Key Points

A mean solar day is defined as 24 hours. A lunar month, the cycle of the Moon's phases, is approximately 29.5 days. A solar year, the cycle of seasons, is approximately 365.25 days.

A lunar year consists of 12 lunar months. Its total length is calculated as $12 \times 29.5 = 354$ days, which is based on the Moon's cycles.

A lunar year ($354$ days) is shorter than a solar year ($365$ days). The difference is approximately $365 - 354 = 11$ days each year.

To account for the extra quarter day in a solar year ($365.25$ days), a leap year with an extra day (February 29) is added every 4 years. A year is generally a leap year if it is divisible by 4.

For greater accuracy in solar calendars, a century year is not a leap year unless it is also divisible by 400. For example, the year 1900 was not a leap year, but the year 2000 was.

Luni-solar calendars add an extra month, known as an intercalary month or 'Adhika Maasa', to reconcile the 11-day annual difference between the lunar and solar years. This keeps festivals aligned with the seasons.

The lunar year falls short by about 11 days annually. This accumulates to nearly one full month ($\approx 30$ days) every 2 to 3 years, which is when the extra month is added.

The Moon rises approximately 50 minutes later each day. This consistent delay is because the Moon moves in its orbit around the Earth while the Earth rotates.

The phases of the Moon are a result of our viewing angle of the Moon's sunlit portion as it revolves around the Earth. They are not caused by the Earth's shadow falling on the Moon.

A lunar eclipse can only occur on a full Moon day, and a solar eclipse can only occur on a new Moon day. They are rare because the Moon's orbit is tilted with respect to Earth's orbit.

A sidereal year (Earth's orbit relative to stars) is about 20 minutes longer than a tropical year (time between two spring equinoxes). Most modern calendars, like the Gregorian, are based on the tropical year to stay synchronized with seasons.

Festivals based on sidereal calendars slowly shift dates in a tropical calendar. For example, Makar Sankranti's date moves forward by 1 day approximately every 71 years.

Artificial satellites in low Earth orbit complete one full orbit around the Earth in a relatively short and periodic time, typically around 100 minutes.