Q. 30 An earth satellite moves in a ci... [FREE SOLUTION]

91影视

Chapter 13: Q. 30 (page 354)

An earth satellite moves in a circular orbit at a speed of $5500 m / s$ . What is its orbital period?

Short Answer

Expert verified

The orbital period is $4.18 h o u r s .$

Step by step solution

Given information

Speed of orbiting = $4.18 h o u r s .$

Calculation

The centripetal acceleration required for circular motion of satellite is provided by the gravitational force between the satellite and the earth, therefore : $G M_{e} m_{s} / r_{s}^{2} = m_{s} v_{s}^{2} / r_{s}$

Here, $M_{e}$ is the mass of earth, $m_{s}$ is the mass of satellite, G is the gravitational constant, r is the radius of the orbit.

Now solving we get,

$G M_{e} m_{s} / r_{s}^{2} = m_{s} v_{s}^{2} / r_{s} r_{s} = G M_{e} / v_{s}^{2} r_{s} = \frac{(6.67 脳 10^{- 11} N m^{2} / k g^{2}) (5.98 脳 10^{24} k g)}{{(5500 m / s)}^{2}} r = 13.18 脳 10^{6} m$

Orbital period T is given by according to Kepler's Law :

$T = 2 蟺 \sqrt{\frac{r_{s}^{3}}{G M_{e}}} T = 2 蟺 \sqrt{\frac{{(13.18 脳 10^{6} m)}^{3}}{(6.67 脳 10^{- 11} N m^{2} / k g^{2}) (5.98 脳 10^{24} k g)}} T = 2 蟺 \sqrt{5740096.7 s^{2}} T = 2 蟺脳 2395.84 s T = 15053 \sec T = 4.18 hours$

Therefore, time period = $4.18 h o u r s .$

Final answer

The orbital period is $4.18 h o u r s .$

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

An earth satellite moves in a circular orbit at a speed of $5500 m / s$ . What is its orbital period?

Short Answer

Step by step solution

Given information

Calculation

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Physics of Motion

Classical Mechanics

Thermodynamics

Geometrical and Physical Optics

Electric Charge Field and Potential

Study anywhere. Anytime. Across all devices.

91影视

An earth satellite moves in a circular orbit at a speed of 5500m/s. What is its orbital period?

Short Answer

Step by step solution

Given information

Calculation

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Physics of Motion

Classical Mechanics

Thermodynamics

Geometrical and Physical Optics

Electric Charge Field and Potential

Study anywhere. Anytime. Across all devices.

An earth satellite moves in a circular orbit at a speed of $5500 m / s$ . What is its orbital period?