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HeatDeath · 07-28-2019, 05:36 PM

Code:

- - - - T Y - A B Q
 - - - - - X F O C Z
- - - - - - - E D R
 - - - - - S - -

I think it's actually possible to leave orbit having expended only one point of fuel.

In the above diagram, O is the planet, A, B, C, D, E, and F are gravity hexes surrounding the planet. Q, R, X, and Z are empty hexes in free space just beyond the gravity hexes. S and Y are empty hexes in free space a little farther out.

In the rules as written, a spaceship is launched from the planet surface by booster rockets, resulting in the spaceship having zero velocity and a full fuel load in (for example) hex C. If the spaceship does nothing, it will fall back to the planet in the next turn. So it has to boost. Let's consider its options.

O - Boosting in the direction of the planet is just an expensive way to commit suicide.
Z - Boosting in direction Z is an expensive waste of fuel. Your boost plus the gravity arrow in C will put you right back in C with zero velocity.
Q and R - These are the hexes you actually boost towards to enter orbit. Boosting towards Q, plus the gravity arrow in C, puts you into hex B, with a heading that, combined with B's gravity arrow, will carry you to A, and eventually around the planet in a counter-clockwise 1-hex-per-turn orbit. Similarly, boosting towards R will put you in D on an orbital trajectory.
B and D - Now here's where things get interesting. We'll consider case D in detail - bear in mind that B is similar, but in the opposite direction.

We boost towards D. That direction, plus the gravity arrow from C, puts us into hex E, with vector C->E, a velocity of 2 hexes per turn (1 "west" plus 1 "southwest", see the compass rose below). By diving obliquely towards the planet we effectively gave ourselves a gravity-assist velocity boost of 1 hex per turn. Which is both realistic and pretty awesome.

On our next turn, this vector would normally carry us to hex S, but recall that in getting to E, we passed through D and E. So we have to add in those gravity arrows. That puts us in hex X, exactly halfway around the planet from where we started. Cool.

So now we're in hex X, with a vector E->X, but we're not quite free and clear of any gravity arrows. Our vector would takes us to hex T, but recall that we passed through hex F to get here. Adding hex F's gravity arrow puts us in hex Y. If we do nothing else (and I've done the math right) we will continue to coast 1 hexes per turn on this vector (1 "northwest"), through hex Y and beyond. We've escaped Earth's (or whatever planet's) orbit using only 1 point of fuel.

Incidentally, if you do this from Earth, you end up heading in the general vicinity of a Mars intercept course, having only spent one point of fuel. Which is pretty nice if you're a transport and you don't have a huge amount of fuel to spare.

Particularly if you want to evade the Corsair that just boosted from Clandestine at the same time!

Code:

--  --  NW  NE  --  --
  --  W   **   E  --
--  --  SW  SE  --  --

07-28-2019, 05:36 PM	#7
HeatDeath Join Date: May 2012	Re: Triplanetary - Landing and Takeoff Code: - - - - T Y - A B Q - - - - - X F O C Z - - - - - - - E D R - - - - - S - - I think it's actually possible to leave orbit having expended only one point of fuel. In the above diagram, O is the planet, A, B, C, D, E, and F are gravity hexes surrounding the planet. Q, R, X, and Z are empty hexes in free space just beyond the gravity hexes. S and Y are empty hexes in free space a little farther out. In the rules as written, a spaceship is launched from the planet surface by booster rockets, resulting in the spaceship having zero velocity and a full fuel load in (for example) hex C. If the spaceship does nothing, it will fall back to the planet in the next turn. So it has to boost. Let's consider its options. O - Boosting in the direction of the planet is just an expensive way to commit suicide. Z - Boosting in direction Z is an expensive waste of fuel. Your boost plus the gravity arrow in C will put you right back in C with zero velocity. Q and R - These are the hexes you actually boost towards to enter orbit. Boosting towards Q, plus the gravity arrow in C, puts you into hex B, with a heading that, combined with B's gravity arrow, will carry you to A, and eventually around the planet in a counter-clockwise 1-hex-per-turn orbit. Similarly, boosting towards R will put you in D on an orbital trajectory. B and D - Now here's where things get interesting. We'll consider case D in detail - bear in mind that B is similar, but in the opposite direction. We boost towards D. That direction, plus the gravity arrow from C, puts us into hex E, with vector C->E, a velocity of 2 hexes per turn (1 "west" plus 1 "southwest", see the compass rose below). By diving obliquely towards the planet we effectively gave ourselves a gravity-assist velocity boost of 1 hex per turn. Which is both realistic and pretty awesome. On our next turn, this vector would normally carry us to hex S, but recall that in getting to E, we passed through D and E. So we have to add in those gravity arrows. That puts us in hex X, exactly halfway around the planet from where we started. Cool. So now we're in hex X, with a vector E->X, but we're not quite free and clear of any gravity arrows. Our vector would takes us to hex T, but recall that we passed through hex F to get here. Adding hex F's gravity arrow puts us in hex Y. If we do nothing else (and I've done the math right) we will continue to coast 1 hexes per turn on this vector (1 "northwest"), through hex Y and beyond. We've escaped Earth's (or whatever planet's) orbit using only 1 point of fuel. Incidentally, if you do this from Earth, you end up heading in the general vicinity of a Mars intercept course, having only spent one point of fuel. Which is pretty nice if you're a transport and you don't have a huge amount of fuel to spare. Particularly if you want to evade the Corsair that just boosted from Clandestine at the same time! Code: -- -- NW NE -- -- -- W ** E -- -- -- SW SE -- -- Last edited by HeatDeath; 07-28-2019 at 05:53 PM.