Earth and Space - The Earth, Moon, and Sun Cycles

Explain why a 'Leap Year' occurs every four years in the Gregorian calendar.

A leap year adds one extra day ($366$ days total) to the calendar every four years.

Since the Earth takes approximately $365.25$ days to orbit the Sun, the $0.25$ day is ignored for three years. In the fourth year, these fractions are summed: $0.25 + 0.25 + 0.25 + 0.25 = 1.0$ day. This ensures the calendar remains synchronized with the Earth's astronomical seasons.

During which season is the Northern Hemisphere tilted away from the Sun, and what is the effect on daylight hours?

The Northern Hemisphere is tilted away from the Sun during the Winter Solstice (around December 21st).

When the Northern Hemisphere is tilted at $-23.5^\circ$ relative to the Sun's direct rays, the Sun appears lower in the sky. This results in shorter daylight hours and less concentrated solar energy per unit area, leading to colder temperatures.

Calculate the approximate orbital speed of the Earth if its average distance from the Sun ($r$) is $1.5 \times 10^8 \text{ km}$ and the period ($T$) is $365$ days.

$v \approx 107,000 \text{ km/h}$

Using the formula $v = \frac{2\pi r}{T}$, where $r = 150,000,000 \text{ km}$ and $T = 365 \times 24 \text{ hours} = 8760 \text{ hours}$. Substituting the values: $v = \frac{2 \times 3.14159 \times 1.5 \times 10^8}{8760} \approx 107,589 \text{ km/h}$.