Homework 2 Question 3 (William Matzko)

I inserted an extra planet of 0.01 Solar masses at (-1.9, 1.9, 1.9) AU with velocity (1E-08, 1.2E-03, 1.8E-08) Au/day (for some reason it started my planet out at 1.65 AU instead of ~3.3 AU). This caused the most change in the inner planets. Mercury became unbound (e>1) about 1800 years in. Venus went out to ~5 AU about 2000 years in and was on the verge of becoming unbound. Earth went out to ~ 10 AU about 1500 years in and became unbound. Mars experience a relatively small change in semimajor axis; it slowly went inwards to 1 AU and started to go back out. Its eccentricity experienced severe oscillations, but it did not become unbound. It also experienced large oscillations in its inclination. Jupiter was the only outer planet that was significantly disturbed enough to bother mentioning. Its semimajor axis was relatively constant around 5 AU, but its eccentricity and inclination sharply increased and began to level off. An image of all 15 relevant plots is attached. The graphs of my planet are also attached separately. All other unmentioned planets were not significantly affected—their a, e, and i were relatively unchanged. My planet was at ~1.66 AU for much of the simulation, but went out to ~1.68 about 2300 years in. Its eccentricity is incredibly high (~0.99) for the duration of the simulation. Its inclination started out high, about 135 degrees, but it was down to 40 degrees by the end. 

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