1. Orbital Mechanics & Other Fun Stuff Part II Gravity Assist and Relativity Tom Rudman Thursday Morning Space Odyssey Crew

2. 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

3. 1 st Venus Fly-by 2 nd Venus Fly-by Earth Fly-by Jupiter Fly-by Arrival at Saturn In Orbit around Saturn Example, How Cassini Made it to Saturn Photo NASA

4. 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 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

5. 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 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

6. 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

7. 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) W f 10/3 Wf3Wf3 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?