Choosing an Observing Night Under Time, Altitude, and Cloud Constraints
Your school's astronomy club has a 20-minute telescope setup window, and all students must board buses at 8:45 p.m. The plan is for every student to see both a waxing crescent Moon and Jupiter, which sits at 34° altitude in the southwest at 8:00 p.m. The observing field has a 12° tree line to the west. District policy cancels observing if forecast cloud cover exceeds 60% or if any target is below 15° altitude at the 8:10 p.m. start of observations. Local data for three candidate evenings (sunset 7:42 p.m.) are:
| Evening | Moon altitude at 8:10 p.m. (west) | Illuminated fraction | Moonset | Cloud cover |
|---|---|---|---|---|
| Mon | 19° | 12% | 9:15 p.m. | 30% |
| Tue | 25° | 24% | 10:00 p.m. | 65% |
| Wed | 31° | 37% | 10:50 p.m. | 80% |
Two students have already argued that the crescent is Earth's shadow falling on the Moon, and a parent has asked why the club cannot simply wait and observe 'when the Moon is bigger.'
1. Which evening should the club choose? Justify your choice against each stated constraint, and explain how the session should be sequenced once it begins.
Read the worked answer
Apply each constraint to each row. Cloud cover ≤ 60% eliminates Tuesday (65%) and Wednesday (80%), regardless of their more favorable altitudes. That leaves Monday. Monday's Moon altitude of 19° at 8:10 p.m. clears the 15° policy threshold and the 12° tree line, and moonset at 9:15 p.m. is after the bus departure, so the Moon is legally and practically observable for the whole window. The cost is a thin 12% crescent, which is still an easy naked-eye and telescopic target as long as students look early.
Sequencing matters because the Moon is descending toward the tree line at roughly 0.25° per minute: it will be near 10° by 8:45 p.m. So the Moon must be first, immediately at 8:10 p.m., with Jupiter second. Jupiter stays at about 34° altitude in the southwest through departure and is unaffected by the western tree line, so it can absorb any delay in telescope alignment. Set the telescope on the Moon while it is highest, let students cycle through in a fixed order, then slew to Jupiter.
Also flag the parent's question: apparent lunar size varies only about 10–14% between perigee and apogee, and that variation is independent of phase, so 'waiting until the Moon is bigger' does not produce a crescent and does not justify violating the cloud policy.
2. Use the Monday geometry to refute the 'Earth's shadow' explanation, and describe a short demonstration with standard classroom equipment that makes the refutation visible.
Read the worked answer
At 8:10 p.m. on Monday the Sun is just below the western horizon and the Moon is 19° above that same horizon, with the lit 12% on the side facing down and west - toward the Sun. Earth's shadow always points directly away from the Sun, so at that moment it extends eastward and downward on the opposite side of the sky. A body in the western sky, on the Sun's side of Earth, cannot be inside it. A lunar eclipse requires the Moon to be roughly opposite the Sun (full phase, about 180° elongation), which is why eclipses occur only at full moon and never at crescent phase.
Demonstration in about three minutes: darken the room, place a lamp at one end, and hold a ball at arm's length. Students see that the lit half faces the lamp and the dark half faces away - the darkness is the ball's own unlit hemisphere, not a shadow cast onto it. Rotate the ball about 40° and the lit fraction shrinks to a crescent whose horns point away from the lamp, matching the Moon's orientation relative to the Sun. Then have a student stand between lamp and ball to cast a genuine shadow, and show that the shadow falls on the far side, opposite the lamp. The contrast between 'unlit half' and 'shadow cast on the far side' is the whole argument.
3. Suppose the club repeats the session at the same 8:10 p.m. time exactly one week after the chosen Monday. Predict what would be visible, and justify the prediction from the phase cycle.
Read the worked answer
On Monday the Moon is 12% illuminated, which corresponds to a waxing crescent roughly 3–4 days after new. Seven days later the Moon is roughly 10–11 days after new, so the illuminated fraction should be about 85% - a waxing gibbous, not a crescent. Because the Moon rises later each day by roughly 50 minutes, a gibbous Moon that is 10–11 days old rises in early-to-mid afternoon, so by 8:10 p.m. it would already be high in the south to southwest and well above the 12° tree line, and it would not set until well after midnight. In practical terms the one-week-later session is easier, not harder: the target is higher, brighter, and lasts past the bus departure.
The observer should also predict the orientation of the bright limb: it still faces the Sun, which by 8:10 p.m. is below the western horizon, so the western limb is illuminated. The pedagogical point is that phase and position in the sky are linked through elongation from the Sun, so a club that logs altitude, illuminated fraction, and moonset each week accumulates a data set from which students can reconstruct the phase cycle rather than memorize it.