Question 2 · Física I URV 2023

a. Assuming the orbit is circular, are the kinetic energy, the gravitational potential energy, and the total mechanical energy constant? Justify your answers thoroughly.

Solución: All three energies ($U$, $K$, and $E$) are constant.

b. Assuming the orbit is elliptical, are the kinetic energy, the gravitational potential energy, and the total mechanical energy constant? Justify your answers thoroughly.

Solución: Potential energy $U$ and kinetic energy $K$ are not constant; total mechanical energy $E$ is constant.

c. For any quantities that were not constant in the previous sections, specify at which orbital positions they attain their maximum and minimum values. Explain in detail.

Solución: Kinetic energy $K$: maximum at periapsis, minimum at apoapsis. Potential energy $U$: minimum at periapsis, maximum at apoapsis.