While preparing its budget for the next fiscal year, NASA wants to report to the
ID: 2011466 • Letter: W
Question
While preparing its budget for the next fiscal year, NASA wants to report to the nation a rough estimate of the cost (per kilogram) of launching a modern satellite into near-Earth orbit. You are chosen for this task, because you know both physics and accounting.a) Determine the energy, in kW·h, necessary to place a 1.0-kg object in low-Earth orbit. In low-Earth orbit, the height of the object above the surface of Earth is much smaller than Earth's radius. Take the orbital height to be 270 km.
b)If this energy can be obtained at a typical electrical energy rate of $0.12 / kW·h, what is the minimum cost of launching a 390 kg satellite into low-Earth orbit? Neglect any effects due to air resistance.
Explanation / Answer
a) m = 1.0 kg, h = 270 km, radius of earth R = 6378 km, mass ofearth M = 5.98*1024 kgenergy at earth surface E = -GmM/R
energy in orbit E' = -GmM/(R + h)
energy needed W = E' - E = GmM*[1/R - 1/(R + h)] =2.39*106 J = 2.39*103 kJ =2.39*103 kW-s
= 2.39*103/3600 kW-h = 663 kW-h
b) for m' = 390 kg
W' = 663 kW-h * 390
cost = $0.12*663* 390= $ 31028.4 a) m = 1.0 kg, h = 270 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)] =2.39*106 J = 2.39*103 kJ =2.39*103 kW-s
= 2.39*103/3600 kW-h = 663 kW-h
b) for m' = 390 kg
W' = 663 kW-h * 390
cost = $0.12*663* 390= $ 31028.4
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