Question 15 - Figure it out - Page 127-132 - Chapter 5 Class 8 - Tales by Dots and Lines (Ganita Prakash II)

Transcript

Question 15 We all know the typical sunrise and sunset timings. Do you know when the moon rises and sets? Does it follow a regular pattern like the sun? Let’s find out. The following graph shows the moonrise and moonset time over a month: (i) Find out on what dates amavasya (new moon) and purnima (full moon) were in this month.The Rule of the Moon A full moon (Purnima) sits exactly opposite the sun, meaning it rises right as the sun is setting (around 18:00). A new moon (Amavasya) sits right next to the sun, meaning it rises and sets at the exact same time the sun does (rising near 06:00 and setting near 18:00). Finding Purnima Look at the yellow line (moonrise). When does it hit the 18:00 mark? It crosses 18:00 exactly on Day 15. Finding Amavasya Look at the yellow line again. When does it hit the 06:00 morning mark? It crosses 06:00 exactly on Day 30. (You can also verify this by checking the blue moonset line for Day 30, which hits exactly at 18:00!) Question 15 (ii) What do you notice? What do you wonder?Notice The lines form perfect diagonal staircases that repeat themselves. The moon does not rise at the same time every day. Instead, the yellow line creeps higher and higher up the graph. Wonder By looking at the grid, you can wonder (and mathematically prove!) exactly how much the moon is delayed each day. Because the line travels a full 24 hours (from 00:00 to 24:00) over roughly 29.5 days, it gets delayed by about 50 minutes every single day. That is why the lines slope upward!