Motion of Orbiting Satellites
A satellite in orbit has no engine. Gravity alone pulls it inward; sideways inertia bends that pull into a closed path. Topic 6.6 combines two equations ($v = \sqrt{GM/r}$, $T = 2 \pi \sqrt{r^3 / GM}$) with one sign convention ($U_g = 0$ at infinity, so $U_g < 0$ everywhere closer in). Get the signs right and orbital mechanics follows. Get them wrong and you end up claiming ISS astronauts are weightless because gravity ran out.
Fig. 6.6.1 A satellite in a stable circular orbit. Gravity (red, inward) is the only force; the velocity (blue, tangent) is just inertia. Right panel shows per-unit-mass energy: $K$ positive, $U_g$ twice as deep on the negative side (zero at infinity), and $E = K + U_g$ negative with $|E| = K$.
OrbitLab · Open the sandbox →The three traps are everyday intuition extended past where it works. Impetus reasoning: students think satellites need an engine, because everything else in their experience needs pushing. The constant-speed ellipse: the formula $v = \sqrt{GM/r}$ for circular orbits gets lifted onto an ellipse, missing that $r$ now varies and $K$ trades against $U_g$. The positive-$U_g$ orbit: the surface-bound $U_g = mgh$ intuition gets carried into a regime where $U_g = 0$ at infinity is forced, and students end up insisting that $U_g$ must be positive. The lesson drills all three; the diagnostic finds which one is yours.
The work
3 ways in · any order
Lesson
Motion of orbiting satellites
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Two equations, three energies, three misconceptions. The lesson derives $v$ and $T$ from $F_\text{grav} = F_c$, runs a worked example at $r = 2 R_E$ using the $g R_E^2$ shortcut, lays out why $U_g < 0$ at every finite radius, and closes with a ten-scenario applet that drills the three native traps.
Diagnostic
10-item topic check
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Ten items: circular and elliptical orbits, sign of $U_g$, how $E$ depends on $r$, and the three native traps (tangential-force orbits, constant-speed ellipses, positive-$U_g$ orbits). Wrong answers tag the specific misconception and route you into a targeted drill.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.