Calculate the work required to launch a satellite into a low earth orbit at 160 km above the earth’s surface. the answer will depend on the launch location (there’s a reason nasa likes to use cape canaveral, and european space agency uses french guiana … and it ain’t the nice weather), so be sure to specify where that is (or, if you’re up to it, give the answer in terms of the launch location.) which takes more work: getting to an orbital height of 160 km above surface of the earth, or getting to the speed needed to maintain that orbit

Explanation:

The work done by the weight force is given by

W=mgh where h is the height difference between both points, since the work depends on the height of the place from which we send the rocket, we can generalize the work done to reach 160 km

W=mg(160000-h)  with 160 km expressed in meters, let's take cape canaveral for example with a height of 3 m above sea level, let's take an average rocket mass as 70000 Kg

W=70000*9.8*(160000-3)=1.097*10^11 Joules

“The west-to-east rotation of the Earth causes all points on Earth (except the poles themselves) to move eastward with some velocity,” NASA

This eastward velocity is greatest at the equator with the Earth rotating at a speed of roughly 1,040 mph. This rotational speed decreases as objects move closer to the poles, up to 0 in the poles

 That's the reason NASA uses Cape canaveral, since it is closer to the poles ergo giving an extra rotational velocity to the rocket to reach its destination

If we assume conservation of energy both activities take the same amount of work, reach to that height and getting to the speed needed

it takes about 30 days for it to break down