Compute the work required to launch a 1000-kg satellite vertically to a height of 1000 km. 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 Nm2/kg2 .

Explanation:

In order to calculate the work from r = a to r = b we only need to convert 1000 km into 1,000,000 m.

Since, the given data is as follows.

           G =

        = 1000 kg

           a =

           b =

              =

Now, we will calculate the work as follows.

              W =

                   =

                   =

thus, we can conclude that work required to launch the satellite is .

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach