Example #5: Gravitation and Satellites
Another major category of forces that produce uniform circular motion is gravitation. At a radius, **r**, from the center of the Earth, the gravitational field strength, **g**, can be calculated as: Alternatively, we can also state that for a satellite in circular orbit that gravity supplies the unbalanced central force required to keep it in orbit. Thus, the field strength of the Earth's gravitational field, **g**, is equivalent to the centripetal acceleration experienced by a satellite in circular orbit at radius **r** from the center of the Earth. The formula derived above is the speed of a satellite orbiting a central mass, **M**, at a center-to-center distance of **r**. This speed can also be expressed as where **T** is the period, or time for the satellite to make one complete revolution. Substituting this expression for **v** into our earlier equation gives us a statement of Kepler's 3rd Law. |