Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 31

Two satellites are in circular orbits around Jupiter. One, with orbital radius \(r,\) makes one revolution every \(16 \mathrm{h}\) The other satellite has orbital radius \(4.0 r .\) How long does the second satellite take to make one revolution around Jupiter?

Short Answer

Expert verified
Answer: The period of the second satellite is 128 hours.

Step by step solution

01

Write down the given information

The first satellite has an orbital radius r and a period of 16 hours. The second satellite has an orbital radius of 4.0r. We want to find the period (T) of the second satellite.
02

Use Kepler's Third Law

Kepler's Third Law states that \(\frac{T^2_1}{T^2_2} = \frac{r^3_1}{r^3_2}\).
03

Substitute the known values

Substitute the values for the first satellite into the equation: \(\frac{(16 \ \text{h})^2}{T^2_2} = \frac{(r)^3}{(4.0r)^3}\)
04

Simplify the equation

Simplify the equation to find the period of the second satellite: \(\frac{256 \ \text{h}^2}{T^2_2} = \frac{r^3}{64r^3}\)
05

Solve for the period of the second satellite

Cancel out the \(r^3\) on both sides of the equation and solve for \(T_2\): $\frac{256 \ \text{h}^2}{T^2_2} = \frac{1}{64} \\ T^2_2 = 256 \ \text{h}^2 \times 64 \\ T^2_2 = 16384 \ \text{h}^2 \\ T_2 = \sqrt{16384 \ \text{h}^2} \\ T_2 = 128 \ \text{h}$
06

State the answer

The second satellite takes 128 hours to make one revolution around Jupiter.

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

During normal operation, a computer's hard disk spins at 7200 rpm. If it takes the hard disk 4.0 s to reach this angular velocity starting from rest, what is the average angular acceleration of the hard disk in $\mathrm{rad} / \mathrm{s}^{2} ?$
Centrifuges are commonly used in biological laboratories for the isolation and maintenance of cell preparations. For cell separation, the centrifugation conditions are typically \(1.0 \times 10^{3}\) rpm using an 8.0 -cm-radius rotor. (a) What is the radial acceleration of material in the centrifuge under these conditions? Express your answer as a multiple of \(g .\) (b) At $1.0 \times 10^{3}$ rpm (and with a 8.0-cm rotor), what is the net force on a red blood cell whose mass is \(9.0 \times 10^{-14} \mathrm{kg} ?\) (c) What is the net force on a virus particle of mass \(5.0 \times 10^{-21} \mathrm{kg}\) under the same conditions? (d) To pellet out virus particles and even to separate large molecules such as proteins, superhigh-speed centrifuges called ultracentrifuges are used in which the rotor spins in a vacuum to reduce heating due to friction. What is the radial acceleration inside an ultracentrifuge at 75000 rpm with an 8.0 -cm rotor? Express your answer as a multiple of \(g\).
A velodrome is built for use in the Olympics. The radius of curvature of the surface is \(20.0 \mathrm{m}\). At what angle should the surface be banked for cyclists moving at \(18 \mathrm{m} / \mathrm{s} ?\) (Choose an angle so that no frictional force is needed to keep the cyclists in their circular path. Large banking angles are used in velodromes.)
Grace, playing with her dolls, pretends the turntable of an old phonograph is a merry-go-round. The dolls are \(12.7 \mathrm{cm}\) from the central axis. She changes the setting from 33.3 rpm to 45.0 rpm. (a) For this new setting, what is the linear speed of a point on the turntable at the location of the dolls? (b) If the coefficient of static friction between the dolls and the turntable is \(0.13,\) do the dolls stay on the turntable?
A curve in a stretch of highway has radius \(R .\) The road is unbanked. The coefficient of static friction between the tires and road is \(\mu_{s} .\) (a) What is the fastest speed that a car can safely travel around the curve? (b) Explain what happens when a car enters the curve at a speed greater than the maximum safe speed. Illustrate with an FBD.
See all solutions

Recommended explanations on Physics Textbooks

Quantum Physics

Read Explanation

Radiation

Read Explanation

Circular Motion and Gravitation

Read Explanation

Medical Physics

Read Explanation

Fluids

Read Explanation

Oscillations

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