![]() In Lesson 3, the equation for the acceleration of gravity was given as g = (G The acceleration value of a satellite is equal to the acceleration of gravity of the satellite at whatever location that it is orbiting. Similar reasoning can be used to determine an equation for the acceleration of our satellite that is expressed in terms of masses and radius of orbit. ![]() m 2/kg 2, M central is the mass of the central body about which the satellite orbits, and R is the radius of orbit for the satellite.Taking the square root of each side, leaves the following equation for the velocity of a satellite moving about a central body in circular motion Then both sides of the equation can be multiplied by R, leaving the following equation. Observe that the mass of the satellite is present on both sides of the equation thus it can be canceled by dividing through by M sat. Since F grav = F net, the above expressions for centripetal force and gravitational force can be set equal to each other. This net centripetal force is the result of the gravitational force that attracts the satellite towards the central body and can be represented as F grav = ( G If the satellite moves in circular motion, then the net centripetal force acting upon this orbiting satellite is given by the relationship F net = ( M sat ![]() The central body could be a planet, the sun or some other large mass capable of causing sufficient acceleration on a less massive nearby object. In this part of Lesson 4, we will be concerned with the variety of mathematical equations that describe the motion of satellites.Ĭonsider a satellite with mass M sat orbiting a central body with a mass of mass M Central. The mathematics that describes a satellite's motion is the same mathematics presented for circular motion in Lesson 1. The same simple laws that govern the motion of objects on earth also extend to the heavens to govern the motion of planets, moons, and other satellites. The motion of objects is governed by Newton's laws.
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