The ace pilot, Wash, attempts to put the ship Serenity (50,000 kg) in orbit at an altitude of 400 km around a planet (called Haven), which is about the same size as the Earth (D = 12,800 km). He has slowed to an approach velocity of 2 km/s. (recall: G = 6.67 x10-11 N m2 kg-2) Unfortunately, on approach, Serenity’s engines fail and she begins to plummet towards the surface. If the ship accelerates at 1.8g, what is the mass of the planet?  What would the acceleration of the ship be at 350 km? Is a constant acceleration safe to assume? Assume that the average acceleration over the 50 km, what is the velocity of Serenity at the height of 350-km?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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The ace pilot, Wash, attempts to put the ship Serenity (50,000 kg) in orbit at an altitude of 400 km around a planet (called Haven), which is about the same size as the Earth (D = 12,800 km). He has slowed to an approach velocity of 2 km/s. (recall: G = 6.67 x10-11 N m2 kg-2)

  1. Unfortunately, on approach, Serenity’s engines fail and she begins to plummet towards the surface. If the ship accelerates at 1.8g, what is the mass of the planet?
  2.  What would the acceleration of the ship be at 350 km? Is a constant acceleration safe to assume?
  3. Assume that the average acceleration over the 50 km, what is the velocity of Serenity at the height of 350-km?
  4. Upon entry, the ship hits the atmosphere at 350 km (with a density of 0.1 kg m-3). The ship slows to a terminal velocity of 1550 m/s. How big is the heat shield that slows the ship?
  5. How quickly does the ship slow (ignore gravity)?
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