I'm attempting to automate interplanetary transfers using Vizzy, however I am finding that when I depart my starting planet I have slightly too much velocity (35 m/s or so). I'm predicting my velocity by adding the V-infinity of my hyperbolic orbit to the orbital velocity of my starting planet. My current theory is that because of the use of patched conics and spheres of influence cause the amount of velocity I have when crossing into the sun's SOI is higher than the theoretical V-infinity, and that this is where the error is coming from. I'm hoping that by knowing the distance from the planet where it's SOI terminates I will be able to account for this.
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15 ivanKohan4.0 years ago
Mercury 111,780 km;
Venus 616,960;
earth 924,820 ;
Mars 577,630 ;
Jupiter 48,141,000;
Saturn 54,744,000 ;
Uranus 51,755,000 ;
Neptune 86,925,000;
for the moon relative to Earth 66,282 km. g=F/h2 g-the force of attraction in space, F-the force of attraction of the planet, h-height .
P0=P(M/m)^2/5 or P0=P(5√(m/m)2), P0 - the radius of the planet of the sphere of activity, P - the distance between the celestial bodies (planet / sun, moon /earth), and m-the mass of the planet, m-the mass of the sun -
Mod sflanker4.0 years ago
The going theory, thanks to @pedro16797, is that SOI is based on the distance at which the acceleration due to gravity from the parent body becomes greater than the acceleration due to gravity from the body whose SOI we are trying to determine. I'm assuming at this point that we're talking about the point where the two accelerations are in opposite directions (i.e. the point in between the two bodies). I'll try to verify this experimentally and report back.
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Well, I'm sorry to say I failed to thoroughly research this before asking, and it turns out there is an wikipedia article describing how a sphere of influence is defined. I did however discover through investigation that SR2 tacks on an extra 5% when checking for exit of an SOI. So the equation for the radius of an SOI is:
r_soi = sma * (mass / mass_parent) ^ 0.4
And the equation for the SOI when checking for the exit of an SOI is:
r_exit_soi = 1.05 * r_soi