While preparing its budget for the next fiscal year, NASA wants toreport to the
ID: 1725587 • Letter: W
Question
While preparing its budget for the next fiscal year, NASA wants toreport to the nation a rough estimate of the cost (per kilogram) oflaunching a modern satellite into near-Earth orbit. You are chosenfor this task, because you know both physics and accounting.(a) Determine the energy, in kW·h, necessary to place a1.0-kg object in low-Earth orbit. In low-Earth orbit, the height ofthe object above the surface of Earth is much smaller than Earth'sradius. Take the orbital height to be 370km.
1 kW·h
(b) If this energy can be obtained at a typical electrical energyrate of $0.12 / kW·h, what is theminimum cost of launching a 450 kgsatellite into low-Earth orbit? Neglect any effects due to airresistance.
$ 2
(a) Determine the energy, in kW·h, necessary to place a1.0-kg object in low-Earth orbit. In low-Earth orbit, the height ofthe object above the surface of Earth is much smaller than Earth'sradius. Take the orbital height to be 370km.
1 kW·h
(b) If this energy can be obtained at a typical electrical energyrate of $0.12 / kW·h, what is theminimum cost of launching a 450 kgsatellite into low-Earth orbit? Neglect any effects due to airresistance.
$ 2
Explanation / Answer
a) m = 1.0 kg, h = 370 km, radius of earth R = 6378 km, mass ofearth M = 5.98*1024 kg energy at earth surface E = -GmM/R energy in orbit E' = -GmM/(R + h) energy needed W = E' - E = GmM*[1/R - 1/(R + h)] =3.43*106 J = 3.43*103 kJ =3.43*103 kW-s = 3.43*103/3600 kW-h = 953 kW-h b) for m' = 450 kg W' = 953 kW-h * 450 cost = $0.12*953* 450 = $51435.20
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.