The average distance from Mercury to the Sun is 0.4 AU. That is, the average distance from Pluto to the Sun is 40 AU. e. How many times is the Sun brighter for an observer on Mercury than for an observer on Pluto? What is the difference in brightness (in magnitude)?
The distance from Mercury to the Sun is, on average, 100 times less than Pluto’s distance to the Sun. This means that on Mercury the Sun for the observer will be 1002 = 10,000 times brighter. Every 100 times is 5 magnitudes. This means that the Sun will be 10m brighter. Additional points can be used to evaluate the student’s accounting for the eccentricity of the orbits of these planets and the calculation of the brightness difference at the perihelion-aphelion of these planets (0.2 – Mercury, 0.24 – Pluto – the answer is about 11m).
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