Space debris is becoming an increasingly serious problem for satellites in Earth

Question

Space debris is becoming an increasingly serious problem for satellites in Earth's orbit. This was exemplified in February 2009 by the collision of an active Iridium-33 satellite (600kg) that was launched in 1997 with an inactive Russian Cosmos-2251 satellite (1000kg) that was launched in 1993. The collision occurred at an orbital altitude of 790 km over Siberia and generated over 500 pieces of new space debris that are now being tracked by the U.S space surveillance network. For the rest of the problem, make any necessary assumptions and clearly state them. (a) U.S. authorities have reported a relative impact velocity of 11.7km/s at a relative angle of 102.2deg. Based on this information, let's consider a simple model as follows. Two satellites (1000kg and 600kg) are moving at the same velocity v in magnitude with a relative velocity of 11.7km/s at a relative angle of 102.2deg. For simplicity, assume that the collision was perfectly inelastic and that linear momentum was conserved 102.2 i. What is the pre-impact velocity v of each satellite ii. Estimate the amount of kinetic energy lost due to this collision. (c) Assume that the particles have the velocity as you found in part (a).i and that the density of the debris is about 3000kg/m3. Calculate approximately the kinetic energy for the particles of the size you found in part (b)

Explanation / Answer

a. assuming the two satellites were moving with same speed v
   now relative veolcity , Vr = 11.7 km/s
   relative angle theta = 102.2 deg

   so Vr = 2vsin(theta/2) = 2vsin(102.2/2) = 2vsin(51.1)
   11.7 = 2vsin(51.1)
   i. v = 7.516 km/s
   ii. initial KE of the system = 0.5m1v^2 + 0.5m2v^2
   here m1 = 1000 kg, m2 = 600 kg
   hence initial KE of the system = 45.1922*10^9 J

   for perfectly inelastic collision
   final speed u in direction thets to the horizontal
   hence from conservation of moemntum
   1600*ucos(theta) = 1000*7.516sin(51.1) - 600*7.516sin(51.1)
   ucos(theta) = 1.462
   from momentum balance in vertical direction
   1600usin(theta) = 1600*7.516cos(51.1)
   usin(theta) = 4.7199

   hence
   u^2 = 24.413
   u = 4.941 km/s
   so final KE of the system = 0.5*1600*u^2 = 1.953*10^9 J
   so energy lost = 45.1922 - 1.953 = 45.1921*10^9 J

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.