Midnight Sun Area Ratio When the Earth’s Axial Tilt Changes

Concept Used

The regions experiencing the Midnight Sun lie beyond the polar circles. If the Earth’s axis makes an angle α with the plane of the ecliptic, then the latitude of the polar circle is also α.

The area of one polar cap extending from latitude L to the pole is

A = 2πR²(1 − sin L)

Since both polar regions are considered over a full year, the factor of 2 cancels when taking the ratio.

Step 1: Previous Midnight Sun Area

Initially,

L₁ = 66.5°

Therefore,

A₁ ∝ (1 − sin66.5°)

Step 2: New Midnight Sun Area

After the axis changes,

L₂ = 50°

Therefore,

A₂ ∝ (1 − sin50°)

Step 3: Calculate the Ratio

The required ratio is

A₂/A₁ = (1 − sin50°)/(1 − sin66.5°)

Using

• sin50° ≈ 0.7660
• sin66.5° ≈ 0.9171

Hence,

A₂/A₁ = (1 − 0.7660)/(1 − 0.9171)

= 0.2340/0.0829

≈ 2.82

Physical Interpretation

Reducing the angle from 66.5° to 50° moves the polar circles much closer to the equator. As a result, a much larger portion of the Earth’s surface experiences 24-hour daylight during summer. Therefore, the Midnight Sun region increases significantly.

Final Answer

The ratio of the new area to the previous area is

2.82 (approximately)