Assuming the average Earth Radius R E = 6378 km : The question I have are below: A Falcon 9 launched from Cape Canaveral (

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Assuming the average Earth RadiusR_E= 6378 km:

The question I have are below:

A Falcon 9 launched from Cape Canaveral (28 N Latitude) delivers a satellite directly (i_initial= 28) into a low-Earth circular parking orbit at an altitude ofalt₁= 222 kmwith an augment of perigee of = 180. The satellite needs to be moved into its final GPS orbit with an altitude ofalt₂= 38622 kmand at an inclination ofi_final= 66. Use 3 decimal places in your calculations and answers, as applicable.

Determine the semimajor axis (a_t) for the Hohmann transfer orbit.

Calculate the apse velocities (v₁andv₂) for this Hohmann transfer orbit.

Calculate the initial and final circular velocities (v_c1andv_c2) of the initial and final orbits.

Determine the velocity impulse required in the LEO (v₁) and at apogee (v₂).

Calculate the time of flight (t_f) for this Hohmann transfer. Express your final answer in hours, minutes, and seconds (i.e.,12:25:23or12 hr, 25 min, 23 sec). Use 3 decimal places in your calculations, none required in the final answer.

Now that the satellite is at its new altitude ofalt₂= 38662 km, the satellite needs to be shifted from it is initial inclination ofi_initial= 28to its required inclination ofi_final= 66. Calculate the velocity impulse (v₃) required for a pure inclination change.

Calculate the total change in velocity (v_total) required to perform the Hohmann coplanar transfer to the circular GPS orbit and then a pure inclination change.

Instead of calculating a pure inclination change, calculate the velocity impulse (v₃) to complete the inclination change at apogee of the Hohmann transfer.

Calculate the total change in velocity (v_total) required to perform the Hohmann coplanar transfer to the circular GPS orbit and then an inclination change at apogee of the Hohmann transfer. Note: The final coplanar maneuver at apogee to circularize the GPS orbit is the same as the 2^ndimpulse velocity change in Problem 4.

In this final maneuver, instead of performing 2 maneuvers to complete the final stage of the Hohmann transfer and a separate inclination change, calculate the apogee impulse velocity required to perform a 3-D maneuver to change the inclination and energy to the desired inclination ofi_final= 66and stabilize the movement into the desired circular GPS orbit.

Calculate the total change in velocity (v_total) required to perform the Hohmann transfer and the 3-D maneuver at apogee to change the plane and circularize the orbit. (8 Points)

List calculations for each of the scenarios below (answers in previous questions). Then compare discuss the implications of these results for the total change in velocity (v_total) required in each of the scenarios:

Performing a coplanar Hohmann transfer to the circular GPS orbit, then a pure inclination change .

Performing the first Hohmann transfer to raise apogee to the GPS orbit, then a pure inclination change at apogee, followed by a coplanar maneuver at apogee to establish the circular GPS orbit .

Performingthe first Hohmann transfer to raise apogee to the GPS orbit, then a 3-D maneuver at apogee to change the plane and circularize the orbit ).