Wong Amy

Good news everyone, you are going on a mission!

Recently, my dear intern Amy acquired a new car – a Beta Romeo.
Now, she asks me to deliver it to her home planet, the Mars. Even
though her family owns the entire western hemisphere of the planet,
Amy won't be considering paying the delivery fee. Using the ship for
private needs is an abuse of company properties, I say! So let’s do it.
However, massive increase in prize of dark matter makes me having
second thought about the trip. I’ll have to be more carful about the
expensive ship fuel and combine the shipment with another delivery.
Oh my, yes! An order just came in - a delivery to the planet Neptune!
Robot Santa Claus is ordering new wapons in order to deal with all the
naughty people on Earth.

Let’s find a suitable date for the delivery, assuring no extra distance
being required while dropping off Amy’s car along the way. I’m also
thinking about the most unsuitable day for such space travel. Actually,
I’m wondering, when these particular conjunctions, as seen from the
Sun, have been observed during the millennium, when Fry was frozen.

You are looking for the day, month and year (GMT) on which the Sun,
Earth, Mars and Neptune align to a straight line within minimal angle
difference. You can ignore the inclination of the planets, concentrating
on the orbit around the Sun only.

AB.CD.2EFG is the date when all three planets are on the same side of
                         the Sun.

HI.JK.2LMN is the date when Mars is on the exact opposite side of the
                       Sun to Earth and Neptune, still aligning to a straight line
                       within minimal angle difference.

The cache is located at the following coordinates:

N 50° 3(I).(G)(H)(B*C)     E 6° (A+J)(N).(F)(K)(E-D+L-M)

Sincerely,
Prof. Hubert Farnsworth