Editing GPIS 7: Mars Awaits
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[[File:GPIS_7_2.png|frame|center|alt=Escape velocity|'''Escape Velocity''' – You know from earlier flights that burning prograde at periapsis increases your apoapsis, and the longer you burn, the higher it is raised, making your orbit’s eccentricity increase. When eccentricity exceeds 1.0 (parabolic), the path becomes a hyperbola that approaches but mathematically never reaches a line (asymptote) which is also the departure direction. For a more complete, well-illustrated, and very easy to understand discussion of escape trajectories and many other aspects of orbital mechanics and space flight, see Wayne Lee’s book To Rise From Earth (reference details can be found at the end of chapter 8).]]<br clear=all> | [[File:GPIS_7_2.png|frame|center|alt=Escape velocity|'''Escape Velocity''' – You know from earlier flights that burning prograde at periapsis increases your apoapsis, and the longer you burn, the higher it is raised, making your orbit’s eccentricity increase. When eccentricity exceeds 1.0 (parabolic), the path becomes a hyperbola that approaches but mathematically never reaches a line (asymptote) which is also the departure direction. For a more complete, well-illustrated, and very easy to understand discussion of escape trajectories and many other aspects of orbital mechanics and space flight, see Wayne Lee’s book To Rise From Earth (reference details can be found at the end of chapter 8).]]<br clear=all> | ||
− | '''Transfer Orbits and Launch Window''' – The minimum energy trajectory to travel from one planet’s orbit to another is an elliptical orbit around the Sun which just touches both orbits; this is called a Hohmann transfer orbit. The Hohmann transfer is also generally the slowest trajectory. For travel to inner planets, the Earth’s orbit is the apoapsis point, and the target planet (e.g., Venus) is the periapsis. If the target planet is farther out, the periapsis of the transfer orbit is at the Earth, and the apoapsis is at (in our case) Mars, as shown in the figure below. A spacecraft on a Hohmann transfer will take 259 days to reach Mars and will move through precisely half an orbit (180°) around the Sun. If you have more available ΔV, non-Hohmann transfers are possible, and these are generally faster. In the figure below, the Hohmann transfer is shown in brown, and the higher- ΔV transfer orbit is red. Note that for the Hohmann case, the intercept occurs at the apoapsis of the transfer orbit, where the orbital speed is minimum, | + | '''Transfer Orbits and Launch Window''' – The minimum energy trajectory to travel from one planet’s orbit to another is an elliptical orbit around the Sun which just touches both orbits; this is called a Hohmann transfer orbit. The Hohmann transfer is also generally the slowest trajectory. For travel to inner planets, the Earth’s orbit is the apoapsis point, and the target planet (e.g., Venus) is the periapsis. If the target planet is farther out, the periapsis of the transfer orbit is at the Earth, and the apoapsis is at (in our case) Mars, as shown in the figure below. A spacecraft on a Hohmann transfer will take 259 days to reach Mars and will move through precisely half an orbit (180°) around the Sun. If you have more available ΔV, non-Hohmann transfers are possible, and these are generally faster. In the figure below, the Hohmann transfer is shown in brown, and the higher- ΔV transfer orbit is red. Note that for the Hohmann case, the intercept occurs at the apoapsis of the transfer orbit, where the orbital speed is minimum,thusrequiringlessΔVtoslowdownforMarscapturethanthenon-Hohmanncase. Withthe Delta Glider, we can largely ignore such issues, since there is plenty of fuel, but with real current boosters, these energy issues are very important for interplanetary flights. |
[[File:GPIS_7_3.png|frame|center|alt=Transfer orbits|'''Transfer Orbits''' – The sizes and shapes of these sample orbits are exaggerated for illustrative purposes. The Hohmann transfer is well known as the minimum energy and slowest transfer orbit, but other transfer orbits are possible. | [[File:GPIS_7_3.png|frame|center|alt=Transfer orbits|'''Transfer Orbits''' – The sizes and shapes of these sample orbits are exaggerated for illustrative purposes. The Hohmann transfer is well known as the minimum energy and slowest transfer orbit, but other transfer orbits are possible. | ||
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