An unpowered automated spacecraft of mass 4.2×103 kg4.2 \times 10^3 \text{ kg}4.2×103 kg is performing a flyby of a recently discovered rogue exoplanet named Zephyr-9. As the spacecraft descends deeper into the gravitational field of Zephyr-9, its speed increases.
The table below provides the distance of the spacecraft from the centre of mass of Zephyr-9 and its speed at two different tracking positions, AAA and BBB:
| Position | Distance from centre of mass / m\text{m}m | Speed / m s−1\text{m s}^{-1}m s−1 |
|---|---|---|
| AAA | 6.4×1066.4 \times 10^66.4×106 | 2.4×1032.4 \times 10^32.4×103 |
| BBB | 4.0×1054.0 \times 10^54.0×105 | 3.6×1033.6 \times 10^33.6×103 |
Assuming Zephyr-9 is spherical and isolated, calculate the mass of Zephyr-9.
Use G=6.67×10−11 N m2 kg−2G = 6.67 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2}G=6.67×10−11 N m2 kg−2.
