posted by ronny on .
Your spacecraft is in a circular, geostationary orbit around earth and you would like to fly to the moon. Draw a suitable Hohmann transfer orbit that will get you there. How long does the journey take? (Neglect the gravitational fields of the moon and the sun for this problem, approximate the lunar orbit by a circle and consider an ideal transfer orbit.)
A geosycnchronous orbit is one with a period equal to the earth's rotational period, which, contrary to popular belief, is 23hr-56min-4.09sec., not 24 hours. Thus, the required altltude providing this period is ~22,238.64 miles, or ~35,787.875 kilometers. The orbital velocity of satellites in this orbit is ~10,088.25 feet per second or ~6,877 MPH. The point on the orbit where the circular velocity of the launching rocket reaches 10,088.25 fps, and shuts down, is the point where the separated satellite will remain.
The required Hohman Transfer velocity to transfer from the geostationary orbit to the lunar orbit, a mean distance of 239,000 miles away, is 13,544fps. The spacecraft will arrive at the lunar orbit with a velocity of 3340fps, taking ~136 hours to get there.
Sufficient propulsion capability will be needed to execute an orbital plane change of from ~18.5º to 28.5º.