Final answer:
To calculate Earth's average speed in its orbit, you find the circumference of its orbit (C) using the formula C = 2πr where r is the average distance from Earth to the Sun, then divide that by the time it takes for one orbit. The average speed of Earth in its orbit around the Sun is approximately 29.5 kilometers per second.
Step-by-step explanation:
The average distance between Earth and the Sun is 150 million kilometers (1 AU), which is 1.5 x 1011 meters. Earth takes one year (approximately 3 x 107 seconds) to complete one orbit around the Sun. To calculate the average speed of Earth in its orbit, we use the formula for speed (v) = distance (d) / time (t).
First, we find the circumference of Earth's orbit by using the formula C = 2πr, with r being the average distance (radius) from Earth to the Sun. So we get C = 2π(1.5 x 1011 m). Then, we divide the circumference by the orbital period:
C = 2π(1.5 x 1011 m) = 9.42 x 1011 m
v = C / t = (9.42 x 1011 m) / (3 x 107 seconds)
This calculation gives us an average speed of approximately 29.5 kilometers per second (29,500 m/s), which is Earth's orbital speed around the Sun.