Gravitational Effects: How Jupiter Impacts Mars' Orbit

[Frannas]

I know this question may be a bit vague, and probably needs better wording, but I struggle to rephrase it.

What is the effect that a larger planet eg. Jupiter has on a smaller nearby planet eg. Mars?
This question is based mainly on the orbital path of both planets, how is it influenced?

 

[Philosophaie]

The Force exerted between the two is:

F=\frac{G*Mmars*Mjupiter}{R^2}

R is the distance from Mars to Jupiter
G is the Gravitational Constant
M is the mass of the two respective planets

http://en.wikipedia.org/wiki/Gravitational_constant

 

[tony873004]

Jupiter causes Mars' orbit to precess.

 

[BobG]

Jupiter does contribute to the precession of Mars's rotational axis, but that won't change the orbital path.

If Jupiter is on the same side of the Sun as Mars, then the acceleration of gravity due to Jupiter should be subtracted from the gravitational acceleration due to the Sun. If Mars were in a circular orbit (which it's not), then the reduced net acceleration would mean Mars was going too fast for a circular orbit, which would create an elliptical orbit with apogee on the opposite side of the Sun than Mars & Jupiter.

If Jupiter is on the opposite side of the Sun as Mars, then the opposite occurs. Acceleration due to Jupiter has to be added to the acceleration due to the Sun, which increases the net acceleration, meaning Mars is going too slow to maintain a circular orbit. Perigee will be on the opposite side of the Sun from Mars.

Which is why Mars isn't and can't be in a perfectly circular orbit.

If the Jupiter/Mars conjunction/opposition always occurred in exactly the same spot, then the orbit would slowly become more elliptical. Since Jupiter is so much further away when in opposition, perigee would decrease at a slower rate than apogee increased, meaning the semi-major axis would slowly increase. If the conjunction/opposition rotated around Mars's orbit, then you'd have a slow cyclic increase/decrease in your parameters. Jupiter's orbit is 6.307 times longer than Mars's orbit, meaning the latter would be the case.

Slowly is an understatement. Using the mass of Jupiter, the mass of the Sun, and the semimajor axes of Mars and Jupiter, and Newton's Universal Law of Gravitation, you should be able to calculate how much Jupiter adds or subtracts from the acceleartion due to the Sun. The effect of Jupiter is so small it will barely be detectable except by a long term analysis of Mars's orbit.