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Launch an Satellite

NASA is planning to launch an unmanned satellite into a circular orbit at an elevation of 650 km. Engineers need to know the work required to launch the satellite into its orbit in the vertical direction.

What is known:

• Newton's Law of Gravitation states that two bodies with mass given as m₁and m₂ attract each other with a force
  
  F_G = Gm₁m₂/r²
  
  where r is the distance between the bodies ( from their centers) and G is the gravitational constant, G = 6.6 7x 10^-11 N-m²/kg².
• The mass of the earth is 5.98 x 10²⁴ kg and is assumed to be concentrated at its center. The average radius of the earth is 6.37 x 10⁶ m.
• The mass of the satellite is 173 kg and the satellite is launched to an orbit 650 km above the surface of the earth.

• The vertical thrust force needed to move the satellite up equals the gravitational force in magnitude, but points to the opposite direction.
• Consider a small interval between the earth's surface and the orbit of the satellite. Find the work when the satellite moves through this small interval.