Orbital Mechanics

• Orbital Mechanics refers to the general description of how bodies move in force fields (such as gravity) given that 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., they obey 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 simple and useful relation describing this interrelation between total orbital speed and proximity 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? 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

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.