Problem 1.1 What is the relationship between e, and e, and the usual Cartesian vectors i and j? By differentiating these expressions with respect to time, show that: è, - be ég --be, Problem 1.2 The position of a satellite is given by r = re. It's velocity is given by v = r. Using the results from question 1, show that: v = fe, + reg The angular momentum per unit mass is given by: h= r x v. Find an expression for the angular momentum of the satellite. Which direction does it point? Problem 1.3 The velocity of a satellite in orbit is given by v = r. Using the results of question 1, show that the acceleration is: (F-T8²)e, + (r²8)eo 1 d rdt Problem 1.4 The gravitational force acting on an orbiting satellite is given by: μπλ F = where is the gravitational parameter and m is the mass of the satellite. Write down the vector equation of motion and then write down its radial (direction e,) and azimuthal (direction e) components.

Problem 1.1 What is the relationship between e, and e, and the usual Cartesian vectors i and j? By differentiating these expressions with respect to time, show that: è, - be ég --be, Problem 1.2 The position of a satellite is given by r = re. It's velocity is given by v = r. Using the results from question 1, show that: v = fe, + reg The angular momentum per unit mass is given by: h= r x v. Find an expression for the angular momentum of the satellite. Which direction does it point? Problem 1.3 The velocity of a satellite in orbit is given by v = r. Using the results of question 1, show that the acceleration is: (F-T8²)e, + (r²8)eo 1 d rdt Problem 1.4 The gravitational force acting on an orbiting satellite is given by: μπλ F = where is the gravitational parameter and m is the mass of the satellite. Write down the vector equation of motion and then write down its radial (direction e,) and azimuthal (direction e) components.