Estimates of the heights of lunar mountains can be made by measuring the lengths of their shadows when the Sun angle on them is relatively low. If a shadow length on a photograph of an isolated mountain on a flat plain is measured at 5 km when the solar elevation angle (angle above the horizon as seen by someone on the Moon) is about 6°, what is the mountain height above the plain? (A diagram might help, and the small-angle formula in Chapter 1, Universe, 11th ed. will be useful.)

Question

Quizplus · Accepted Answer

Using the small-angle formula and trigonometry, the height (h) of the mountain can be calculated using the shadow length (L) and the solar elevation angle (θ). The formula is h = L * tan(θ). Given L = 5 km and θ = 6°, h ≈ 5 * tan(6°) ≈ 0.5 km or 500 m.

Estimates of the Heights of Lunar Mountains Can Be Made