We have that from the Question it can be said that the gravitational force is given as
F=12.864N
From the Question we are told
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.)
Generally the equation for Gravitational Force is mathematically given as
[tex]F=G \frac{m1m2}{r^2}\\\\r=900km+6.37*10^6\\\\r=7.27 * 10^6\\\\F=\frac{6.67*10^-11(1700)(5.98810^{24})}{7.26*10^6}^2\\\\[/tex]
F=12.864N
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The work done in propelling the satellite is 5 x 10¹⁰ J.
The given parameters;
The work done in propelling the satellite is calculated as follows;
[tex]W = \frac{GMm}{r}[/tex]
where;
Substitute the given parameters and solve for the work done;
[tex]W = \frac{(6.67\times 10^{-11})\times (5.98 \times 10^{24}) \times (800)}{(6.37 \times 10^{6})} \\\\W = 5 \times 10^{10} \ J[/tex]
Thus, the work done in propelling the satellite is 5 x 10¹⁰ J.
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