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Answer :
a) the mean value of r, the average distance between Earth and the Sun, is 149,600,000 km.
b) the mean velocity of Earth is approximately 9,473 km/s.
(a) The mean value of r, or the mean distance between Earth and the Sun, can be calculated by finding the average of the perihelion and aphelion distances.
To calculate the mean value of r:
1. Add the perihelion and aphelion distances together: 147,100,000 km + 152,100,000 km = 299,200,000 km.
2. Divide the sum by 2 to find the average: 299,200,000 km / 2 = 149,600,000 km.
Therefore, the mean value of r, the average distance between Earth and the Sun, is 149,600,000 km.
(b) The mean velocity of Earth can be calculated using the formula for the average speed of an object over a given distance and time.
To calculate the mean velocity of Earth:
1. Determine the total distance traveled by Earth during one complete orbit. This can be found by adding the perihelion and aphelion distances together: 147,100,000 km + 152,100,000 km = 299,200,000 km.
2. Determine the time it takes for Earth to complete one orbit around the Sun. This is approximately 365.25 days or 31,557,600 seconds.
3. Divide the total distance by the total time: 299,200,000 km / 31,557,600 s ≈ 9,473 km/s. Therefore, the mean velocity of Earth is approximately 9,473 km/s.
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