The largest launch vehicle available can put your large telecommunications satel

Question

The largest launch vehicle available can put your large telecommunications satellite into a 400 km perigee, 4000 km apogee equatorial orbit. You need to figure out a way to transfer it to GEO with a Hohmann transfer. Among the approaches that you can take are: 1. Perigee burn to put the apogee at GEO followed by an apogee burn to circularize the orbit 2. Initial orbit apogee burn to put the perigee (which becomes the apogee) in GEO followed by a transfer orbit apogee burn to circularize the orbit 1. For each approach, draw the initial, transfer and final orbits. Show the locations of each impulse (Delta V). Use the chart to define the various velocities, V's and Delta V's. Make sure your definition is unambiguous so you do not get confused when applying the equations (for ex., the velocity needed at the end of the first burn in scenario 2 is that of a perigee of the transfer orbit and might therefore be defined as v_pt2, p for perigee, t for that of the transfer orbit, 2 for scenario 2, while the initial velocity before that burn may have been defined as v_ai2 for apogee and i for initial orbit). Calculate the corresponding Delta V's needed for each scenario. Justify which one you would choose. How long, in hrs, does the selected transfer take?

Explanation / Answer

According to the given problem,

Hohmann transfer orbit is an orbital maneuver using two engine impulses which, under standard assumptions, move a spacecraft between two coplanar circular orbits.

The transfer is initiated by firing the spacecraft's engine in order to accelerate it so that it will follow the elliptical orbit; this adds energy to the spacecraft's orbit. When the spacecraft has reached its destination orbit, its orbital speed (and hence its orbital energy) must be increased again in order to change the elliptic orbit to the larger circular one.

For further details on that orbit, please refer the Wikipedia link below!!

For GeoSynchronous Orbits, radius of the orbit R2= 42,164 km (from the earth centre)
In present orbit, R1 = 4000 km altitude = 4000 + 6378 = 10378 km, where first impulse is given

For Earth, Standard gravitational parameter U = GM = 3.98 * 105 km3/s2

Difference in Velocity = (U/R1)* [ (2 R2 / (R1 + R2))-1]
= (3.98 *105/10378)* [ (2*42164 / (42,164 + 10378)) - 1]
=1.653 km/s

Time taken for transfer = *[(R1+R2)3/8U]
= * [(42,164 + 10378)3/(8*3.98*105)]
= 21,204 s
= 5.89 hrs

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