Transcript Rocket Propulsion

Orbital Mechanics &
Other Fun Stuff
Part II Gravity Assist
and Relativity
Tom Rudman
Thursday Morning
Space Odyssey Crew
Those Were the Easy Ones, Now We Go Beyond Mars
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
NASA Cartoon
1st Venus 2nd Venus Fly-by
Fly-by
Earth Fly-by
In Orbit
around Saturn
Jupiter Fly-by
Arrival at Saturn
Photo NASA
Example, How Cassini Made it to Saturn
• 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
Nay Nay
Only took
you 200 yrs
• 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
Simple Elliptical Orbit
– 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
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
• 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?
Michael Okuda's warp scale.
Velocity & Power
• No science so we’ll use Star Trek’s estimate
• 1 billion Megawatts/Cochrane
Warp 9.2 (max)
Wf10/3
Warp 6 (nom)
Wf3
• 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
Warp 9.2 = 1630 x speed light
*Miguel Alcubierre, University of South Wales (now Max
Planck Institut fur Gravitationsphysik)
“The warp drive: hyper-fast travel within general relativity”
Source: wikipedia.org