**DietmarW**

Was the term dVmax / dVused really intended this way? Means we target 5 stars in 90 Meur with minimal DV and this counts as settlement of the milky way? Quite boring for the people living in these ships. (1.0 + dVmax / dVused) would have rewarded "real" settlement. Congratulations to the teams who discovered this first.

**lihy**

If humans continue to do this, the other side of the Milky Way will be occupied by the creatures of Centaur.

**DietmarW**

There is some truth in this. But it has drawbacks: Weather is still quite cold here, and my table generating machines produced a lot of cosy warmth the last days. Now its cold again.

**Anastassios@JPL**

The indomitable GTOC spirit has shown we can fly missions on the cheap. Now, can we spend a bit more and break through the Error Barrier and settle throughout the galaxy?

**drayflah**

Theoretically the last term in the score function could be infinite, which makes all the efforts to maximize the other terms meaningless...

**DietmarW**

Theoretically yes. In practice it is very easy to determine the absolute limit for <= 5 stars: Follow sols path for about 90 Myr and collect all stars along this path which are "near", means have low dP^2 + (30*dV)^2 values, dP = relative position, dV = relative velocity wrt. sol with dP in kpc and dV in kpc/Myr. For all these stars - select the best 100 or 200 - search for low deltaV transfers from sol. Select the best and upload the best combinations of 2, 3, 4 and 5 stars as submission. The best submission shows the optimal value. To refute this assumption try to beat 0.540000E+04 / 0.617327E+02 which is the factor I determined using exactly this method which you can see in the leaderboard.

"which makes all the efforts to maximize the other terms meaningless..." unfortunately is nevertheless true.

**IngoA**

Dietmar, a question just out of curiosity: How near do the passing stars in your solution come to our solar system?

**DietmarW**

If you mean position wise I have to check. But position is irrelevant if there is a huge velocity difference. Its the combination which matters. Its like a rendezvous maneuver, we don't use the ability of the mother ship to continue its flight. That this works is due to the fact that even 90 myr is only part of a single revolution and that the orbits are circular. Each student should be able to solve this exercise. Another observation: The fact that the finite and easily computable limit for the last term is big doesn't mean that it is easy to prove that the other terms are irrelevant. The settler tree could in principle grow exponential, which the admirable NUDT solution shows. But I am probably not the only one who observed issues with the quadratic terms inside the E_r error function in combination with the huge constant denominator in g_r(r). This means diminishing J-returns for dense settler populations. E_r restricts the exponential grow of settlements in a way that it is very hard (perhaps impossible) to break the 0.540000E+04 / 0.617327E+02 barrier. I would like to hear the opinion of other teams, specially from NUDT.

**DietmarW**

A small correction: (1.0 + dVmax / dVused) would of course not fix the issue, I meant something like dVmax / ( dVmax + dVused) or any other term growing when you reduce dVused, but only in a limited way.

**DietmarW**

Congratulations to ESA + NUDT. Seems dVmax / dVused created a bait. Some of us snapped the bait, some pretended to do so. NUDT cleverly did't show us their progress to lure us into a stasis. Only who trusted JPL had a chance. The ones who lost faith (like us) have to live with the consequences. Which is fair. What a fantastic competition!

**esparano**

I was also initially skeptical of the dVused denominator, but it turns out it's not exploitable! I can't pretend we didn't search for a near-divide-by-zero!

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