Orbital Transfers Between Orbital Planes & Mechanics IT Assignment Help

Assignment Task

This homework was developed to provide a survey of topics since the last midterm addressing:
1. Orbital transfers between orbital planes
A. To a circular final orbit (GEO-stationary 24 hour)
B. To an elliptical final orbit (Molniya 12 hour)
2. Proximity maneuvers resulting in rendezvous and docking
3. Basic oscillations of rigid bodies based on their mass properties.
Due to time remaining in this course, we have curtailed the derivations and also simplified the working assumptions for the third problem. In the second case, we have identified a minimization technique for reducing velocity deltas. We will all be looking for ways to adapt this to the non-circular target orbit problem. Notes from the lectures accompany this homework. Pertinent excerpts were Included as appendices here for each of the problems.we concluded with a discussion about deploying geostationary satellites via Hohman out of plane transfers from low circular orbit. Some distinctions should be identified. The period of the final orbit is about 24 hour And the inclination is usally zero degrees with respect to the equator. Geostationary matches the rotational rate of the Earth to remain above a fixed longitude or meridian. Geosynchronous allows wandering but a closed path with a remaining inclination or eccentricity. Were the Earth’s path not bent by solar orbit, we could consider its rotational period asath 23 hours and about 56 minutes. Since one revolution around requires additional rotation of a little less than a degree to return to “noon”, the effective period is 24 hours. Close enough for our purposes. We will apply the point mass gravitational constant for target orbit accordingly. For this exercise we will assume that a cargo spacecraft launches due east from a prospective Spaceport at a given latitude. For the Kennedy Space Center, assume 28.5 degree latitude. For Guyanna Space Center, about 8 degrees north latitude – and Baikonur about 47 deg.  As discussed in class as well, generally, elliptical transfer (180 degree) transfer orbits between circular orbits in different planes are economized in terms of delta velocity by performing all or most of the plane change at further distance from the primary. Performing some of the plane change at the lower altitude can reduce velocity expenditures a little further, however, and can be solved as an analytical variational calculus problem. What might be easier is Adding ( and subtracting) a few degrees from the two plane changes involved. Also, be careful about performing the plane change. Use the general form of the Pythagorean theorem reflecting the vector additions. The Shuttle when it was in this business of delivering comm sats to GEO (e.g., TDRSS), usually Deployed the transfer stage at an altitude of 160 nmi. Lower altitudes would result in higher velocity deltas. Vice versa for higher altitudes

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