Question

If from the base station , the rocket system of $A$ has been operated, so that its rocket has been fired in forward direction thus reducing the speed of $A$ by $0.5$%, then which of the following will happen?

• A. Its orbit becomes elliptical with semi-major axis $9505.3km$.
• B. Its total energy becomes $-6.714\times {10}^{9}J$.
• C. Its new time period becomes $9219.67s$
• D. All of the above

Answer 1

The correct option is D All of the above

New radius will be $R={\left(0.995\right)}^2\left(9600\right)\approx 9505.3km$.

Total energy will be $\frac{1}{2}m{v}^2-\frac{GMm}{R}$. Putting value of v to be $0.995\sqrt{\frac{GM}{R}}$, we get energy to be $-6.714X{10}^{9}J$.

By Kepler's law, $T^2\alpha R^3$, using this relation, we get new time period as $9219.67s$. Use $T_i=\frac{2\pi R}{V}$ as initial time period.

Hence, all options are correct.