Geodesy and Celestial Mechanics

A great circle is the largest possible circle that can be drawn on a sphere, whose plane passes through the center of the sphere. The Equator is the only line of latitude that forms a great circle because it lies in Earth's equatorial plane. All other latitudes are smaller circles.

The International Date Line roughly follows the 180° meridian of longitude, which is directly opposite the Prime Meridian (0°). While it zigzags to avoid dividing land areas and island groups, the 180° meridian represents its theoretical position. The 0°, 90°, and 100° meridians are all far from the Date Line.

The boundary line between USA and Canada is known as 49^th parallel. 

The Sun's diameter is approximately 109 times that of Earth. This means you could fit about 1.3 million Earths inside the Sun by volume. The Sun accounts for 99.86% of the total mass in our solar system.

Earth completes one revolution around the Sun in approximately 365.25 days. We use 365 days for simplicity, adding a leap day every 4 years to account for the quarter day. The exact orbital period is 365 days, 5 hours, 48 minutes, and 45 seconds.

Earth's radius is approximately 6,400 km, making its diameter about 12,800 km. Earth is nearly spherical but slightly flattened at the poles. This measurement is crucial for understanding Earth's size relative to other planets and for calculations involving gravity and orbital mechanics.

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Due to the centrifugal force generated by the earth's rotation, the planet bulges slightly at the equator. The equatorial circumference is about 40,075 km, while the polar circumference is about 40,008 km, giving a difference of roughly 75 km.

At the equator, days and nights are approximately equal (12 hours each) throughout the year because the equator always receives 12 hours of daylight and 12 hours of darkness due to Earth's geometry and axial tilt.

Of the solar radiation reaching Earth's atmosphere, about 51% reaches the surface. The atmosphere absorbs approximately 19% and clouds reflect about 30% back to space. This percentage is crucial for understanding Earth's energy balance and climate system.

Because the Earth is a sphere that rotates on its axis, points along the Equator travel the greatest linear distance in a single 24-hour rotation, resulting in the highest rotational speed. As you move toward the poles, the radius of rotation decreases, reducing the linear speed to zero at the poles.

Jupiter's diameter is approximately 11 times that of Earth (about 140,000 km vs 12,750 km). This makes Jupiter about 10 times larger than Earth in linear dimensions. In terms of volume, Jupiter is over 1,300 times larger than Earth due to the cube of the radius in volume calculation.

At the equator, Earth's rotational speed is approximately 1,670 km/hr. At 45° latitude, we multiply this by the cosine of 45° (approximately 0.707), giving about 1,180 km/hr. The closest option is 1,120 km/hr, which accounts for the precise calculation including the fact that 45° latitude has a smaller circumference than the equator.