A satellite is to be launched to a circular orbit with radius 42164.2 km and zero inclination. Thesatellite will first be launched to a parking orbit 280 km above the Earth. Next, it will be boostedto the higher orbit using a Hohmann transfer. Since the launch latitude is 28.5 degrees, thesatellite will also need a plane change to get to the direct inclination. You may assume that, due to the launch location and azimuth, the Earth provides 408 m/s of ?help?.

a)What should the launch azimuth be? [1]

b) Calculate the deltaV required to get to the parking orbit. You may ignore drag and gravity losses.

c)Next, we?re going to do a Hohmann transfer to the desired orbit. Draw a sketch of themaneuver. Assume that all firings occur when we cross the Equator. Carefully indicate themajor axis (2a) of the elliptical transfer orbit. Write down the value of a. Now calculate thedeltaV to get into the elliptical transfer orbit.

d) Let?s continue with our Hohmann transfer. What is the apogee velocity of the transfer ellipse?

e)What is the velocity of the circular orbit with radius 42164.2 km?

f) How much deltaV do we need to make a plane change from the apogee of the ellipse? Howabout if we make the plane change after we?ve entered into the circular orbit?

g)We?re going to do the plane change and the maneuver from elliptical to circular in onedeltaV maneuver. Use the vector sketch below to help you calculate the combined deltaVthat is required. If your trigonometry is rusty, you may want to peek at the equation sheet.

h)Which maneuver do you think is better?(1) circularization followed by plane change, (2)plane change and then circularization, or (3) plane change and circularization combined?Explain your answer and motivate it quantitatively