Interest in the exploration of Jupiter and its moons remain as strong today as it was in the early days of space travel with the arrival of Pioneer 10 into the Jovian system in 1973. Jupiter has been the most visited of the Solar System’s outer planets as all missions to the outer Solar System have used Jupiter flybys. New probes are currently en route to Jupiter. Sending a spacecraft to Jupiter is challenging, mostly due to large fuel requirements and the effects of the planet’s harsh radiation environment.

Jupiter

Part 1: Mission Design using a Hohmann Transfer Orbit

Using the method of patched-conic technique, the goal of part 1 is to determine the characteristics of an interplanetary Earth to Jupiter mission based on a heliocentric Hohmann transfer. Assume coplanar concentric planetary orbits and use the data found in the Appendix.

In particular, find:

1. the Hohmann-transfer flight time in days, the semimajor axis, and eccentricity.
1. the hyperbolic departure velocity from Earth, \(v_{\infty/E}^+\) (km/s).
1. the necessary \(\Delta v\) from a circular parking orbit of altitude 600 km above the earth that will place the spacecraft on the Hohmann ellipse to Jupiter.
1. the hyperbolic arrival velocity, \(v_{\infty/J}^-\) (km/s).
1. the necessary \(\Delta v\) for insertion into a retrograde circular capture orbit of altitude 10,000 km above Jupiter.
1. the phase angle of Jupiter at departure (the position of Jupiter at launch time).
1. In the case of a flyby mission to Jupiter, assuming a closest approach at an altitude of 1,000,000 km on the sunlit side of the planet, determine the eccentricity/semimajor axis of the post-flyby trajectory as well as the delta-v gained by the spacecraft by Jupiter’s gravity. Can Saturn be reached using this gravity assist? (sketch the post-flyby orbit in relation to the circular orbits of Jupiter and Saturn).

Be sure to include all annotated sketches in your solution.

Part 2: Document a Real Mission

The goal of Part 2 is to identify and document a past (or present) mission to Jupiter. First select a particular mission. Then search the literature (from web sources, archival academic papers or books) for scientific and technical information pertaining to the mission.

2.1 Describe and document the following (but not limited to)

1. the mission goals, science objectives,
1. the principal mission phases,
1. the mission key dates, such as departure, and arrival dates, flight time, the dates of the flybys to planets for gravity assists,
1. the delta-v’s obtained by gravity assists,
1. the delta-v needed for orbit insertion.

2.2 Outline the key qualitative and quantitative differences between this real space mission and the theoretical mission analyzed in Part 1.

2.3 Conclude by discussing the benefits and drawbacks of the work performed in Part 1.

Include all graphical data without omitting the sources.

Complete your report by making sure that all sources are properly cited in the paper.

Appendix: Data

Jupiter semimajor axis \(a_J =\) 5.2026 AU
Earth semimajor axis \(a_E=\) 1 AU
SOI radius \(r_{SOI,J}\) of Jupiter = 3.228610 x 10\(^{-1}\) AU
SOI radius \(r_{SOI,E}\) of Earth = 6.183155 x 10\(^{-3}\) AU
Gravitational parameter \(\mu_J\) of Jupiter = 126.7 x 10\(^6\) km\(^3\)/s\(^2\).
Gravitational parameter \(\mu_E\) of Earth = 398,600 km\(^3\)/s\(^2\)
Gravitational parameter \(\mu_S\) of the Sun = 132.7 x 10\(^9\) km\(^3\)/s\(^2\)
Astronomical Unit 1 AU = 149,597,871 km
Radius of Earth = 6,398 km
Radius of Jupiter = 71,490 km

Rubrics/Comments

Part 1: 60 points

Most of the material is covered in lectures 11, 12 and 13.
Define all symbols. Do not use the same symbol (notation) for different quantities. example: use the same notation \(e\) for the various eccentricities.
Sketch all figures with labels and captions, and refer to these figures in your solution. These figures play a big part of the solution.
Your solution should not just be a list of equations: add some explanation for full credit.
You should use 2 unit vectors to define vector quantities (sketch them on your figures). The same vectors should be shown consistently on the figures.
in g), be careful: the distance 1,000,000 km refers to an altitude (not a radial distance to the planet’s center)
for heliocentric quantities use astronomical units (AU, AU/TU, etc).
for planetocentric (e.g geocentric) quantities use standard units (km, km/s, km\(^2\)/s, etc).
make sure you differentiate heliocentric velocities from planetocentric (geocentric/jupitercentric) velocities: this is done in the notation: \[ \boldsymbol{v}_{P/S} \quad (heliocentric) \] \[ \boldsymbol{v}_{P/J} \quad (jupitercentric) \] \[ \boldsymbol{v}_{P/E} \quad (geocentric) \]

Point Distribution:

a: 5 pts
b: 5 pts
c: 5 pts
d: 10 pts
e: 15 pts
f: 5 pts
g: 15 pts. To answer the question regarding Saturn, use Saturn semimajor axis of 9.5 AU as the radius of its circular orbit. You can use a graphing utility like gnuplot, maple, matlab, etc to plot ellipses (circle) \(r= p/(1+e \cos(\theta-\theta_0))\) in polar coordinates (with \(p\) in AU units). Your graph should show 3 curves: the Hohmann transfer orbit, the post-flyby orbit, and Saturn circular orbit.

This is not a homework, hence higher quality of delivery (presentation) of your project is expected.

Part 2: 40 points