asen 5050 spaceflight dynamics interplanetary prof. jeffrey s. parker university of colorado –...
DESCRIPTION
Schedule from here out Lecture 29: Interplanetary 3 11/7: Interplanetary 2 11/10: Entry, Descent, and Landing 11/12: Low-Energy Mission Design 11/14: STK Lab 3 11/17: Low-Thrust Mission Design (Jon Herman) 11/19: Finite Burn Design 11/21: STK Lab 4 Fall Break 12/1: Constellation Design, GPS 12/3: Spacecraft Navigation 12/5: TBD 12/8: TBD 12/10: TBD 12/12: Final ReviewTRANSCRIPT
ASEN 5050SPACEFLIGHT DYNAMICS
Interplanetary
Prof. Jeffrey S. ParkerUniversity of Colorado – Boulder
Lecture 29: Interplanetary 1
Announcements• HW 8 is out
– Due Wednesday, Nov 12.– J2 effect– Using VOPs
• Reading: Chapter 12
Lecture 29: Interplanetary 2
Schedule from here out
Lecture 29: Interplanetary 3
• 11/7: Interplanetary 2
• 11/10: Entry, Descent, and Landing• 11/12: Low-Energy Mission Design• 11/14: STK Lab 3
• 11/17: Low-Thrust Mission Design (Jon Herman)• 11/19: Finite Burn Design• 11/21: STK Lab 4
• Fall Break
• 12/1: Constellation Design, GPS• 12/3: Spacecraft Navigation• 12/5: TBD
• 12/8: TBD• 12/10: TBD• 12/12: Final Review
Space NewsOrion’s EFT-1
Lecture 29: Interplanetary 4
Quiz #14
Lecture 29: Interplanetary 5
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Quiz #14
Lecture 29: Interplanetary 6
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N
S
Atm motion
S/C motion(inertial)
Perigee Point
V ~ 8 km/sVatm ~ 0.48 km/stheta ~ 3.1 deg
θ
Quiz #14
• Problem 2
Lecture 19: Perturbations 7
Sun
Quiz #14
• Problem 3
Lecture 19: Perturbations 8
Sun
Quiz #14
Lecture 29: Interplanetary 9
Quiz #14
Lecture 29: Interplanetary 10
ASEN 5050SPACEFLIGHT DYNAMICS
Interplanetary
Prof. Jeffrey S. ParkerUniversity of Colorado – Boulder
Lecture 29: Interplanetary 11
Interplanetary
• History
• Planets
• Moons
• Small bodies
Lecture 29: Interplanetary 12
Today: tools, methods, algorithms!
Building an Interplanetary Transfer
• Simple:– Step 1. Build the transfer from Earth to the planet.– Step 2. Build the departure from the Earth onto the
interplanetary transfer.– Step 3. Build the arrival at the destination.
• Added complexity:– Gravity assists– Solar sailing and/or electric propulsion– Low-energy transfers
Lecture 29: Interplanetary 13
Patched Conics
• Use two-body orbits
Lecture 29: Interplanetary 14
Patched Conics
• Gravitational forces during an Earth-Mars transfer
Lecture 29: Interplanetary 15
Sphere of Influence
• Measured differently by different astrodynamicists.– “Hill Sphere”– Laplace derived an expression that matches real trajectories
in the solar system very well.
• Laplace’s SOI:– Consider the acceleration of a spacecraft in the presence of
the Earth and the Sun:
Lecture 29: Interplanetary 16
Sphere of Influence
• Motion of the spacecraft relative to the Earth with the Sun as a 3rd body:
• Motion of the spacecraft relative to the Sun with the Earth as a 3rd body:
Lecture 29: Interplanetary 17
Sphere of Influence
• Laplace suggested that the Sphere of Influence (SOI) be the surface where the ratio of the 3rd body’s perturbation to the primary body’s acceleration is equal.
Lecture 29: Interplanetary 18
Sphere of Influence
• Laplace suggested that the Sphere of Influence (SOI) be the surface where the ratio of the 3rd body’s perturbation to the primary body’s acceleration is equal.
Lecture 29: Interplanetary 19
Primary Earth Accel
Primary Sun Accel
3rd Body Sun Accel
3rd Body Earth Accel
Sphere of Influence
• Laplace suggested that the Sphere of Influence (SOI) be the surface where the ratio of the 3rd body’s perturbation to the primary body’s acceleration is equal.
Lecture 29: Interplanetary 20
Primary Earth Accel
Primary Sun Accel
3rd Body Sun Accel
3rd Body Earth Accel
=
Sphere of Influence
• Find the surface that sets these ratios equal.
Lecture 29: Interplanetary 21
After simplifications:
Sphere of Influence
• Find the surface that sets these ratios equal.
Lecture 29: Interplanetary 22
Earth’s SOI: ~925,000 kmMoon’s SOI: ~66,000 km
Patched Conics
• Use two-body orbits
Lecture 29: Interplanetary 23
Interplanetary Transfer
• Use Lambert’s Problem • Earth – Mars in 2018
Lecture 29: Interplanetary 24
Interplanetary Transfer
• Lambert’s Problem gives you:– the heliocentric velocity you require at the Earth departure– the heliocentric velocity you will have at Mars arrival
• Build hyperbolic orbits at Earth and Mars to connect to those.– “V-infinity” is the hyperbolic excess velocity at a planet.
Lecture 29: Interplanetary 25
Earth Departure
• We have v-infinity at departure
• Compute specific energy of departure wrt Earth:
• Compute the velocity you need at some parking orbit:
Lecture 29: Interplanetary 26
Earth Departure
Lecture 29: Interplanetary 27
Departing from a circular orbit, say, 185 km:
Launch Target
Lecture 29: Interplanetary 28
Launch Target
Lecture 29: Interplanetary 29
Launch Targets
• C3, RLA, DLA
Lecture 29: Interplanetary 30
(In the frame of the V-inf vector!)
Launch Targets
Lecture 29: Interplanetary 31
Mars Arrival
• Same as Earth departure, except you can arrive in several ways:– Enter orbit, usually a very elliptical orbit– Enter the atmosphere directly– Aerobraking. Aerocapture?
Lecture 29: Interplanetary 32
Aerobraking
Lecture 29: Interplanetary 33
Comparing Patched Conics to High-Fidelity
Lecture 29: Interplanetary 34
Gravity Assists
• A mission designer can harness the gravity of other planets to reduce the energy needed to get somewhere.
• Galileo launched with just enough energy to get to Venus, but flew to Jupiter.
• Cassini launched with just enough energy to get to Venus (also), but flew to Saturn.
• New Horizons launched with a ridiculous amount of energy – and used a Jupiter gravity assist to get to Pluto even faster.
Lecture 29: Interplanetary 35
Gravity Assists• Gravity assist, like pretty much everything else, must obey the
laws of physics.
• Conservation of energy, conservation of angular momentum, etc.
Lecture 29: Interplanetary 36
So how did Pioneer 10 get such a huge kick of energy, passing by Jupiter?
Designing Gravity Assists• Rule: Unless a spacecraft performs a maneuver or flies
through the atmosphere, it departs the planet with the same amount of energy that it arrived with.
• Guideline: Make sure the spacecraft doesn’t impact the planet (or rings/moons) during the flyby, unless by design.
Lecture 29: Interplanetary 37
Turning Angle
How do they work?
• Use Pioneer 10 as an example:
Lecture 29: Interplanetary 38
INTO FLYBY
OUT OF FLYBY
Gravity Assists• We assume that the planet doesn’t move during the flyby
(pretty fair assumption for initial designs).– The planet’s velocity doesn’t change.
• The gravity assist rotates the V-infinity vector to any orientation.– Check that you don’t hit the planet
Lecture 29: Interplanetary 39
Gravity Assists• We assume that the planet doesn’t move during the flyby
(pretty fair assumption for initial designs).– The planet’s velocity doesn’t change.
• The gravity assist rotates the V-infinity vector to any orientation.– Check that you don’t hit the planet
Lecture 29: Interplanetary 40
Designing a Gravity Assist
• Build a transfer from Earth to Mars (for example)– Defines at Mars
• Build a transfer from Mars to Jupiter (for example)– Defines at Mars
• Check to make sure you don’t break any laws of physics:
Lecture 29: Interplanetary 41
Designing a Gravity Assist
• Another strategy:– Build a viable gravity assist that doesn’t necessarily
connect with either the arrival or departure planets.– Adjust timing and geometry until the trajectory becomes
continuous and feasible.
Lecture 29: Interplanetary 42
Gravity Assists
Lecture 29: Interplanetary 43
Please note!
This illustration is a compact, beautiful representation of gravity assists.
But know that the incoming and outgoing velocities do NOT need to be symmetric about the planet’s velocity! This is just for illustration.
Gravity Assists
• We can use them to increase or decrease a spacecraft’s energy.
• We can use them to add/remove out-of-plane components– Ulysses!
• We can use them for science
Lecture 29: Interplanetary 44
Announcements• HW 8 is out
– Due Wednesday, Nov 12.– J2 effect– Using VOPs
• Reading: Chapter 12
Lecture 29: Interplanetary 45