Here is a diagram. With just the gravitational force and with a circular acceleration, the following must be true in the direction of the center of the planet and circle :. I could solve this for the velocity needed for an orbit with radius r - but I won't. Instead let me find the kinetic energy needed for an orbit. Multiplying both sides of that equation be r over 2, I get:. Now for energy. If I consider the satellite or spacecraft and the Earth as the system, then there is no external work on the system so:.
Now let's pretend. Suppose we are in orbit at a distance r 1 from the center of the Earth. This means that we would have to have an energy of:.
Mission Command now wants the spacecraft at a lower orbit, say r 2. In fact, you need to duck as it comes by after completing one orbit! You have managed to throw the ball into orbit around the Earth so that it is now an Earth satellite. Putting satellites into orbit involves the same kinds of actions and ideas.
First of all the satellite is placed on top of a huge rocket to carry it away from the Earth and up through the atmosphere.
Once it is at the required height, sideways rocket thrusts of just the right strength are applied to send the satellite into orbit at the correct speed. If the satellite is thrown out too slowly it will fall to Earth because the centripetal pull of gravity is too great. If the satellite is thrown out too fast it will escape from the Earth's orbit because the gravitational pull is not sufficient to provide the required centripetal force. With the correct launch speed the satellite continues in its falling orbit around the Earth.
It is just a matter of setting the horizontal speed of the satellite such that the gravitational pull of the Earth at the given height tugs it round on its orbital path.
When talking about satellites with pupils it is quite likely that someone will pose the very good question:. Geostationary satellites take 24 hours to orbit the Earth, so the satellite appears to remain in the same part of the sky when viewed from the ground. Orbital motion Gravity provides the force needed to maintain stable orbit of planets around a star and also of moons and artificial satellites around a planet.
Explaining orbits For an object to remain in a steady, circular orbit it must be travelling at the right speed. There are three possible outcomes: If the satellite is moving too quickly then the gravitational attraction between the Earth and the satellite is too weak to keep it in orbit.
If this is the case, the satellite will move off into space. If the satellite is moving too slowly then the gravitational attraction will be too strong, and the satellite will fall towards the Earth. Occasionally satellites will orbit in paths that can be described as ellipses.
In such cases, the central body is located at one of the foci of the ellipse. Similar motion characteristics apply for satellites moving in elliptical paths. The velocity of the satellite is directed tangent to the ellipse.
The acceleration of the satellite is directed towards the focus of the ellipse. And in accord with Newton's second law of motion , the net force acting upon the satellite is directed in the same direction as the acceleration - towards the focus of the ellipse. Once more, this net force is supplied by the force of gravitational attraction between the central body and the orbiting satellite.
In the case of elliptical paths, there is a component of force in the same direction as or opposite direction as the motion of the object. As discussed in Lesson 1 , such a component of force can cause the satellite to either speed up or slow down in addition to changing directions.
So unlike uniform circular motion, the elliptical motion of satellites is not characterized by a constant speed. In summary, satellites are projectiles that orbit around a central massive body instead of falling into it.
Being projectiles, they are acted upon by the force of gravity - a universal force that acts over even large distances between any two masses. The motion of satellites, like any projectile, is governed by Newton's laws of motion. For this reason, the mathematics of these satellites emerges from an application of Newton's universal law of gravitation to the mathematics of circular motion.
The mathematical equations governing the motion of satellites will be discussed in the next part of Lesson 4. The fact that satellites can maintain their motion and their distance above the Earth is fascinating to many.
How can it be? What keeps a satellite up? One might think that an inward force would move a satellite right into the center of the circle; but that's only the case if the satellite were in a rest position.
Being that the satellite is already in motion in a tangential direction, the inward force merely turn from its straight-line tangential direction.
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