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

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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 $4.18 h o u r s .$

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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

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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

Turning Points in Physics

Rotational Dynamics

Scientific Method Physics

Further Mechanics and Thermal Physics

Oscillations

Nuclear Physics

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?