Final answer:
Earth's average speed in orbit around the Sun is approximately 29,800 m/s. Over the period of a year, Earth returns to its starting point, resulting in an average velocity of 0 m/s since there is no net displacement. the correct answer is a) (a) 29,800 m/s, (b) 0 m/s.
Step-by-step explanation:
To calculate Earth’s average speed relative to the Sun, we use the formula for speed, which is distance divided by time.
Given that the average distance of Earth’s orbit around the Sun (which can be approximated as circular) is 1.5 × 10¹¹ meters and knowing that one complete orbit takes one year, we can calculate Earth's average speed by considering the circumference of the orbit (2πr, where r is the radius of the orbit) and the time period of one year.
(a) The average speed of Earth in its orbit is calculated as follows: Average speed = Total distance / Total time = 2π × (1.5 × 10¹¹ m) / 1 year. To get the speed in meters per second, we need to convert the time period to seconds (1 year = 365.25 days, 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds). The approximate average speed is 29,800 meters per second.
(b) The average velocity of Earth over a period of one year is 0 meters per second because velocity is a vector quantity that includes direction. Since Earth returns to its starting point after one year, the displacement is zero, and therefore, the average velocity is zero.
The correct answer to the problem is (a) 29,800 m/s, (b) 0 m/s.