Quick questions on Orbital motion, Kepler's third law and satellite energy (QCE Physics Unit 3)

For a satellite of mass $m$ in a circular orbit of radius $r$ around a central body of mass $M$, the gravitational force supplies all of the centripetal force:

Substituting $v = 2 \pi r / T$ into $v^2 = G M / r$:

QCAA may ask you to state these as background.

The kinetic energy of a satellite in a circular orbit of radius $r$ is:

The minimum launch speed from radius $r$ that lets a projectile reach infinity with zero kinetic energy:

Expect a satellite or moon table (radii and periods, sometimes a missing column) with a question asking you to verify Kepler's third law or extract $M$ of the central body. Alternatively, a stimulus showing the orbital energies as a function of radius with questions on the virial theorem.

A practical IA2 on orbits is hard to engineer directly, but a frequent design is the simple pendulum used to measure local $g$, then comparing the inferred $G M_E / R_E^2$ against the textbook value. The orbital framework provides the EA-level theory for the Unit 3 justification.

Both depend only on $M$ (the central body) and $r$.

Gravitational potential energy is negative with zero at infinity. The deeper into the well, the more negative.

$v_{\text{esc}} = \sqrt{2} \, v_{\text{orbit}}$ at the same radius. Escape is from infinity; orbit is a bound circular trajectory.

If you mix days and seconds, or kilometres and metres, the constant changes. Always work in SI metres and seconds for QCAA problems.