Orbital Mechanics Orbital Mechanics refers to the description
Orbital Mechanics • Orbital Mechanics refers to the description of how bodies move under gravity, given that total energy and momentum are conserved. • For two spherical objects in which gravity is the only force, this problem is analytic, and both bodies execute elliptical orbits (i. e. , Kepler’s laws).
Vis-Viva Equation • Gravity is an attractive force. As you fall toward a body of mass, you speed up; as you move away, you slow down. • The Vis-Viva equation is a useful relation describing this interrelation between total orbital speed and proximity of an object to the dominant massive body.
Being a Rocket Scientist! • Spaceflight is expensive. Energy is required to lift mass away from the Earth into space ($thousands per kilogram). • Question: What is the minimum energy orbit transfer, requiring the minimum fuel to move from one planet to another? Ø Ans: Hohmann orbit transfers. • In part, want to take advantage of the fact that the Earth is already moving at about 30 km/sec.
Types of Orbit Transfers
Transfer Orbits in the Solar System
Hohmann Transfer Orbits • Consider 2 planets in circular orbits • Hohmann orbit is an ellipse that bridges the planetary orbits • Hohman orbit obey’s Kepler’s laws • The semi-major axis of the transfer is a. T, given by • The period is P T 2 = a T 3 • The eccentricity is • The one-way travel time is t. T = PT/2
Timing for a Mars Visit
Orbit of Voyager
Gravitational Boosts for Voyager
Geostationary Orbits
Issues for Colonizing Other Worlds • TRAVEL - Getting there and back (cost and time). • POLITICS - Who is in charge? Who reaps the benefits? Who “owns”? • GRAVITY - What happens anatomically, physiologically, psychologically, and sociologically in terms of future generations born in different gravity (lower g) environs? • WATER - Finding, bringing, controlling. • ATMOSPHERE - Atmospheres moderate day/night temperature extremes. Also need breathable air. Terra-forming versus building and maintaining specialized habitations. • RADIATION/SOLAR WIND/COSMIC RAYS - What if no ozone? What if no magnetosphere? Might have to live underground.
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