Effect of Earth on Venus/Mars orbits

[naelphin]

If Earth disappeared, would the orbits of Venus or Mars be affected in any way? Would they be perturbed, or would their paths remain the same.

[AndreasJ]

Their paths would remain practically the same, assuming the magicking away of the Earth in itself did not affect them.

[Hornblower]

With Earth magically gone, the orbits of Venus and Mars would come closer to remaining unchanged, rather than undergoing their actual variations which are caused in part by Earth's perturbations.

[tony873004]

I know I've seen some articles about simulations where either Mercury or Venus (I forget) was removed from the system, and over a long period of time, it destabalized everything else. Actually, some simulations suggest that over long periods of time, the solar system in its current configuration is unstable, with Mercury entering a planet-crossing orbit in billions of years from now, where it will either collide with another planet or the sun, or get ejected from the solar system.

My attempt to simulate any of this has failed. Removing planets has always left me the scenerio Hornblower describes. But I can't accurately go billions of years into the future.

About the only thing I've discovered is that if Venus had twice the mass of Jupiter, in a period of hundreds of thousands of years, Mars would get ejected from the solar system, even though everything appeared very stable until just a few decades prior to its ejection. This demonstrates that systems that appear stable may surprisingly fly apart over long periods of time. So perhaps the scenerios I read about are plausable.

[frankuitaalst]

I think both statements above are correct .
On a small timescale the effect of a disappearing Earth is hardly noticeable.
Hereunder is an animation which shows the orbits of Mercury and Venus with and without the Earth-Moon system .
Visually no change . The minimum distance from Venus to the Sun over a time-period of 2 years varies only by 17 * 10^-8 astronimical units as can be seen in the animation. One can get other figures depending upon the time on which Earth disappears ( in this case Jan 1st 2009 ) .

[frankuitaalst]

With Earth magically gone, the orbits of Venus and Mars would come closer to remaining unchanged, rather than undergoing their actual variations which are caused in part by Earth's perturbations.

Indeed , this makes sense .
Here's the result of a quick integration of the orbit of Venus with and without Earth . ( Semi Major Axis expressed in meters)
Venus will move inwards when Earth disappears . It's orbit will be more "stable" as the variations in its orbital parameters will diminuish .
The same can be said about Mars I guess , but Mars' orbit will tend to move a little bit more outwards.