The table below displays physical data for the newly surveyed rocky exoplanet Caelum-8:
Mass / kg1.35×1025Radius / km8600Density of atmosphere at surface / kg m−354Period of rotation about its axis / hours14.2\begin{array}{|l|c|} \hline \textbf{Mass / kg} & 1.35 \times 10^{25} \\ \hline \textbf{Radius / km} & 8600 \\ \hline \textbf{Density of atmosphere at surface / kg m}^{-3} & 54 \\ \hline \textbf{Period of rotation about its axis / hours} & 14.2 \\ \hline \end{array}Mass / kgRadius / kmDensity of atmosphere at surface / kg m−3Period of rotation about its axis / hours1.35×102586005414.2
Calculate the magnitude of the gravitational field strength ggg at the surface of Caelum-8. Give your answer to 3 significant figures.
Two identical autonomous scientific landers, Astraea-1 and Astraea-2, land on flat terrain on Caelum-8.
Astraea-1 lands at the south pole. Astraea-2 lands on the equator.
Each lander has a mass of 1200 kg1200\text{ kg}1200 kg and a volume of 3.6 m33.6\text{ m}^33.6 m3.
Calculate the centripetal acceleration aaa of lander Astraea-2 at the equator due to the rotation of Caelum-8 about its axis.
The thick atmosphere exerts the same buoyant upthrust on each lander. Using your answer to (a), calculate the upthrust acting on each lander.
Explain which lander will experience the greater normal contact force from the ground of Caelum-8.