CBSE Class 11-science Answered

To help you understand Galileo’s insight, we will explain in more depth what he observed. The moons’ orbits are roughly circular. From his perspective on Earth, Galileo could only see the moons’ lateral motion, their motion from left to right and right to left. At the moons’ great distance, their motion toward and away from the Earth was not perceptible. The moons seem to repeatedly move back and forth along a straight line, as objects in SHM do.

When an object moving in uniform circular motion, such as a moon of Jupiter, is observed “edge on,” does the repeated motion actually conform to the equations for SHM? In Concept 1 we show a ball moving up and down in circular motion. The graph shows its vertical displacement and, as you can see, the graph is sinusoidal, like those that represent displacement in SHM.

In Equation 1, you can see why we perceive edge-on uniform circularmotion as SHM. Consider the x displacement of the particle moving inuniform circular motion. The x displacement equals the radius (which we will call A here) times the cosine of the angle ?. The angle ? is the angular displacement. As you may recall from your studies of rotational motion, angular displacement equals the product of angular velocity and time, or?t. As the equation to the right reflects, the function for the xdisplacement is the same function as the one used for calculating the displacement of an object in SHM.

The relationship between uniform circular motion and SHM can also be confirmed qualitatively. At the perceived endpoints of its circular path, a moon of Jupiter would be moving directly away from, or toward, Galileo. In other words, its tangential velocity is directed toward or away from the Earth at these points. Here its velocity should seem to go to zero just as in SHM, and this is what Galileo observed.