When Mercury is at its least value of greatest elongation it is seen 18° from the Earth-Sun line. How long before sunrise (or after sunset) will Mercury be visible at this time?
A)18 minutes
B)a little less than 1 hour
C)2 hours
D)4 hours

Question

Quizplus · Accepted Answer

When a planet is at its greatest elongation, it is at its farthest point from the Sun as seen from Earth. This means it can be visible in the sky before sunrise or after sunset, depending on its position. Since Mercury has an orbital period of only 88 days, it is always relatively close to the Sun and is never visible at midnight. When Mercury is at its least value of greatest elongation, it is seen 18° from the Earth-Sun line. The angle between the Sun and the horizon at sunrise or sunset is usually about 8°, so we can use basic trigonometry to calculate that Mercury will be visible roughly 18/(360/24) = 1 hour before sunrise (or after sunset), which corresponds to choice B.

When Mercury Is at Its Least Value of Greatest Elongation