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NSWPhysicsQuick questions
Module 5: Advanced Mechanics
Quick questions on Conservation of energy in orbital motion explained: HSC Physics Module 5
12short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is kinetic energy in a circular orbit?Show answer
For a satellite of mass $m$ in a circular orbit at radius $r$ around a central body of mass $M$, gravity provides the centripetal force:
What is gravitational potential energy?Show answer
From the radial-field formula:
What is total mechanical energy?Show answer
$$E = K + U = \frac{G M m}{2 r} - \frac{G M m}{r} = -\frac{G M m}{2 r}$$
What is energy changes between orbits?Show answer
Moving from a circular orbit at $r_1$ to one at $r_2$ requires a change in total energy:
What is the counter-intuitive result?Show answer
When the satellite moves to a higher orbit:
What is non-circular orbits?Show answer
For an elliptical orbit with semi-major axis $a$:
What is escape condition?Show answer
If $E \geq 0$, the satellite is unbound and will escape to infinity. The boundary $E = 0$ corresponds to escape velocity:
What is using $U = m g h$?Show answer
That is only valid near Earth's surface. For orbital problems, always use $U = -G M m / r$.
What is forgetting the negative sign in $E$?Show answer
Total mechanical energy of a bound orbit is negative by convention (zero at infinity).
What is assuming faster means more energy?Show answer
At a higher orbit, kinetic energy is lower but total energy is higher. Speed alone is not a measure of total energy in gravity wells.
What is treating $\Delta K$ and $\Delta U$ as equal in magnitude?Show answer
For circular-to-circular transfers, $\Delta U = -2 \Delta K$, so $\Delta E = \Delta K + \Delta U = -\Delta K$.
What is forgetting that $E = 0$ corresponds to escape?Show answer
Any positive total energy means the satellite is no longer bound.