Step 1: Analyze Statement A -- Two satellites in same orbit have same period.
The orbital period of a satellite is given by Kepler's third law: \[ T = 2\pi\sqrt{\frac{r^3}{GM}} \] where $r$ is the orbital radius. If both satellites orbit at the same radius $r$, then $T$ depends only on $r$, $G$, and $M$ (Earth's mass), not on the satellite's own mass. So both have the same $T$. Statement A is TRUE.
Step 2: Analyze Statement B -- Orbital velocity is inversely proportional to $\sqrt{r}$.
Orbital velocity is derived by equating gravitational force to centripetal force: \[ \frac{GMm}{r^2} = \frac{mv^2}{r} \implies v = \sqrt{\frac{GM}{r}} \] Therefore: \[ v \propto \frac{1}{\sqrt{r}} \] Statement B is TRUE.
Step 3: Analyze Statement C -- Escape velocity is independent of altitude.
Escape velocity from a height $h$ above the surface is: \[ v_e = \sqrt{\frac{2GM}{R+h}} \] where $R$ is Earth's radius. As $h$ increases, $v_e$ decreases. So escape velocity depends on altitude. Statement C is FALSE.
Step 4: Summarize the analysis.
A is True, B is True, C is False. This matches option 2: A and B are true, C is false.
Step 5: Cross-check statement C with a common misconception.
At the surface, $v_e = \sqrt{2gR} \approx 11.2$ km/s. At an altitude equal to $R$, $v_e = \sqrt{2GM/(2R)} = v_e^{\text{surface}}/\sqrt{2} \approx 7.9$ km/s. Clearly it changes with altitude.
Step 6: State the final answer.
Statements A and B are true; Statement C is false. \[ \boxed{A \text{ and } B \text{ are true; } C \text{ is false}} \]