Download 1 - Colorado Center for Astrodynamics Research

Voyager Interstellar Mission
Nicholee Page
ASEN 5050: SPACEFLIGHT DYNAMICS
University of Colorado at Boulder
12/13/01
The two Voyager Spacecraft, launched in 1977, are now reaching the end of our solar system.
The primary mission of the Voyager spacecraft was to conduct flybys of Jupiter, Saturn,
Uranus & Neptune, which was completed in 1998. Voyager’s Interstellar Mission (VIM) is
an extension the primary mission. The VIM consists of three exploration phases: termination
shock zone, heliosheath, & interstellar space.
This website introduces the Voyager missions, discusses the astrodynamics of Voyager
spacecraft, and includes a proposal to extend the VIM mission. The proposed VIM extension
involves a return mission to AC+79 3888, the nearest star.
1 Introduction
1.1 Background
The Voyager Mission was designed to take advantage of a rare occurrence of planetary
alignment. The outer planets of Jupiter, Saturn, Uranus, and Neptune are in proper
alignment only every 175 years. This particular alignment allows a spacecraft departing
earth to go from one planet to another with a small amount of onboard fuel. The
technique of increasing the spacecraft's speed by flying by a planet is called gravity
assist.
Since a mission of touring four of the outer planets seemed very expensive, although
possible, NASA funded the Voyager Missions to only perform fly-bys of Jupiter and
Saturn. Thus the spacecraft were built only to last 5 years. But as the mission went on,
with much success, additional flybys of Neptune and Jupiter proved possible with
Voyager II and were added to the mission goals. Since then an additional mission has
been added, called Voyager Interstellar Mission VIM. The VIM consists of three
exploration phases: termination shock zone, heliosheath, & interstellar space. Currently
both spacecraft are nearing the end of the termination shock zone.
1.2 Foundation of Interplanetary Trajectories
The driving design goal for an interplanetary trajectory is often to minimize the mass of
the spacecraft. Because most of the mass is propellant, it is best to minimize the thrust
(delta v) required throughout a mission. The lowest thrust solution is called the minimum
energy solution, or Hohmann Transfer.
To launch a spacecraft from earth to an outer planet, like Jupiter, it is necessary to
consider that it is already orbiting the sun with earth. Essentially, this orbit must be
adjusted to send the spacecraft out to Jupiter. This can be pictured as three parts; circular
orbit around earth, elliptical orbit with earth at one foci and the other at Jupiter (only half
of this orbit will be performed), and a circular orbit around Jupiter, see diagram below.
To reach an outer planet, it is necessary to increase orbital velocity at earth. Therefore,
the transfer orbit will have perihelion, (closest foci to the sun) at earth and the aphelion
(farthest foci from the sun) at Jupiter. To accomplish this, the spacecraft will fire a
thruster in the direction of earth's orbital velocity about the sun, and "coast" the rest of the
way to Jupiter. To orbit Jupiter upon arrival, the spacecraft must fire a reverse thruster
(or perform braking maneuvers) to continue orbiting Jupiter.
For travel to an inner planet, the transfer orbit will have aphelion at earth and aphelion at
the inner planet. This time, however, the direction of thrust when leaving earth will be
opposite that of earth's orbital velocity, to decrease the spacecraft's speed relative to the
sun.
1.3 Basics of Gravity Assist Trajectories
Each planet contains a large amount of the solar system's angular momentum. On a
gravity assist trajectory, the spacecraft captures a small portion of the planet's angular
momentum and is "slung" father into space. Consider the Jupiter transfer example above.
The process of getting to Jupiter will be the same, in this case, however, no reverse
thruster will be fired to keep the spacecraft orbiting Jupiter. To do this the spacecraft
must approach the planet from behind (with forward being the direction of its orbital
velocity about the sun). Jupiter will pull the spacecraft toward itself, increasing the
spacecraft's orbital velocity about the sun. Once past the planet, the spacecraft's speed is
slowed down by the planet's gravity, but the outbound speed is still far greater than the
speed at which it was approaching the planet. A graph of Voyager II's gravity assists is
shown below.
Voyager II Gravity Assist Velocity Changes
2 Voyager Beyond our Solar System
2.1 Importance of the Mission
The Voyager Interstellar Mission (VIM) was designed to extend exploration beyond our
solar system and into the outer limits of the sun’s sphere of influence. This mission will
help scientists gather data about the boundary of our solar system. The spacecraft will
travel through the termination shock, the heliosheath, and into interstellar space gathering
data of interstellar fields, particles and waves.
The termination shock zone is the area around our solar system where the sun's solar
wind and interstellar solar wind interact. At this point the supersonic solar wind from the
sun slows down to subsonic speeds. The exact location of the heliosheath is unknown,
but it is speculated to be between 80 and 90 AU from the sun (1AU is equal to the
distance form the center of the sun to the center of earth). All this time instruments
onboard the spacecraft will be taking measurements for science investigations. For both
Voyagers, this phase is expected to be completed by 2003.
Once through the termination shock zone, the heliosheath phase begins. Here, although
out of the sun's solar wind, the spacecraft will remain under the influence of the sun's
electromagnetic radiation. The thickness of the heliosheath is not accurately known, but
guessed to be between 10 and 90 AU. This part of the VIM could take many years to get
through. Upon passage through the heliosheath, the spacecraft begin interstellar
exploration. This interstellar phase is the ultimate goal of the Voyager Interstellar
Mission.
3-D View of the Solar System Showing Voyager I and II
2.2 Importance to Astrodynamics
The VIM segment of Voyagers Mission is very important for future astrodynamics.
Many farsighted people have hopes of developing a means of traveling to another solar
system, or star. Though this is highly unlikely to happen within our lifetime, each piece
of new knowledge will bring us one step closer. The Voyager spacecraft, along with
Pioneer, are the only spacecraft to explore the path to interstellar space. As Voyager I
and II are tracked, they provide important information regarding the dynamics of our
solar system's boundary. From this data collection, many new astrodynamics techniques
will be developed.
2.3 Development of Solution
Escape velocity from the sun, starting from earth
The approximate amount of velocity required to escape the sun gravity, starting from
earth, can be computed from the following equation:
vesc  2
s
d
where:
d = 149598023
km
s = 1.32712428e11
(distance from center of sun to center of earth)
[km3/s2] gravitational parameter of sun
This approximation yields a velocity of 42.1219 km/s, with respect to the sun.
(see attached matlab code: Vesc)
Estimation of Sun's Sphere of Influence
An estimation of the sun's sphere of influence into interstellar space can be made by the
following equation
SOI Sun
M 
 rs  g  Sun 
 M Gal 
2/5
AU
where:
rs-g = 1.75e9
AU (distance from center of Milky Way to sun)
M Sun
= 1.075e-11 ratio of sun mass to galaxy mass
M Gal
Solving this gives a solution of 71,721 AU.
(see attached matlab code: SOI)
2.4 Analysis of Method
These approximations above give similar results to the quoted values in the Starflight
Handbook, taken from the Jet Propulsion Laboratory (JPL):
Approximations:
Quoted:
Vesc:
42,1219 km/s
42 km/s
SOI:
71,721 AU
100,000 AU
This proves that the analytical estimations are very good approximations. The methods
above assume that the earth is point mass and that only two bodies exist in the system.
The quoted values take into account the other planets as well as the true dimension of
earth.
3 Extension Proposal: Trajectory to Star AC + 79 3888
3.1 Proposal
Traveling to a new frontier has fascinated explorers since the beginning of time. There
are millions of stars in our galaxy alone, yet we are just now exploring the depths of our
solar system. Wouldn't it be incredible if we could get to another star? Well, actually we
can, it just takes a little longer. One of our spacecraft, Voyager 1 is on a trajectory to
drift within 1.6 light years of a star, AC + 79 3888. This is a proposal to use the
minimum energy solution to get to this star.
3.2 Analysis
To make the approximate calculations, the Hohmann transfer method will be used
(example above). In this extension, instead of transferring between two planets rotating
around the sun, the transfer will take place between two stars, rotating about the center of
the galaxy. Due to the vastness of our galaxy, this is a very rough approximation.
The analytical solution is as follows:
Known Parameters:
R(sun) = 1.75e9 AU distance from the center of the galaxy to our sun
R(star) = 1.75e9 + 1.063e6 AU distance from the center of the galaxy to the star
Results:
Once the solar system has been escaped the required change in velocity is
0.0668632595173051 km/s. The time required for such a trip is
118382376.829853 years. This is very large because the spacecraft is traversing halfway
across the galaxy.
(see attached matlab code: VIM)
Using gravity assist of outer planets and a hyperbolic trajectory to the star
Total Trip time = 60,000 years
3.3 Recommendations
From these results, it is proven that the Hohmann transfer is a transfer that requires very
little energy. The thrust required of this mission is very small compared to the distance
the satellite will be traveling. The benefit of this low amount of fuel is not worth the cost
of the time required to complete the transfer. In comparison, the hyperbolic trajectory of
Voyager II puts it at this same star in only 40,00 years. This proves that the minimum
energy solution is not always best in all aspects of the mission. There are times when it is
beneficial to carry additional fuel and get to the destination in a more direct path - here
saving millions of years in trip time. Both of these missions may seem unrealistic
because the amount of time required is much beyond our lifetime. However, it is
important to look into the future and consider that this spacecraft may be discovered by
some other life form orbiting this star.
4 Summary & Conclusions
The twin Voyager Spacecraft were launched by NASA in 1977. The primary mission
was to conduct flybys of Saturn and Jupiter to retrieve data of Saturn's rings and moons
of both planets. Because of great success and proper planetary alignment, Voyager II
also performed flybys of Jupiter and Saturn. Between the two they explored all the giant
outer planets, 48 of their moons, and rings of Saturn.
After they had already completed their primary mission, and an extension, they were sent
on another mission: interstellar space. Today this extended mission, through the
termination zone, heliopause, and into interstellar space, continues to characterize the
outer solar system environment.
5 References
Mallove, E & Matloff, G. The Starflight Handbook: A Pioneer's Guide to Interstellar
Travel. New York. John Wiley & Son. 1989.
Mauldin, J. Prospects for Interstellar Travel. San Diego, CA. American Astronaumical
Society. 1992.
NASA Jet Propulsion Laboratory. Voyager Homepage
<http://www.jpl.nasagov/voyager>
NASA Jet Propulsion Laboratory. Basics of Flight <http://www.jpl.nasagov/basics>
Seeds, M. Foundations of Astronomy. Ed 4. Belmont, CA. Wadworth Publishing
House. 1997.
Vallado, D. Fundamentals of Astrodynamics and Applications. Ed 2. El Segunda, CA.
Microcosm. 2001.
6 Additional Matlab Code
Vesc.m
SOI.m
VIM.m