Orbital Mechanics &

Other Fun StuffPart II Gravity Assist and Relativity

Tom RudmanThursday Morning

Space Odyssey Crew

Those Were the Easy Ones, Now We Go Beyond Mars

NASA Cartoon

The gravity assist technique was championed by Michael Minovitch in the early 1960s, while he was a UCLA graduate student working during the summers at JPL. Ref NASA JPL

Gravity Assist & Jupiter Photo NASA JPL

1st Venus Fly-by

2nd Venus Fly-by

Earth Fly-by

Jupiter Fly-byArrival at Saturn

In Orbit around Saturn

Example, How Cassini Made it to SaturnPhoto NASA

• Up to Now, Newton was close enough for our engineering problems

• However, Albert Einstein Showed that Newton was all wrong (or at least not quite right)

• Now we have to worry about that Einstein guy

Only took you 200 yrs

Nay Nay

• We can mostly ignore Relativity for basic orbital mechanics, Newton was close enough

• Three Examples where it is important– Mercury’s precession of perihelion– GPS navigation accuracy – Traveling Faster then Speed of Light

Relativity Effects on Orbits• Mercury’s precession of perihelion

– Kepler’s Laws would say the elliptical orbits are closed and the same

– Newton showed other planet’s gravity cause the orbits to rotate very slowly

– Neptune was discovered in 1846 because of this affect on Uranus’ orbit

• The centuries of observations showed there was a ~43” of arc per 100 yrs error– Newton’s Laws predicted 8.85’/100 yrs– Nothing could explain it, even postulating a

planet near the Sun (Vulcan, 1859)– Einstein’s General Relativity finally provided

an explanation

– Einstein’s theory agreed with the observed 9.56’/100 yrs

Simple Elliptical Orbit

Elliptical Orbit - Relativity

Relativity Effects on GPS• GPS uses its location and time to determine position of

an observer on Earth, accuracy is in nano seconds• GPS orbits at 20,200 km at a speed of 3.9 km/sec• Special Relativity predicts that the speed of the satellite

decreases the frequency of its atomic clock

– or -7.2 μsec

• General Relativity predicts that the orbit height of the satellite increases the frequency of its atomic clock

– or +45.8 μsec

• These sound small, but without a correction to the clock frequency, they would cause a 10 km a day error

Warp Drive

*Miguel Alcubierre, University of South Wales (now Max Planck Institut fur Gravitationsphysik) “The warp drive: hyper-fast travel within general relativity”

Michael Okuda's warp scale.

Warp 9.2 = 1630 x speed light

Warp 9.2 (max)

Warp 6 (nom)

Wf10/3

Wf3

Velocity & Power• No science so we’ll use Star Trek’s estimate • 1 billion Megawatts/Cochrane

• Warp 9.2 is 1630 Cochranes, ~2 trillion MW• ~100,000 times the world power consumption • Matter/Anti-matter reaction, dilithium crystals control

• Warp 6 is about 1 ly/day (5.9 trillion miles/day)• Warp 9.2 is about 4.5 ly/day

Source: wikipedia.org

• Theory of Relativity says we can’t go faster than the speed of light• Is there some way in the future we maybe able to travel faster?• The Alcubierre* concept, which does not have wide acceptance

– Moves Space-time in a “Warp’ field– Expanding space-time behind the ship– Contracting space-time in front of the ship – Actual velocity within the field is less than the speed of light– It would be like airport moving sidewalks.

• What would this Warped space-time field do to near by planets and other spaceships?