Geodesy and Celestial Mechanics

The Moon is approximately 4.53 billion years old, formed shortly after Earth's formation from debris after a Mars-sized body impacted early Earth (the Giant Impact Hypothesis). Lunar samples brought back by Apollo missions have been radiometrically dated to confirm this age. The Moon formed within about 50 million years after the Solar System's formation.

Earth completes one rotation on its axis in approximately 24 hours, creating day and night. The 365-day figure refers to revolution around the sun.

Mercury completes one orbit around the Sun in approximately 88 Earth days, which is the shortest orbital period of any planet in our solar system. This is because Mercury is the closest planet to the Sun and experiences the strongest gravitational pull, causing it to orbit at the highest velocity among all planets.

Biosphere is the odd one out because it refers specifically to the zone of life on Earth - all living organisms and their interactions. The other three (atmosphere, hydrosphere, lithosphere) are abiotic physical spheres that make up Earth's systems regardless of life presence.

Aryabhatta calculated the Earth's circumference as approximately 24,835 miles (or 4,967 yojanas in ancient Indian units), which is remarkably close to the modern value of 24,901 miles. This demonstrates the sophistication of ancient Indian astronomy and mathematics.

The Astronomical Unit (AU) is defined as the average distance between Earth and Sun, approximately 149.6 million kilometers (93 million miles). It is the standard unit for measuring distances within our solar system. A light-year is the distance light travels in one year (about 63,241 AU). 'Astronomy Unit' is not the correct term.

The Prime Meridian is a longitude line (0°) running from north to south pole, while the Equator, Tropic of Cancer, and Tropic of Capricorn are all latitude lines running east-west. The Prime Meridian is the only longitudinal reference line among the options.

Earth completes one rotation relative to the fixed stars in 23 hours, 56 minutes, and 4 seconds, called a sidereal day. This is slightly less than 24 hours due to Earth's orbital motion.

Earth rotates from West to East (counterclockwise when viewed from above the North Pole). This is why the Sun appears to rise in the East and set in the West. The rotation Eastward causes celestial bodies to appear to move Westward.

A light year is the distance light travels in one year. Since light travels at 299,792,458 m/s, in one year it covers approximately 9.46 trillion kilometers.

Uranus takes approximately 84 Earth years to complete one orbit around the Sun. This long orbital period is due to Uranus's great distance from the Sun - about 2.9 billion km (19.2 AU) at its average distance.

Jupiter takes approximately 11.9 Earth years (about 4,333 days) to complete one revolution around the Sun. This matches option D. Jupiter's long orbital period is due to its large average distance from the Sun - about 5.2 AU or 778 million km.

Earth's sidereal rotation period is 23h 56m 4.09 seconds - the time to rotate 360° relative to fixed stars. This differs from the solar day (24h) because Earth orbits the Sun, requiring slightly more rotation to face the Sun again. Option C incorrectly states 57 minutes instead of 56.

Neptune takes approximately 165 Earth years to complete one orbit around the Sun. This long orbital period is due to its great distance from the Sun.

Pluto's average distance from the Sun is about 5.9 billion km, which matches 5865.6 million km. This is at the Kuiper Belt's edge.