Chapter 12 Solutions — Earth, Moon and the Sun

The stars appear to move across the sky each night because of the Earth's rotation. However, because the Earth also revolves around the Sun, the Earth moves slightly along its orbit each day.

This means the Earth completes a full rotation relative to the stars (a sidereal day) in about 23 hours 56 minutes, which is approximately 4 minutes less than a solar day (24 hours).

Aryabhata's value for one full rotation of the Earth (given in the textbook) is 23 hours 56 minutes 4.1 seconds — very close to the accepted sidereal day.

As a result, stars appear to rise approximately 4 minutes earlier each successive day.

Calculation: 24 hours × 60 min = 1440 min (solar day); sidereal day ≈ 23 × 60 + 56 = 1436 min; difference ≈ 4 minutes.

So Orion, which was overhead at 8:00 PM yesterday, will be overhead approximately 4 minutes earlier today.

8:00 PM − 4 minutes = 7:56 PM.

Because stars appear to rise about 4 minutes earlier each day (due to the Earth's revolution around the Sun), over the course of one full year the accumulated difference is approximately 4 min × 365 days = 1460 minutes ≈ 24 hours = 1 full day.

This means after exactly one year (one complete revolution of the Earth around the Sun), the same group of stars will again rise at the same time of night — midnight.

Since the Earth completes one revolution in about 365 days (and 6 hours, rounded to 365.25 days), the same stars rising at midnight on 21 June will next rise at midnight on approximately 21 June of the following year.

More precisely, the pattern repeats annually because one revolution restores the Earth to the same position in its orbit relative to the Sun and the background stars.

The textbook clearly warns: 'Directly viewing solar eclipse must be strictly avoided. Also, do not view it through sunglasses, binoculars, or telescopes,' and states that the Sun is intense enough to damage the eyes and cause blindness even during an eclipse.

(i) Ravikiran used a solar eclipse goggle — this is a specialised, safe method of viewing a solar eclipse. He was being careful.

(ii) Jyothi used a mirror to project the Sun's image onto a screen — this is a safe indirect viewing method described in the textbook. She was being careful.

(iii) Adithya saw the Sun directly with his eyes — this is dangerous and explicitly warned against in the textbook. He was being careless.

(iv) Aruna attended a programme arranged by a planetarium — the textbook recommends this: 'Participating in such events is the best way to observe a solar eclipse since the organisers not only provide specialised eye protection for solar viewing, but also offer scientific explanations.' She was being careful.