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A 425 kg satellite is orbiting two earth radii from the center of the earth. Calculate...

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andrewmezzo | Student | Valedictorian

Posted November 26, 2012 at 2:14 AM via web

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A 425 kg satellite is orbiting two earth radii from the center of the earth. Calculate the gravitational force and the magnitude of the satellite's acceleration.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted November 26, 2012 at 3:26 AM (Answer #1)

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The mass of the Earth is `5.97219*10^24` kg and the radius of the Earth is `6378.1*10^3` m.

The force of gravitational attraction between two objects with mass m1 and m2 and at a distance r from each other is `F = m1*m2*G/r^2` where G is a constant equal to `6.673*10^-11` m^3*kg^-1*s^-2.

It is given that the 425 kg satellite is 2 Earth radii away from it. The force of gravitational attraction between the two is `(6.67300*10^-11*5.97219*10^24*425)/(2*6378.1*10^3)^2` = 1040.88 N

The magnitude of the satellite's acceleration is `1040.88/425` = 2.44 m/s^2

 

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