One of NASA's satellites is in a parking orbit at an altitude of 200 km above the Earth's surface and at an inclination of 28°. NASA wants to transfer this satellite into a zero- inclination geosynchronous orbit at an altitude of 35,800 km above the Earth's surface. Your job as an intern at NASA is to calculate the total AV needed for the following two options to help NASA design this mission:

Option 1: First, use Hohmann transfer to move the satellite from the 28° inclined- parking orbit to a 28°-inclined geosynchronous orbit. Next, perform a plane change to get the desired zero-inclination geosynchronous orbit.

Option 2: First, change the inclination of the parking orbit to 0°, and then perform a Hohmann transfer to move the satellite from the 0°-inclined parking orbit to the 0° inclined-geosynchronous orbit.

NASA wants you to create a report with detailed calculations for both options, with all solutions given with three decimal places. Draw a sketch for each option's Hohmann transfer, clearly showing the different orbits and velocities. Exaggerate scales as necessary to make your sketch clear.

a) Calculate the total delta-V required for option 1 and draw a sketch for the Hohmann transfer.

b) Calculate the total delta-V required for option 2 and draw a sketch for the Hohmann transfer.

c) Which option should NASA choose? Why?