The average distance between Earth and the sun is 1.50e8 km.
Calculate the average speed, in km/h, of Earth assuming a circular path about the sun. Use the equations v = 2r/T.
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To calculate the average speed of Earth, we can use the equation v = 2πr / T, where v represents the average speed, r is the average distance between Earth and the sun, and T is the period of Earth's orbit (i.e., the time it takes for Earth to complete one revolution around the sun).
Given that the average distance between Earth and the sun is 1.50e8 km, and assuming a circular path, we can use this value as the radius (r) of Earth's orbit.
The period of Earth's orbit can be calculated using the formula T = 2π / ω, where T is the period, and ω is Earth's angular velocity. The angular velocity, ω, can be found using the relation ω = 2π / T', where T' is the time it takes for Earth to complete one rotation on its axis (which is approximately 24 hours).
First, let's calculate ω:
ω = 2π / T' = 2π / 24 hours = π / 12 hours
Now that we have the angular velocity, we can calculate the period of Earth's orbit:
T = 2π / ω = 2π / (π / 12 hours) = 24 hours
Now, we have the values needed to calculate the average speed:
v = 2πr / T = 2π(1.50e8 km) / (24 hours)
≈ 3.14(1.50e8 km) / 24 hours
≈ 4.71e8 km / 24 hours
≈ 1.96e7 km/h
Therefore, the average speed of Earth on its circular orbit around the sun is approximately 1.96e7 km/h.