asen 5050 spaceflight dynamics interplanetary prof. jeffrey s. parker university of colorado –...

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


Schedule from here out


• 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


Quiz #14


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Quiz #14


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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


ASEN 5050SPACEFLIGHT DYNAMICS

Interplanetary

Prof. Jeffrey S. ParkerUniversity of Colorado – Boulder


Interplanetary

• History

• Planets

• Moons

• Small bodies


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


Patched Conics

• Use two-body orbits


Patched Conics

• Gravitational forces during an Earth-Mars transfer


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:


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:


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.


Sphere of Influence



Primary Earth Accel

Primary Sun Accel

3rd Body Sun Accel

3rd Body Earth Accel

Sphere of Influence



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.


After simplifications:

Sphere of Influence

• Find the surface that sets these ratios equal.


Earth’s SOI: ~925,000 kmMoon’s SOI: ~66,000 km

Patched Conics

• Use two-body orbits


Interplanetary Transfer

• Use Lambert’s Problem • Earth – Mars in 2018


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.


Earth Departure

• We have v-infinity at departure

• Compute specific energy of departure wrt Earth:

• Compute the velocity you need at some parking orbit:


Earth Departure


Departing from a circular orbit, say, 185 km:

Launch Target


Launch Targets

• C3, RLA, DLA


(In the frame of the V-inf vector!)

Launch Targets


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?


Aerobraking


Comparing Patched Conics to High-Fidelity


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.


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?

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

How do they work?

• Use Pioneer 10 as an example:


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


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:


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.


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.

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


Announcements• HW 8 is out

– Due Wednesday, Nov 12.– J2 effect– Using VOPs

• Reading: Chapter 12


asen 5050 spaceflight dynamics interplanetary prof. jeffrey s. parker university of colorado –...

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