Part (a)(i)
Correct Answer: Planet B
Detailed solution: Planet B is the closest to the Sun because it has the highest surface temperature ($623\text{ K}$). In a solar system, planets closer to the central star receive more intense radiation per unit area, generally leading to higher surface temperatures compared to planets further away.
Part (a)(ii)
Correct Answer: $-180 ^\circ\text{C}$
Detailed solution: To convert from Kelvin ($\text{K}$) to degrees Celsius ($^\circ\text{C}$), use the formula $T(\text{in K}) = \theta(\text{in } ^\circ\text{C}) + 273$. Rearranging for Celsius gives $\theta = T – 273$. For planet D, the calculation is $93 – 273 = -180 ^\circ\text{C}$.
Part (a)(iii)
Correct Answer: Planet A
Detailed solution: The time taken to fall a fixed height is inversely related to the acceleration due to gravity ($g$). Planet A has the highest gravitational field strength ($23.0\text{ N/kg}$), which is equivalent to the highest acceleration of free fall. A greater acceleration results in a faster increase in velocity, meaning the object covers the $2\text{ m}$ distance in the shortest time.
Part (b)(i)
Correct Answer: Red supergiant; (new) heavier elements; neutron star OR black hole.
Detailed solution: A massive star expands to form a red supergiant. When it explodes as a supernova, it forms a nebula containing hydrogen and new heavier elements. The collapse of the remaining core leaves behind either a neutron star or a black hole, depending on the initial mass of the star.
Part (b)(ii)
Correct Answer: Distance (from Earth) to the galaxy.
Detailed solution: Supernovae have a known peak luminosity (intrinsic brightness). By measuring the apparent brightness observed from Earth and comparing it to this known intrinsic brightness, astronomers can calculate the distance $d$ to the galaxy in which the supernova occurred.
