Question

Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force F, where r is the distance between the bodies and G is the gravitational constant.
F = G m1*m2/r^2
Use Newton's Law of Gravitation to compute the work W required to propel a 800 kg satellite out of the earth's gravitational field. You may assume that the earth's mass is 5.98 x 10^24 kg and is concentrated at its center. Take the radius of the earth to be 6.37 x 10^6 m and G = 6.67 x 10^-11 Nm^2/kg^2. (Round your answer to three significant digits.)

Answer 1

Answer:

W = - 5.01 10¹⁰ J

Explanation:

Work is defined by the expression

      W = ∫ F.dr

Where the blacks indicate vectors, in the case the force is radial and the distance is also radial, whereby the scalar producer is reduced to an ordinary product

      W = ∫ F dr

      W = G m₁m₂ ∫ 1 /r² dr

     W = G m₁ m₂2(-1 / r)

We evaluate between the lower limits r = Re and upper r = ∞

     W = G m₁m₂ (-1 / Re + 1 / ∞)

     W = - G m₁ m₂ / Re

Let's calculate

    W = - 6.67 10⁻¹¹ 800 5.98 10²⁴ / 6.37 10⁶

    W = - 5.01 10¹⁰ J