Transcript ASEN 5050 SPACEFLIGHT DYNAMICS

ASEN 5050
SPACEFLIGHT DYNAMICS
Interplanetary
Prof. Jeffrey S. Parker
University 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
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Schedule from here out
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11/7: Interplanetary 2
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11/10: Entry, Descent, and Landing
11/12: Low-Energy Mission Design
11/14: STK Lab 3
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11/17: Low-Thrust Mission Design (Jon Herman)
11/19: Finite Burn Design
11/21: STK Lab 4
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Fall Break
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12/1: Constellation Design, GPS
12/3: Spacecraft Navigation
12/5: TBD
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12/8: TBD
12/10: TBD
12/12: Final Review
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Space News
Orion’s EFT-1
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Quiz #14
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Quiz #14
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N
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S/C motion
(inertial)
Perigee
Point
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Atm motion
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V ~ 8 km/s
Vatm ~ 0.48 km/s
theta ~ 3.1 deg
θ
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S
Quiz #14
• Problem 2
Sun
Lecture 19: Perturbations
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Quiz #14
• Problem 3
Sun
Lecture 19: Perturbations
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Quiz #14
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Quiz #14
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ASEN 5050
SPACEFLIGHT DYNAMICS
Interplanetary
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 29: Interplanetary
11
Interplanetary
• History
• Planets
Today: tools, methods,
algorithms!
• Moons
• Small bodies
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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
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Patched Conics
• Use two-body orbits
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Patched Conics
• Gravitational forces during an Earth-Mars transfer
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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:
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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:
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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.
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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.
Primary Earth Accel
Primary Sun Accel
Lecture 29: Interplanetary
3rd Body Sun Accel
3rd Body Earth Accel
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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.
Primary Earth Accel
3rd Body Sun Accel
=
Primary Sun Accel
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3rd Body Earth Accel
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Sphere of Influence
• Find the surface that sets these ratios equal.
After simplifications:
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Sphere of Influence
• Find the surface that sets these ratios equal.
Earth’s SOI: ~925,000 km
Moon’s SOI: ~66,000 km
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Patched Conics
• Use two-body orbits
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Interplanetary Transfer
• Use Lambert’s Problem
• Earth – Mars in 2018
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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.
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Earth Departure
• We have v-infinity at departure
• Compute specific energy of departure wrt Earth:
• Compute the velocity you need at some parking orbit:
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Earth Departure
Departing from a circular orbit, say, 185 km:
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Launch Target
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Launch Target
Earth Departure Op ons
Outgoing V ∞
Vector
Locus of all possible
interplanetary injection points
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Launch Targets
• C3, RLA, DLA
(In the frame of
the V-inf vector!)
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Launch Targets
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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?
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Aerobraking
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Comparing Patched Conics to HighFidelity
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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.
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Gravity Assists
• Gravity assist, like pretty much everything else, must obey the
laws of physics.
• Conservation of energy, conservation of angular momentum,
etc.
So how did Pioneer 10 get such
a huge kick of energy, passing
by Jupiter?
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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.
Turning
Angle
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How do they work?
• Use Pioneer 10 as an example:
OUT OF FLYBY
INTO FLYBY
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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
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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
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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:
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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.
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Gravity Assists
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.
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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
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Announcements
• HW 8 is out
– Due Wednesday, Nov 12.
– J2 effect
– Using VOPs
• Reading: Chapter 12
Lecture 29: Interplanetary
45