In figure 5 we can see that for the orange ellipse the speed is less than the circular speed, for the green circle the speed is the circular speed and for the red ellipse the speed is greater than the circular speed but not as large as the escape speed. In figure 6 we can see that for the blue parabola its velocity is the escape velocity and for the yellow hyperbola the body’s speed is greater than the escape velocity.
An interesting thought experiment to do is to imagine that the gravitational constant was decrease or increased and so as a result the equations for Circular and Escape speed will allow bodies to escape that would not have enough speed to escape the gravitational field. This change will mean that difference bodies will have difference speeds and as a result the necessary speed for a type of orbit changes. If the gravitational constant was increased then both the circular and escape velocities would increase. This could potentially mean that more bodies would be in orbit as less would have the necessary escape speed but it would be hard to tell whether more orbits would be more or less circular because the percentage of bodies with different speeds is not known.
…show more content…
This is how much the orbit is stretched out compared to a circle and it is irrespective of the size of the orbit. The eccentricity of a circular orbit is precisely 0, elliptical orbits have an eccentricity between 1 and 0, the closer the eccentricity is to 0 the more like a circle the ellipse is and the closer to 1 the eccentricity is, the more stretched out the orbit is. If the eccentricity is exactly 1 then the orbit is parabolic so the object is just able to escape the gravity of the parent body. Moreover, if the eccentricity is greater than 1 then the orbit is a hyperbola and so would easily escape the gravity