Physics of the space environment phys 3280 30 assignment a

Question

Physics of the Space Environment Assignment   

Q1. Based on the geocentric dipole approximation with the geomagnetic north pole's Longitude=73⁰ W and latitude = 81⁰ (N), compute for a place ,X, close to Toronto at longitude= 73⁰ W and latitude = 44⁰ (N):

a) Magnetic field strength (intensity) at the surface of the Earth

b) The inclination of the magnetic field.

c) The shell parameter L and the height of the apex point of that local magnetic field line.

Q2. A 20 keV proton has a pitch angle at the apex of α₀ = 20⁰ and moves along a dipole field line with shell parameter L = 3.

a) Compute the gyro radius of the proton at the magnetic equator (apex).

b) Compute the gyro radius of the proton at its mirror points.

c) Compute the geocentric distance and magnetic latitude of the mirror points.

d) Compute the oscillation period.

Q3. Sketch the Earth with the L = 3 magnetic field line, draw the apex pitch angle and indicate the positions of the mirror points.