Motions Of Satellites And Spacecraft

Space Debris Traced By NASA In Earth Orbit
Source : NASA

Newton’s universal law of gravity and Kepler’s laws describe the motions of earth terrestrial satellites and interplanetary spacecraft, as well as planets. Sputnik, the first artificial earth satellite, was launched into space on October 4, 1957 by what was then the Soviet Union. Satellites have been put into orbit around the earth, and spacecraft also orbited the Moon, Venus, Mars, Jupiter, Saturn, and a number of asteroids and comets.

Once an artificial satellite is in orbit, its behavior is no different from that of a natural satellite. Satellites like our moon. When the satellite is high enough to be free from atmospheric friction, it will stay in orbit forever. However, while there is no difficulty in servicing a satellite once it is in orbit, a large amount of energy is required to lift the spacecraft out of the earth and accelerate it to orbit speed.

To illustrate how a satellite is launched, imagine a weapon firing a bullet horizontally from the top of a high mountain, borrowed from a similar diagram by Newton. Imagine further if the air friction could be eliminated and nothing happens. The only force that acts on bullet after exiting the muzzle is the gravitational force between bullet and the earth.

When the bullet is fired at a speed that we can call va, the gravitational force acting on it pushes it downards the earth, where it hits the ground at point a. However, if it is given a higher muzzle velocity vb, its higher velocity will carry it further before it hits the ground at point b.

(a) For paths a and b, the velocity is not enough to prevent gravity from pulling the bullet back to Earth;
in case c, the velocity allows the bullet to fall completely around Earth. (b) This diagram by Newton in his De Mundi Systemate, 1731 edition,
illustrates the same concept shown in (a).

If bullet is given a sufficiently high initial muzzle velocity vc, the curved surface of the earth will cause the ground to maintain the same distance from bullet so that the bullet will fall in a complete circle around the earth. The speed required for this, the so-called circular satellite velocity, is about 8 kilometers per second or in more familiar units about 17,500 miles per hour.

Each year nations like Russia, the United States, China, Japan, India and Israel put more than 50 new satellites into orbit, as does the European Space Agency (ESA), a consortium of European nations. These satellites are used for weather tracking, ecology, global positioning systems, communications, and military purposes, to name a few applications. Most satellites are launched into low earth orbit as this requires the minimum launch energy. With an orbital speed of 8 kilometers per second, they rotate around the planet in about 90 min. Some of the very low orbits of the earth are not indefinitely stable because the atmosphere of these satellites creates frictional drag from the occasional swelling of the earth’s atmosphere, which eventually leads to energy loss and “disintegration” of the orbit.

Most of the exploration of the solar system has been carried out by robotic spacecrafts sent to other planets. In order to escape from Earth, these ships must reach the escape speed, the speed required to move away from Earth forever, which is approximately 11 kilometers per second (approximately 25,000 miles per/h). After escaping from Earth, these ships glide towards their targets, with only minor trajectory adjustments being made by small-thruster rockets on board. During interplanetary flight, these spacecrafts follow orbits around the sun that only change when they pass close to one of the planets.

In the direction of its destination, a spacecraft is deflected into a modified orbit by the gravitational force of the planet, gaining energy or losing energy in the process. The spacecraft controllers were able to use a planet’s gravity to redirect a passing spacecraft to a second target. For example, Voyager 2 used a series of gravity-assisted encounters to generate successive flybys of Jupiter (1979), Saturn (1980), Uranus (1986), and Neptune (1989). The Galileo space probe, launched in 1989, flew past Venus once & earth twice to get the energy you need to complete your ultimate goal of orbiting Jupiter.

If we want to orbit a planet, we need to use a rocket to slow the spacecraft when it is near its target so that it can be trapped in an elliptical orbit. Additional rocket thrust is required to bring a vehicle down from orbit for a surface landing. Finally, when a return trip to Earth is planned, the landed payload must contain enough fuel to repeat the entire process in reverse.