Newton's constant of gravitation  G is 6.67×10-11 in the system of units we use with mass in kilograms, length in meters, and time in seconds.  The radius of Earth is approximately 6.378 ×106 m, and its mass is  5.97 × 1024 kg.  With all this you can evaluate conservation of energy from Earth's surface and find an escape velocity of about 11.2 km/s from   Now suppose we wanted to orbit a spacecraft in low Earth orbit just a few hundred km above the surface.  How fast would it have to go to stay in a circular orbit?       7.9 km/s, that is about 11.2 / √2.     11.2, the same as the escape velocity     15.8, that is 11.2 * √2.     5.6, half the escape velocity

Physics for Scientists and Engineers, Technology Update (No access codes included)
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Author:Raymond A. Serway, John W. Jewett
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Chapter13: Universal Gravitation
Section: Chapter Questions
Problem 13.43P
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Newton's constant of gravitation  G is 6.67×10-11 in the system of units we use with mass in kilograms, length in meters, and time in seconds.  The radius of Earth is approximately 6.378 ×106 m, and its mass is  5.97 × 1024 kg.  With all this you can evaluate conservation of energy from Earth's surface and find an escape velocity of about 11.2 km/s from

 

Now suppose we wanted to orbit a spacecraft in low Earth orbit just a few hundred km above the surface.  How fast would it have to go to stay in a circular orbit?

 

   

7.9 km/s, that is about 11.2 / √2.

   

11.2, the same as the escape velocity

   

15.8, that is 11.2 * √2.

   

5.6, half the escape velocity

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