Log out Go to App
Go to App

Learning Materials

Features

Discover

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 × 10^-3 m/s².

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 ≈ 1.496 × 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 = (2πr) / 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 × 24 hours/day × 60 minutes/hour × 60 seconds/minute ≈ 3.156 × 10^7 seconds Now, plug in the values to find the speed: v = (2π × 1.496 × 10^11 meters) / (3.156 × 10^7 seconds) ≈ 2.978 × 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 × 10^4 m/s)^2 / (1.496 × 10^11 meters) ≈ 5.932 × 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 × 10^-3 m/s².

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A ball having a mass of \(1.00 \mathrm{~kg}\) is attached to a string \(1.00 \mathrm{~m}\) long and is whirled in a vertical circle at a constant speed of \(10.0 \mathrm{~m} / \mathrm{s}\) a) Determine the tension in the string when the ball is at the top of the circle. b) Determine the tension in the string when the ball is at the bottom of the circle. c) Consider the ball at some point other than the top or bottom. What can you say about the tension in the string at this point?

A penny is sitting on the edge of an old phonograph disk that is spinning at 33 rpm and has a diameter of 12 inches. What is the minimum coefficient of static friction between the penny and the surface of the disk to ensure that the penny doesn't fly off?

A car accelerates uniformly from rest and reaches a speed of \(22.0 \mathrm{~m} / \mathrm{s}\) in \(9.00 \mathrm{~s}\). The diameter of a tire on this car is \(58.0 \mathrm{~cm}\). a) Find the number of revolutions the tire makes during the car's motion, assuming that no slipping occurs. b) What is the final angular speed of a tire in revolutions per second?

Calculate the centripetal force exerted on a vehicle of mass \(m=1500 .\) kg that is moving at a speed of \(15.0 \mathrm{~m} / \mathrm{s}\) around a curve of radius \(R=400 . \mathrm{m} .\) Which force plays the role of the centripetal force in this case?

A small block of mass \(m\) is in contact with the inner wall of a large hollow cylinder. Assume the coefficient of static friction between the object and the wall of the cylinder is \(\mu\). Initially, the cylinder is at rest, and the block is held in place by a peg supporting its weight. The cylinder starts rotating about its center axis, as shown in the figure, with an angular acceleration of \(\alpha\). Determine the minimum time interval after the cylinder begins to rotate before the peg can be removed without the block sliding against the wall.
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Measurements

Read Explanation

Medical Physics

Read Explanation

Oscillations

Read Explanation

Waves Physics

Read Explanation

Atoms and Radioactivity

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free