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Using the average distance of Earth from the Sun, and the orbital period of Earth, find the centripetal acceleration of Earth in its motion about the Sun. Compare this value to that of the centripetal acceleration at the equator due to Earth’s rotation.

a) Higher, Higher
b) Higher, Lower
c) Lower, Higher
d) Lower, Lower

User Arvil
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1 Answer

6 votes

Final answer:

The centripetal acceleration of Earth in its orbit around the Sun is lower than the centripetal acceleration at the equator due to Earth's rotation.

Step-by-step explanation:

To calculate the centripetal acceleration of Earth in its orbit around the Sun, we can use the formula ac = v2 / r, where ac is the centripetal acceleration, v is the orbital velocity, and r is the radius of the orbit. The average distance from Earth to the Sun (the radius of Earth's orbit) is approximately 149.6 million kilometers (1 AU), and the orbital period is about 365.25 days. The orbital velocity v can be found using v = 2πr / T, where T is the orbital period in seconds.

Once we have the orbital velocity, we square it and divide by the radius (converted to meters) to find the centripetal acceleration. To compare it with the centripetal acceleration at the equator due to Earth's rotation, we consider that the equatorial radius of the Earth is about 6378 km and the rotation period is 24 hours. We can find the equatorial speed using a similar formula and then calculate the centripetal acceleration.

After performing the calculations, it is found that the centripetal acceleration due to Earth's rotation at the equator is higher than the centripetal acceleration of Earth in its orbit around the Sun. The correct answer would therefore be (b) Higher, Lower.

User Dougiebuckets
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