Question

1. Write a general expression of the flux f received from the Sun as a function of luminosity of the Sun L, distance from the Sun r and the zenit distance z (angle between the zenit and the line of sight to the Sun).

2. Compute the fractional change in f due to the variations in r for the Earth (as in the ratio between f at perihelium and f at apohelium, for the same z). Also calculate the fractional change in f due to variation in z at noon (such as for the days when the Sun is highest and lowest in the sky when it crosses the meridian; keep r fixed and assume Northern latitude 45?). Are your results consistent with statement above that an inclination of the Earth's axis to the orbit is more significant for causing seasons?

3. At present repeat the above calculation for Mercury, Mars, Jupiter, and Uranus. Which result dominates for each of these planets?

4. Although teaching "astronomy for poets", I often encountered the misconception that seasons are due to one hemisphere of the Earth being closer to the Sun than the other. Show that this has negligible effect.