vb, its higher speed carries it farther before it hits the ground at point b.
Here is another PhET simulation about projectile motion.
If our bullet is given a high enough muzzle velocity, vc, the curved surface of Earth causes the ground to remain the same distance from the bullet so that the bullet falls around Earth in a complete circle. The speed needed to do this—called the circular satellite velocity—is about 8 kilometres per second, or about 17,500 miles per hour in more familiar units.
Here is another PhET interactive where you can see the effects of gravity on the orbits of the Earth, Moon and the International Space Station.
Anik Satellites
Launched in 1972, Anik (Inuktitut for “brother”) A1 was the first domestic communication satellite to be placed in a geostationary orbit. It relayed telephone calls, data, and television for ten years. When joined by Anik A2 and Anik A3, in 1973 and 1975 respectively, it made Canada the first country to use satellites for domestic communication.
Ongoing Anik satellite launches have interesting Canadian news footage, an archived sample of which can be found at https://www.youtube.com/watch?v=Sw00n