58. A spacecraft is in a circular orbit of radius, equal to 3.0 x 10^4 km around

Question

58. A spacecraft is in a circular orbit of radius, equal to 3.0 x 10^4 km around a 2.0 x 10^30 kg pulsar. The magnetic field of the pulsar at that radial distance is 1.0 x 10^2 T directed perpendicular to the velocity of the spacecraft. The spacecraft is 0.20 km long with a radius of 0.040 km and moves counterclockwise in the xy-plane around the pulsar. a) What is the speed of the spacecraft? b) If the magnetic field points in the positive z-direction, is the emf induced from the back to front of the spacecraft or from side to side? c) Compute the induced emf. d) Describe the hazards for astronauts inside any spacecraft moving in the vicinity of a pulsar.

Explanation / Answer

Given that          the mass of the space craft is m1          mass of the pulsar is m = 2.0*1030kg         distancebetween the pulsar and the spacecraft is d= 3*104 km         The radius of thecraft is r = 0.20 km = 200 m
The force between pulsar and spacecraft as                               F=Gmm1/d2 then        Gm1m/d2 = m1v2/d           ( since spacecraft moving in circular orbit)                               v = Gm/d                                  = 6.67*10^-11*2.0*10^30/3*10^4 m/s                                  = 6.66*10^7 m/s From the right hand rule the induced emf isdirected along sides only .   so the induced emf is produce through the diameterof the spacecraft .                    Induced emf is given by,                             = Blv                               =1.0*102 T *2r*v                              = 1.0*102 T *2* 200m *v                              = 26.64*10^11 m/s The force between pulsar and spacecraft as                               F=Gmm1/d2 then        Gm1m/d2 = m1v2/d           ( since spacecraft moving in circular orbit)                               v = Gm/d                                  = 6.67*10^-11*2.0*10^30/3*10^4 m/s                                  = 6.66*10^7 m/s From the right hand rule the induced emf isdirected along sides only .   so the induced emf is produce through the diameterof the spacecraft .                    Induced emf is given by,                             = Blv                               =1.0*102 T *2r*v                              = 1.0*102 T *2* 200m *v                              = 26.64*10^11 m/s then        Gm1m/d2 = m1v2/d           ( since spacecraft moving in circular orbit)                               v = Gm/d                                  = 6.67*10^-11*2.0*10^30/3*10^4 m/s                                  = 6.66*10^7 m/s From the right hand rule the induced emf isdirected along sides only .   so the induced emf is produce through the diameterof the spacecraft .                    Induced emf is given by,                             = Blv                               =1.0*102 T *2r*v                              = 1.0*102 T *2* 200m *v                              = 26.64*10^11 m/s

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