Target orbit

[Spricigo]

Contract asKs

Position Vigilant 4 in a adjusted orbit around minmus

Orbit details ap -399km, pe 230km, inclination 80°, long An 360, arg pe88°

current orbit: ap 1085km pe 230km, inclination 81°, long An 1°, arg pe 86° (tanks KER)

 

game its not drawing the orbit, if i understood I need to burn prograde at pe to put in the required escape trajectory. (with aceptable deviation)

may someone confirm/deny it . and if its not the case explain what kind of manuever i need to do?

 

[Reusables]

39 minutes ago, Spricigo said:

ap -399km

Wow, really?

Then you're right, burn at Pe with slight correction on inclination. (Raise it)

[bewing]

.... You can't have an Ap below your Pe. That violates the mathematical definition of the Ap.

It's a mathematically impossible orbit. I assume this is from a modded game (I know you like mods).

Edited April 20, 2017 by bewing

[Reusables]

38 minutes ago, bewing said:

.... You can't have an Ap below your Pe. That violates the mathematical definition of the Ap.

It's a mathematically impossible orbit. I assume this is from a modded game (I know you like mods).

Mathematicians like to use some exploits to generalize equations/formulae/object/class/whatever while keeping it simple. In this case, they decided to call hyperbolic orbit 'elliptic(or conic) orbit with negative Ap'.

For Simplicity!

 

EDIT: In this general representation of 'conic sections', hyperbola has negative semi-major axis and eccentricity bigger than 1.

Reference: http://mathworld.wolfram.com/ConicSection.html & https://en.m.wikipedia.org/wiki/Semi-major_and_semi-minor_axes

Edited April 20, 2017 by Reusables
Mo' explanation

[diomedea]

Can confirm, it's a hyperbolic escape trajectory. The current orbit (Ap = 1085 Km; Pe = 230 Km above Minmus surface) should have velocity = 98.574 m/s at periapsis. The required orbit (Ap = -399 Km) has velocity = 290.261 m/s at periapsis, so you have to burn prograde at periapsis for DV = 191.687 m/s (beyond the slight normal change to meet inclination, LAN and LPE).

[Spricigo]

@bewing mathematicians are weird people.  Its perfectly fine for then to use an value that makes no sense in reality if it solves the equations correctly.  And then they use code words like by definition  to explain where their made up numbers comes from. 

By definition the apoapsis of a hyperbolic orbit is negative.  

[diomedea]

Concur math is often weird, but sometimes what makes it weird is our inability to see its meanings. Hyperbolae are not intuitive loci for us to see, but their resemblance with ellipses goes beyond them all being conics and the identical equations used. It may help see the geometric properties of hyperbolae by looking at figure 4.14 in this document.

While by definition true anomaly is = 0° at the periapsis, Ellipses have Ap at 180° true anomaly, which places the Ap on the opposite direction from the mainbody center (real focus of the conic). On the contrary, hyperbolae have the Ap aligned on the same direction of Pe: Ap lies at the conjunction of the major axis (which goes from the focus to the Pe) with the conjugate branch of the hyperbola (the one imaginary branch we never see depicted in KSP). With that figure 4.14, the center of the hyperbola is where the two asymptotes cross (with an ellipse, center is where the two axes, major and minor, cross); please note for ellipse SMA = distance (center - apsis) (valid with both apsides) and this is valid too with an hyperbola, SMA = distance (center - apsis), however the direction of the center from the real focus is the opposite than with an ellipse, so SMA can clearly be seen as a negative distance. Because taken on the negative side of the major axis, the distance (real focus, apoapsis) is negative too.

As known, one single equation is valid for both ellipses and hyperbolae: SMA = (Ap + Pe) / 2, the identity isn't a convention invented by mathematicians but because values have a true geometric meaning.

Hope the above is clear enough, in case I'll have to draw a different figure to try to convey it better.

[Spricigo]

4 minutes ago, diomedea said:

Hope the above is clear enough, in case I'll have to draw a different figure to try to convey it better.

Yep, very clear and helpfull.

However I'll still call mathematician weird while abusing notation here and there to drive them mad. >8] (notice: to err is human, to blame other even more)