Practice: Logic & Calculations

The 50-Minute Delay

Observation: You noticed in the chapter that the Moon rises about 50 minutes later every day. Why?

The Physics:

1. Earth rotates $360^\circ$ in 24 hours.
2. While Earth rotates, the Moon revolves around Earth in the same direction.
3. In 24 hours, the Moon moves about $12^\circ$ to $13^\circ$ in its orbit.
4. So, when Earth completes one full rotation (360 degrees), the Moon is no longer in the same spot—it has moved ahead!
5. Earth has to rotate an extra $13^\circ$ to catch up to the Moon.

The Math:

• Earth rotates $360^\circ$ in $1440$ minutes (24 hrs).
• Speed of rotation: $1440 / 360 = 4$ minutes per degree.
• Extra rotation needed: $\approx 12.5^\circ$.
• Time taken: $12.5^\circ \times 4 \text{ min/degree} = 50$ minutes.

Conclusion: That is why Moonrise is delayed by 50 minutes daily.

Activity Analysis: Shadow Sticks (Activity 11.3)

Goal: Find the shortest shadow to determine “Local Noon”.

Procedure:

1. Place a stick vertically on flat ground.
2. Mark the tip of the shadow every 10 minutes from 11:00 AM to 1:00 PM.
3. Measure the length of the shadow at each mark.

Outcome:

• The shadow is longest in the morning and evening.
• The shadow is shortest exactly when the Sun is at its highest point in the sky.
• This moment is Local Noon. It might not be exactly 12:00 PM on your watch (which follows Standard Time for the whole country).