An Introduction to Modern Astrophysics · Problem 20.3
The Formation of Planetary Systems — Carroll & Ostlie
Physics — Astrophysics · mercury-surface-temperature
Problem
For Mercury, a slowly rotating planet with no appreciable atmosphere, Eq. (19.5) for a planet's surface temperature must be modified. In particular, the assumption that the temperature is approximately constant over the entire surface of the planet is no longer valid. (a) Assuming (incorrectly) that Mercury is in synchronous rotation about the Sun, show that the temperature at a latitude north or south of the subsolar point (the point on the equator closest to the Sun) is given by Since the planet is actually in a 3-to-2 resonance, this expression is only an approximate description for the temperature at Mercury's surface. (b) Make a graph of vs. . Mercury's albedo is 0.06. (c) What is the approximate temperature of the planet at the subsolar point? (d) At what latitude does the temperature drop to 273 K? This is the freezing point of water at the surface of Earth. (e) Would you expect to find ice on Mercury at a temperature of 273 K? Why or why not?Intuitive explanation
The key insight is that Mercury's slow rotation means different latitudes receive vastly different solar heating—the subsolar point gets intense direct radiation while the terminator region gets almost none. You'll balance the incoming solar energy absorbed at each latitude (accounting for the cosine of the angle to the Sun) with the thermal radiation each patch emits, then solve for the local equilibrium temperature. This transforms the usual "one-temperature planet" model into a latitude-dependent one where the factor captures how the solar beam's intensity varies with angle from the subsolar point.
Intuitive explanation
The key insight is that Mercury's slow rotation means different latitudes receive vastly different solar heating—the subsolar point gets intense direct radiation while the terminator region gets almost none. You'll balance the incoming solar energy absorbed at each latitude (accounting for the cosine of the angle to the Sun) with the thermal radiation each patch emits, then solve for the local equilibrium temperature. This transforms the usual "one-temperature planet" model into a latitude-dependent one where the factor captures how the solar beam's intensity varies with angle from the subsolar point.