Final answer:
The average speed of Earth in its orbit around the sun is calculated using the circumference of Earth’s orbit and the orbital period. After converting the orbital period from days to seconds, and using the formula for circumference, the calculated average speed is approximately 29.5 km/s.
Step-by-step explanation:
The student is asking about the average speed of the Earth in its orbit around the sun. To calculate this, we need the circumference of the orbit (which is a circle with the given average radius of 1.5×10¸ km) and the time it takes to complete one orbit, which is approximately 365 days. Using the formula for the circumference of a circle (C = 2πr), we can find the total distance traveled in one year. The speed is then the total distance divided by the time taken to cover that distance. First, convert 365 days into seconds (since speed is often measured in km/s):
365 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 31,536,000 seconds. Now, calculate the circumference using the radius: C = 2π×1.5×10¸ km = 9.42×10¸ km. Finally, divide the circumference by the time in seconds to get the speed: 9.42×10¸ km / 31,536,000 s ≈ 29.85 km/s. The average speed of the Earth around the sun is therefore approximately 29.8 km/s, which rounds to 29.5 km/s when considering significant figures, making option 2 the closest answer.