Gravitational Slingshots or How to steal momentum Michael Krucker & Thomas Meier
18.03.2016 Michael Krucker & Thomas Meier 1 Navigation in space
• Navigation in space is fundamentally different than on earth • There is only one method to change magnitude and/or direction of the velocity vector of a spacecraft: • Apply thrust with some kind of rocket engine • Problem: • Spacecraft with orbital speed of earth around the sun, falling towards the sun is sped up. When reaching orbit of venus, orbital speed is much greater than orbital speed of venus • So we need to slow it down
18.03.2016 Michael Krucker & Thomas Meier 2 Delta-v
• The Delta-v is a measure of the ability of a space vehicle to change its impulse • A space mission needs a specific amount of delta-v to all its maneuvers, including launch, deep space maneuvers, orbital insertion and deorbiting • Once launched, the remaining delta-v budget is fixed
18.03.2016 Michael Krucker & Thomas Meier 3 Hohmann-transfer
• To change the orbit of a spacecraft, the simplest and most fuel effective way is called Hohmann-transfer • It uses 2 burns of the engine • Can be used for various near-earth maneuvers and travels to mars an venus
18.03.2016 Michael Krucker & Thomas Meier 4 Gravitational slingshot
• What if the delta-v budget does not suffice to perform a Hohmann-transfer to your target? • You can steal some impulse from another body by performing an elastic collision • This impulse can be used to change the direction or the magnitude of the velocity vector of our spacecraft
18.03.2016 Michael Krucker & Thomas Meier 5 Gravitational slingshot
18.03.2016 Michael Krucker & Thomas Meier 6 Gravitational slingshot
• You can even invert the direction and add 2 times the orbital velocity of your assisting body • As the planet is so much more massive than your space probe, the effect on the planet is negligible
18.03.2016 Michael Krucker & Thomas Meier 7 Gravitational slingshot
18.03.2016 Michael Krucker & Thomas Meier 8 Gravitational slingshot
18.03.2016 Michael Krucker & Thomas Meier 9 Examples
• MESSENGER • Target: mercury orbit • Gravity assist on earth • 2 gravity assists on venus • 3 gravity assists and aerobreaking on mercury • Final orbital injection burn
18.03.2016 Michael Krucker & Thomas Meier 10 Examples
• Ulysses • Target: circumpolar solar orbit • Hohmann-transfer to jupiter • Swing-by on jupiter to change orbit inclination by 80.2°
18.03.2016 Michael Krucker & Thomas Meier 11 Examples
• Voyager I & II • Target: Close fly-bys of the outer planets • Gravitational assists on jupiter and saturn for both probes • Additional assists on uranus and neptune for voyager 2 • Voyager I & II now in interstellar space
18.03.2016 Michael Krucker & Thomas Meier 12 Oberth-effect
• If it is not enough, to steal impulse from all the planets on your way, you can additionally take some fuel with you and burn it • The best point to burn your fuel is, when you are deep inside a gravity well (near a planet during a slingshot maneuver) • You get an increase of your invested delta-v by a factor of • Example: • 50 km/s escape velocity • 5 km/s burn • Factor of 4.6 • Final velocity increase: 23 km/s
18.03.2016 Michael Krucker & Thomas Meier 13 Future (ITN)
• With increasing computing power, it is possible to do gravitational calculations of the whole solar system • This yields pathways connecting various lagrange points (Interplanetary transport network) • This pathways can be used to do very fuel efficient orbital transfers
18.03.2016 Michael Krucker & Thomas Meier 14 • Questions?
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