The average distance between Earth and the Sun is defined as 1 astronomical unit (AU), which is approximately 149.6 million kilometers (93 million miles). The Earth's orbit around the Sun is not a perfect circle but rather an ellipse, so the distance varies slightly throughout the year.
To calculate how many astronomical units Earth travels every year, we need to determine the circumference of Earth's orbit. The formula for the circumference of an ellipse is given by:
C = 2π * sqrt((a^2 + b^2) / 2)
Where: C = Circumference of the ellipse a = Semi-major axis of the ellipse (average distance from the Sun) b = Semi-minor axis of the ellipse
For Earth's orbit, the semi-major axis (a) is equal to 1 AU, and the semi-minor axis (b) is very close to the semi-major axis.
Using these values, we can calculate the circumference of Earth's orbit:
C = 2π * sqrt((1^2 + 1^2) / 2) C ≈ 2π * sqrt(1 / 2) C ≈ 2π * sqrt(0.5) C ≈ 2π * 0.707 C ≈ 4.44π
Therefore, Earth travels approximately 4.44π AU in its orbit around the Sun every year.
To determine how far Earth travels per second in miles or kilometers, we need to divide the yearly distance by the number of seconds in a year. There are 31,536,000 seconds in a standard year (365 days).
Distance per second = (4.44π AU) / (31,536,000 seconds)
Now we can convert this value to miles or kilometers by multiplying it by the conversion factor for AU.
Distance per second in miles ≈ (4.44π AU) * (93 million miles / 1 AU) / (31,536,000 seconds)
Distance per second in kilometers ≈ (4.44π AU) * (149.6 million kilometers / 1 AU) / (31,536,000 seconds)
Calculating these values gives:
Distance per second in miles ≈ 16.65 miles/second
Distance per second in kilometers ≈ 26.77 kilometers/second
Please note that these calculations provide approximate values due to the simplified assumptions made for the elliptical shape of Earth's orbit.