Orbits between the moon and it's planet

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nopatience

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If you were falling into an orbit around Jupiter between Jupiter and one of its moons, would that moon have an effect on your speed and or orbital position?<br /><br />in other words, would the gravity from a moon effect your orbital insertion?<br /><br />say if Cassini was falling into Saturn, would the trajectory have to be a certain distance from the moons?<br /><br />
 
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nacnud

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Yes the gravity from the moon would have to be considered but once evaluated it might turn out to be very small depending on the situation.
 
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spacester

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On a purely scientific basis, yes the nearby moon would have an effect.<br /><br />But on a purely practical basis, the effect can be ignored in most cases.<br /><br />Trajectories are generally calculated using the "patched conic" method. The central premise of this method is that you only have to account for one body at a time.<br /><br />Before you get to Jupiter, your course is assumed to be completely controlled by the Sun's gravity. When you get close enough to Jupiter, you simply switch from that assumption to being completely controlled by Jupiter.<br /><br />The distance from Jupiter at which you make this mathematical transition is called the sphere of influence (see below for Jupiter's SOI)<br /><br />If you were to come within the moon's SOI, you would want to use patched conics to take into account how much the moon would bend your trajectory. In practice, that would be very close to the moon indeed to matter much.<br /><br />The patched conic method is surprisingly accurate, however if you want to do precise targeting (ala Cassini at Saturn), it gets very much harder. You have to run an N-body simulation on a powerful computer to take into account all the moons, as well as the other planets.<br /><br />***<br />From the link, for easy reference:<br />rP = Dsp [Mp/Ms]^(2/5)<br /><br />Where<br />Dsp = the distance between the Sun and the Planet <br />Mp = mass of the planet <br />Ms = mass of the Sun <br />Example: Jupiter and Earth<br />Jupiter: <br />The Sun is 1047 times more massive than Jupiter (MSun/MJ = 1047). The distance between the two is 5.02 AU (AU = Astronomical Units = 150 million km). So<br />rJ = (5.2 x 1.5x108km) [1/1047]2/5 = 48.3 million km<br />The most distant satellites of Jupiter are about 1/2 this distance away from the planet. Jupiter's radius is 73,500 km <br />so in terms of the planets radius, RJupiter: rJ = 657 RJupiter <br />***<br />Note that SOI is a bit arbitrary, for best <div class="Discussion_UserSignature"> </div>
 
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CalliArcale

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Just as a sidenote, Galileo used gravitational interactions with the Galilean satellites to adjust its trajectory more than would've been possible with its engine alone. But the Jovian system is special for having four significantly large moons. Saturn has only one super-moon: Titan. The other moons are believed to have a gravitational affect on the ring system, and undoubtedly on each other as well, but the effect may only be significant over a long period of time. <div class="Discussion_UserSignature"> <p> </p><p><font color="#666699"><em>"People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff."</em>  -- The Tenth Doctor, "Blink"</font></p> </div>
 
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