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Chapter 9: Problem 65

What is the acceleration of the Earth in its orbit? (Assume the orbit is circular.)

Short Answer

Expert verified
Answer: The approximate acceleration of Earth in its orbit around the Sun is 5.932 脳 10^-3 m/s虏.

Step by step solution

01

Determine the radius of the Earth's orbit

The average distance from the Earth to the Sun, which represents the radius of the Earth's orbit, is approximately 93 million miles or 1 Astronomical Unit (AU). To use the centripetal acceleration formula, we should convert this distance to meters: 1 AU 鈮� 1.496 脳 10^11 meters
02

Find the Earth's orbital speed

The Earth takes about 365.25 days to complete one orbit around the Sun. To find the speed (v), we can use the formula: v = (2蟺r) / T, where r is the radius of the Earth's orbit and T is the period of revolution (time taken for one complete orbit). First, convert the time to seconds: 365.25 days 脳 24 hours/day 脳 60 minutes/hour 脳 60 seconds/minute 鈮� 3.156 脳 10^7 seconds Now, plug in the values to find the speed: v = (2蟺 脳 1.496 脳 10^11 meters) / (3.156 脳 10^7 seconds) 鈮� 2.978 脳 10^4 m/s
03

Calculate the centripetal acceleration

Now that we have the radius of the Earth's orbit (r) and its orbital speed (v), we can use the centripetal acceleration formula: a = v^2 / r Plug in the values to find the acceleration: a = (2.978 脳 10^4 m/s)^2 / (1.496 脳 10^11 meters) 鈮� 5.932 脳 10^-3 m/s^2
04

Express the result

The acceleration of the Earth in its orbit, assuming it is circular, is approximately 5.932 脳 10^-3 m/s虏.

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Most popular questions from this chapter

A carousel at a carnival has a diameter of \(6.00 \mathrm{~m}\). The ride starts from rest and accelerates at a constant angular acceleration to an angular speed of 0.600 rev/s in \(8.00 \mathrm{~s}\). a) What is the value of the angular acceleration? b) What are the centripetal and angular accelerations of a seat on the carousel that is \(2.75 \mathrm{~m}\) from the rotation axis? c) What is the total acceleration, magnitude and direction, \(8.00 \mathrm{~s}\) after the angular acceleration starts?

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A point on a Blu-ray disc is a distance \(R / 4\) from the axis of rotation. How far from the axis of rotation is a second point that has, at any instant, a linear velocity twice that of the first point? a) \(R / 16\) b) \(R / 8\) c) \(R / 2\) d) \(R\)

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