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ASTR120 Challenge Problem #1: Determining Shadow Sizes of Moons in Our Solar System - Prof, Assignments of Astronomy
In this challenge problem, students are required to calculate the size of shadows cast by moons on their parent planets using algebra, geometry, and the planetary calculator at <http://janus.astro.umd.edu/astro/calculators/scalc.html>. Students are assumed to have spherical moons and circular orbits. The problem includes a table of shadow sizes and asks students to identify which moons cast the largest shadows. Additionally, students are asked to determine the size of earth's shadow on the moon and express their answer in terms of both earth and moon radii.
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ASTR120 Challenge Problem #1 – (Hamilton)
Optional, due before Midterm
In this challenge problem you will work out how large a shadow moons in our Solar System cast on their parent planets.
a) Draw an accurate picture and use algebra and geometry to determine the size of the shadow cast by a moon on its parent planet. Assume that the moon is spherical and that all orbits are circular. Type your equation into the planetary calculator at http://janus.astro.umd.edu/astro/calculators/scalc.html and produce a table of shadow sizes. Which moons cast the largest shadows?
b) How big is the Earth’s shadow cast on the Moon? Rewrite your answer in terms of both Earth and Moon radii.