Final answer:
The average speed of the Earth in its orbit around the Sun is approximately 30 kilometers per second, which equals 30,000 meters per second when converted.
Step-by-step explanation:
To calculate the average speed of the Earth in its orbit around the Sun, we will use the given average distance between the Earth and the Sun and the time it takes for the Earth to complete one orbit. The average distance between Earth and the Sun is 1.5 x 10¹¹ meters (which is about 150 million kilometers), and it takes Earth 1 year to complete an orbit. A year has approximately 3 x 10⁷ seconds.
Speed is calculated using the formula speed = distance/time. First, we calculate the circumference of Earth's orbit, which is 2πr where r is the radius of the orbit. Since the average distance between the Earth and the Sun (the radius) is 1.5 x 10¹¹ meters, the orbit's circumference is 2π x (1.5 x 10¹¹ meters).
Next, we divide this distance by the time it takes to complete one orbit to get the average speed:
Plugging in the values we get:
Average speed (V) = (2π x 1.5 x 10¹¹ meters) / (3 x 10⁷ seconds)
V = (9.42 x 10¹¹ meters) / (3 x 10⁷ seconds)
V ≈ 30 kilometers per second
To convert the average speed from kilometers per second to meters per second, we simply multiply by 1,000 (since 1 kilometer = 1,000 meters).
Average speed in meters per second = 30 km/s x 1,000 = 30,000 meters per second.