This is the boss. No calculator. Take $\pi = 3.14$, and the survey log hands you $GM$ already multiplied out, so every root today lands on a clean power of ten: $\sqrt{2.5 \times 10^{7}} = \sqrt{25} \times \sqrt{10^{6}} = 5000$. Split the mantissa from the exponent, take the root of each, put them back together. Powers of ten are furniture here, not obstacles.

One planet, one long problem, and every answer feeds the next: the field at the orbit, then the orbital speed, then the period, then the escape speed. Write each line down — one early slip rolls all the way to the launch pad. The last board asks not for a number but for a decision, which is what mission control actually does for a living.

Everything from the chapter rides in it. 5★ under par here is the chapter crown. Clock in.