Solve problems involving the third law of planetary motion using 𝑇𝑎2 𝑟𝑎3 = 𝑇𝑏 2 𝑟𝑏 3 = 4𝜋2 𝐺𝑀. The following subject matter may be assessed in the internal assessments.

Jupiter has a moon, Ganymede, which orbits at a distance of 1.070 × 10⁹ m from Jupiter's centre with an orbital period of 7.155 days. Another moon, Callisto, orbits Jupiter with a period of 16.69 days. Determine the orbital radius of Callisto. Show your working.

A newly discovered exoplanet orbits a star with mass \(2.4 \times 10^{30}\) kg. The orbital period of the exoplanet is 420 days. A second planet in the same system has an orbital radius of \(1.8 \times 10^{11}\) m. Determine the orbital radius of the exoplanet. Show your working.

Jupiter has a moon called Europa with an orbital period of 3.55 days and an orbital radius of 6.71 × 10⁸ m. Another moon, Ganymede, orbits Jupiter at a radius of 1.07 × 10⁹ m. Calculate the orbital period of Ganymede in days. Show your working.