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For a satellite to orbit Earth at a constant distance, its centripetal acceleration
must be equal to Earth's gravitational acceleration. If a satellite is to orbit with
a constant circular radius of 7,500,000 m, what is the approximate required
velocity of the satellite? (Recall that Earth has a mass of 5.97 1024 kg and G
= 6.67 * 10-11 N·m²/kg?)
A. 6143 m/s
B. 8452 m/s
C. 7287 m/s
D. 6562 m/s

Sagot :

Newton's second law, the law of universal gravitation and the centripetal acceleration allows to find the correct answer for the question about the speed of the satellite is:

     c) The speed of satellite is: 7287 m/s

Law of Universal Gravitation and Newton's Second Law.

Newton's second law states that the force on a body is proportional to the product of the mass times the acceleration of the body and the attraction between the bodies is expressed in the law of universal gravitation

             F= ma

             F =[tex]G \frac{Mm}{r^2}[/tex]  

Where f is the force, m and M the mass of each body, the acceleration and r the distance between them.

Let's substitute.

         [tex]a= G \frac{M}{r^2}[/tex]  

The centripetal acceleration is the acceleration towards the center of the movement, it is given by the relation.

           [tex]a = \frac{v^2}{r}[/tex]  

Where a is  the acceleration, v is the tangential speed and r the radius of the circle

Let's substitute.

          [tex]G \frac{M}{r^2} = \frac{v^2}{r} \\v= \sqrt{\frac{GM}{r} }[/tex]

indicate that the radius of the orbit is r= 7500000m = 7.5 10⁶ m

Let's calculate.

         [tex]v= \sqrt{\frac{6.67 \ 10^{-11} \ 5.97 \ 10^{24 }} { 7.5 \ 10^6 } } \\v= \sqrt{53.093 \ 10^6}[/tex]

         v= 7,287 10³ m/s

When reviewing the answers, the correct result is:

    c)   the speed is:  7287 m/s

In conclusion using Newton's second law, the law of universal gravitation and the centripetal acceleration we can find the correct result for the question about the speed of the satellite is:

     c)   the speed is:  7287 m/s

Learn more about the law of universal gravitation and centripetal acceleration here:  brainly.com/question/14113448

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