Final answer:
To ensure an artificial satellite maintains orbit and does not fall to Earth, it must have sufficient altitude, correct orbital velocity, and comply with Kepler's Third Law for orbital mechanics, while factors like atmospheric drag and the gravity-gradient force are also considered.
Step-by-step explanation:
To ensure that an artificial satellite keeps orbiting Earth rather than falling back to Earth's surface, several factors must be taken into account. First, the satellite must be at a sufficient altitude to be free of significant atmospheric drag, which can slow it down and cause it to lose altitude gradually until it re-enters the Earth's atmosphere. Furthermore, the satellite must have the correct orbital velocity to balance the gravitational pull of the Earth, which is approximately 8 kilometers per second for circular orbits close to the planet.
Kepler's Third Law applies to artificial satellites just as it does to natural satellites like the Moon. This law relates the square of the orbital period of a satellite to the cube of the average distance from the center of the body it is orbiting. Therefore, using this law with known values of Earth's and the satellite's radius, the satellite's orbital period can be computed.
Lastly, any deviations from a perfectly circular orbit could mean that the satellite's distance from Earth may change periodically, and careful planning is needed to ensure that it will neither stray into the atmosphere nor escape into space. Additionally, the gravity-gradient force must be considered for satellites with significant length or those with irregular shapes.