Why do planets have elliptical orbits?
At first glance it may seem odd that a force such as gravity, which pulls the planets straight in toward the center of mass, should result in elliptical orbits! But in fact it is quite straightforward to understand why this should be so. It is certainly possible to set up a satellite so that it has a circular orbit (a circle is just an ellipse whose foci coincide). Gravity can only pull in the direction toward the planet. The inertia of the satellite makes it want to travel in a straight line, but if it does so, its velocity is no longer perfectly perpendicular to the pull of gravity, so gravity pulls it in; this will remove part of the velocity, but as the satellite is also falling inward, it gets a new component of velocity due to the acceleration of gravity. In a circular orbit, we know that the ground speed is constant, so these two effects must perfectly cancel one another out to leave the speed of the satellite unchanged. Now imagine that we fire the satellite’s boosters so that
