Six artificial satellites circle a space station at constant speed. The mass m o

Question

Six artificial satellites circle a space station at constant speed. The mass m of each satellite, distance L from the space station, and the speed v of each satellite are listed below. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible. Rank each satellite based on its period. Rank from largest to smallest. To rank items as equivalent, overlap them. 1. m=200kg,L= 5000 m, v=120 m/s 2. m=800kg,l= 10,000 m, v=40m/s 3. m=400kg,L= 2500 m, v=80m/s 4. m=100kg, L=2500 m, V=160m/s 5. m=300kg, L=10,000m, V=80 m/s 6. m=200kg, L=5000 m, V=160 m/s Rank each satellite based on its acceleration. Rank from largest to smallest. To rank items as equivalent, overlap them. 1. m=100kg, L=2500m, V=160 m/s 2. m=400kg, L=2500m, V=80 m/s 3. m=300kg, L=10,000m V=80m/s 4. m=800kg, L=10,000m V=40 m/s 5. m=200kg, L=5000m, V=120m/s 6. m=200kg, L=5000m, V=160m/s

Explanation / Answer

ex1: 2p(5000)/T=120 --> multiply both sides by T, then divide by120 to get T. Answer= 261.80 Do the same for the rest and the order should be: 4, 3, 1, 2, 6, 5 To rank according to acceleration use the formula for centripetal acceleration (ac): ac= v^2/r 1: (160)^2/2500= 10.24 2: (80)^2/2500= 2.56 3: (80)^2/10,000= .64 4: (40)^2/10,000= .16 5: (120)^2/5000= 2.88 6: (160)^2/5000= 5.12 So then the acceleration would rank as: 1, 6, 5, 2, 3, 4

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