Solve problems involving the gravitational field strength at a distance from an object using 𝑔 = 𝐹 𝑚 = 𝐺𝑀 𝑟2.

A research station is located on a dwarf planet with mass 2.40 × 10²² kg. An astronaut of mass 85.0 kg stands on the surface of the dwarf planet at a distance of 1.20 × 10⁶ m from its centre. Calculate the gravitational field strength experienced by the astronaut at this location. Show your working.

A student investigates gravitational field strength at various altitudes above the surface of a planet. The table below shows data collected during the investigation. Refer to the table. Determine the mass of the planet. Show your working.

The diagram shows a spacecraft positioned at a specific distance from the centre of a moon. The moon has a mass of \(7.35 \times 10^{22}\) kg and a radius of \(1.74 \times 10^{6}\) m. The spacecraft is located \(5.22 \times 10^{6}\) m from the moon's centre. What is the magnitude of the gravitational field strength experienced by the spacecraft at this location?

A space station orbits a planet at an altitude of 4.20 × 10⁵ m above the planet's surface. The planet has a radius of 3.80 × 10⁶ m and a mass of 8.50 × 10²³ kg. An astronaut of mass 75.0 kg is performing a spacewalk outside the station. Determine the gravitational field strength experienced by the astronaut at this altitude. Show your working.