For many problems involving dynamics, there is a shortcut to calculating what you need to know. See how the concepts of work and energy can help you solve problems that would be too cumbersome with Newton's Laws as the only tools in your toolbox.

In teaching Introductory College or University Physics to undergraduates or advanced high school students, problems involving elliptical orbits are frequently presented with the objective of enriching the students' understanding of orbital mechanics. An exercise nearly always encountered in these first-year classes consists of relating the velocity of a satellite (whose mass is treated as being insignificant compared to that of the central body) at its apoapsis to the velocity of the satellite at its periapsis. Some students will choose to solve the problem using conservation of angular momentum, while others will use conservation of energy relationships.
The teacher is able to assure the students that the relationships are equivalent (both physical laws must hold), though it is by no means obvious that this is so by inspection alone.