1. Through the steps of this problem, you will be determining the semimajor axis ( a ) of this orbit. Use 3 decimal places in your calculations and answers, as applicable. Points are noted next to each Part.
   1. Calculate the magnitude of the position vector ( r ₀ ) and velocity vector (v ₀ ). (3 Points per Part)
   2. Calculate the specific mechanical energy () for this orbit. (4 Points)
   3. Calculate the semimajor axis ( a ) for this orbit. (5 Points)
2. Through the steps of this problem, you will be determining the magnitude of the eccentricity vector ( e ) for this orbit. Use 3 decimal places for > 0 figures or 3 significant figures for < 0 figures in your calculations and answers, as applicable. Points are noted next to each Part.
   1. Calculate the dot product ( r ₀ v ₀ ) of the position vector (r ₀ ) and velocity vector (v ₀ ). (4 Points)
   2. Calculate the components of the eccentricity vector. (8 Points)
   3. Calculate the magnitude of the eccentricity vector ( e ) (4 Points)
3. Through the steps of this problem, you will be determining the inclination ( i ) of this orbit. Use 3 decimal places in your calculations and answers, as applicable. Points are noted next to each Part.
   1. Calculate the components of the specific angular momentum vector ( h ). Hint: This is the cross product of the position and velocity vectors ( r ₀ xv ₀ ). (4 Points)
   2. Calculate the magnitude of the specific angular momentum vector. (4 Points)
   3. Calculate the inclination ( i ) of this orbit. Be sure you conduct the appropriate quadrant check as well. (8 Points)
4. Through the steps of this problem, you will be determining the longitude of the ascending node () for this orbit. Use 3 decimal places in your calculations and answers, as applicable. Points are noted next to each Part.
   1. Calculate the components of the ascending node vector ( n ). Hint: this is the cross product of the "K" and angular momentum vectors ( K xh ). (4 Points)
   2. Calculate the magnitude of the ascending node vector. (4 Points)
   3. Calculate the longitude of the ascending node () for this orbit. Be sure to perform the appropriate quadrant check as well. (8 Points)
5. Through the steps of this problem, you will be determining the argument of perigee () for this orbit. Use 3 decimal places for > 0 figures or 3 significant figures for < 0 figures in your calculations and answers, as applicable. Points are noted next to each Part.
   1. Calculate the dot-product of the ascending node and eccentricity vector components ( ne ). (4 Points)
   2. Using values given or calculated up to this point, explain how we determine the required equation to calculate the argument of perigee () for this orbit and identify the correct Equation. (4 Points)
   3. Calculate the argument of perigee () for this orbit. (8 Points)
6. Through the steps of this problem, you will be determining the true anomaly ( ₀ ) for this orbit. Use 3 decimal places for > 0 figures or 3 significant figures for < 0 figures in your calculations and answers, as applicable. (15 Points)
   1. Calculate the dot product of the eccentricity and position vectors ( er ₀ ). (4 Points)
   2. Using values given or calculated up to this point, explain how we determine the required equation to calculate the true anomaly ( ₀ ) for this orbit and identify the correct Equation. (4 Points)
   3. Calculate the true anomaly ( ₀ ) for this orbit. (7 Points)
7. A rocket is launched from Kwajalein Missile Range in the Marshall Islands ( 9.24 N, 267.29 E ) that is delivering a microsatellite to a parking orbit at an inclination of i = 21.5 . Using this information and details from Example 3.2, calculate the launch azimuth () of the rocket so it is positioned to place the satellite in orbit with the correct inclination ( i ) and initially moving away from the equator after orbital insertion. Use 3 decimal places in your calculations and answer. (6 Points)