Question: A telescope captures light from a star that appears every 11 days. If observations began on day 1, on which day will the 20th observation occur? - Imagemakers
Why a Star’s 20th Appearance Falls on Day 220: A Simple Look at Celestial Cycles
Why a Star’s 20th Appearance Falls on Day 220: A Simple Look at Celestial Cycles
Ever wondered when deep-sky observations align with a periodic celestial event? Take a star visible every 11 days—like a quiet cosmic rhythm. Starting on day one, tracking each appearance calculates a pattern — not just for curiosity, but for timing scientific observation or planning sky-gazing moments. So, on which day will the 20th observation take place?
When a star appears every 11 days and observations begin on day 1, each occurrence follows a steady count. The first is day 1, the second day 1 + 11 = day 12, the third day 23, and so on. This repeats: day numbers follow the formula: 1 + 11 × (n – 1). For the 20th observation, plug in n = 20.
Understanding the Context
Mathematically: Day = 1 + 11 × (20 – 1) = 1 + 11 × 19 = 1 + 209 = 210.
Wait—day 210? Actually, no. Because the 1st observation is counted as day 1, not 0. So day 20 is day 1 + (19 increments of 11) = 1 + 209 = 210. Yet the star’s repeating cycle means surge signals appear every 11 days, not 11 after each. Correctly, each sighting lands on day numbers: 1, 12, 23, 34, etc. So for the 20th, it’s 1 + 11×19 = 210. But wait—this assumes day 1 counts as the first appearance. Let’s clarify:
If day 1 is the first observation, and the star recurs every 11 days, then:
Observation 1 → day 1
Observation 2 → day 1 + 11 = 12
Observation 3 → 1 + 22 = 23
Observation n → day: 1 +
