Apply Kepler's 3rd Law to calculate the transfer time (time between burns) for a satellite to complete a Hohmann Transfer.

The major assumption in this problem is that the burn times are negligible relative to the transfer time.

Typically in introductory physics Kepler's 3rd Law is applied to a circular orbit, however it can also be applied to an elliptical orbit. By knowing initial and final radii of the desired circular orbits, we can determine the length of the major, and thus semi major axis of the elliptical orbits. Plugging the semi-major axis into Kepler's 3rd we can look at the total time for the elliptical orbit. Next we need to see that the Hohmann Transfer is just half of an elliptical orbit.

I often see the misconception that a circular orbit exists when an object is exclusively under the influence of gravity, but something else must provide a force on an object in order for an orbit to be elliptical; This is not true. I think it goes back to how many people teach physics. Treating orbits as a part of circular motion, then later looking at Kepler's Laws as an independent phenomenon. The idea that an orbit can be elliptical goes back to the conservation of Mechanical Energy as well as the conservation of Angular Momentum, but in physics those are taught as two separate topics, so the links between circular and elliptical orbits seem to get lost... That perhaps is a topic for another video.

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