Gravitational effects of planets on each other

[Gully Foyle]

Hi there.

As a molecular biologist my knowledge of physics is fairly limited to the topics I learned before college, but recently I have developed an interest in learning a bit more about it. More to the point a certain question has been puzzling me for some time now and I was wondering if anyone with some expertise could help me.

I'll start by stating what I do know:
1) All objects in the universe attract one another due to the force of gravity.
2) Gravity only has any real effect when very large masses are involved, such as stars or planets.
3) The force exherted by the gravity of an objet decreases exponentially as the distance from it increases.
4) The major forces we feel on Earth are due to the gravity of the sun (keeping us in orbit around it) and the gravity of the moon (causing tides amongst other things).

My question is then; do the planets cause a significant force of attraction on each other, or are they too far apart and too small for the force to be registerable?

I'd appreciate any help with this question, either as a direct answer, or just pointing me in the direction of some information that can allow me to learn how to figure it out for myself. Any calculations with exact data would be great as well.

 

[granpa]

the effects tend to cancel out over time unless the planets are in resonance with each other

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

 

[Phyisab****]

Yes the effects "register." It's just a matter of how much effect you consider to be enough to "register." Considering the system to be just the Earth, Sun, and Moon is an approximation, where including the effects of other planets would give higher order corrections. In fact this full n-body problem is not easily analytically solvable (although some quick research seems to indicate some progress was made on this in the 90's, can anyone elaborate?) and exhibits chaotic or near chaotic effects when considered to a high precision. http://en.wikipedia.org/wiki/N-body_problem

 

[Chronos]

Planetary gravitational effects are miniscule compared to the sun, but, are measurable. It is extraordinarily difficult to project these effects with accuracy over long periods of time, as phyisab noted.

 

[twofish-quant]

2) Gravity only has any real effect when very large masses are involved, such as stars or planets.

Not true. One really cool experiment is the Cavendish experiment

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

In your home for about $100, you can put together an experiment in which you get to see the gravitational force exerted by a brick.

3) The force exherted by the gravity of an objet decreases exponentially as the distance from it increases.

1/r^2. That's a lot more force than exponential.

4) The major forces we feel on Earth are due to the gravity of the sun (keeping us in orbit around it) and the gravity of the moon (causing tides amongst other things).

My question is then; do the planets cause a significant force of attraction on each other, or are they too far apart and too small for the force to be registerable?

Yes. Any sort of calculations concerning the position of the planets have to take into account the other planets. Jupiter and Saturn make a huge difference. Also once you look at the effects of the planets, you end up with a nice ballet.

 

[twofish-quant]

Also to bring this connection with molecular biology.

One question that has come up is how unusual the solar system is for having eight "well-behaved" planets. Which is to say that it seems that the planets are orbiting each other in a way, that you don't have them flinging each other into weird orbits. This is good, because if you have planets going into weird orbits, it makes life difficult to evolve.

Something that people are interested in seeing is how common or rare having a "well-behaved" planetary system is. Which is to say if you put the planets in some random set of orbits, will they get into a state where they will not cause "bad things" to happen over the course of billions of years.

 

[jtbell]

3) The force exherted by the gravity of an objet decreases exponentially as the distance from it increases.

"Exponentially decreasing" means something like $e^{-kr} = 1/e^{kr}$, not $r^{-2} = 1/r^2$.

 

[Gully Foyle]

Thanks for all the responses. I'm glad to hear the effects are detectable. I suppose my next question would be what exactly are the effects? I'm guessing they would be changes to the orbits:

To take an example - the effect of gravity between Mars and Earth.

As Mars orbits the sun at approximately twice the rate of the Earth and orbits in the same direction at a higher orbit, there are times when Mars 'overtakes us'. So as Mars apporaches us, before it 'overtakes us' its gravity will cause us to slow down, and the effect of Earth's gravity on Mars would cause it to speed up slightly. Similarly once it has 'overtaken us' the effect of its gravity on us will start speeding us back up again, while the effect of the Earth's gravity on Mars would cause it to slow down, cancelling out the overall changes in the speed of the orbits.

A second effect would then be perpendicularlly to this - each time the planets get close Earth would be pulled away from the sun, whilst Mars is pulled towards it. I'm not sure exactly how this would cancel out though - surely when Mars is on the other side of the sun the effects of its gravity on us are far less, and therefore unable to 'correct' for the earlier change it made to our orbit. This would therefore mean that over time Earth would drift into a higher orbit, and Mars would fall into a lower orbit? Unless the effects of all the other planets stabilise us?

I suppose my next question would be how would you detect these effects? My first guess would be to use a telescope and measure the position of Mars each night against a background of static faraway stars, then calculate the change in speed over time as it comes close to us, and then moves firther away again. But surely this would not be accurate enough to detect such small changes?

Also to bring this connection with molecular biology.

One question that has come up is how unusual the solar system is for having eight "well-behaved" planets. Which is to say that it seems that the planets are orbiting each other in a way, that you don't have them flinging each other into weird orbits. This is good, because if you have planets going into weird orbits, it makes life difficult to evolve.

Something that people are interested in seeing is how common or rare having a "well-behaved" planetary system is. Which is to say if you put the planets in some random set of orbits, will they get into a state where they will not cause "bad things" to happen over the course of billions of years.

I've always assumed that it had something to do with the composition of the planets in a solar system. Gas giants form further away from the stars as they are formed of gases which are thrown further from supernovae. Rocky planets like Earth and Mars will form closer to the sun. Gravity again? It does seem an interesting question though and is very much related to my line of enquiry.

As for the relation to molecular biology - I always find cosmological inquiries a little dull as they tend to overlook the key principle of evolution - life adapts to the environment. This doesn't just mean that lineages out-compete one another here on Earth. ALL life we can observe has adapted to be capable of living on Earth. A more interesting question from a biological perspective is whether it is possible for life to exist in completely different planetary conditions. We already know that oxygen - once considered to be a vital substance for all life, was in fact a waste product produced by early autotrophs that was actually poisonous to the majority of life. Who knows what other 'fundamental requirements' for life might prove to be unnecesary; DNA, the need for water, even the carbon basis of life forms might simply have evolved in this form on Earth because of the position of our planet in the cosmos.

 

[Janus]

I suppose my next question would be how would you detect these effects? My first guess would be to use a telescope and measure the position of Mars each night against a background of static faraway stars, then calculate the change in speed over time as it comes close to us, and then moves firther away again. But surely this would not be accurate enough to detect such small changes?
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Such changes(called perturbation) are detectable. In fact, it was perturbations of Uranus that led to the discovery of Neptune in 1846. Uranus was moving in a way that could only be easily explained if there were a another massive body orbiting beyond it. Analysis of these movements even told us where we needed to look to find this body.

 

[Gully Foyle]

Thanks Janus, I'll start looking up some astrophysics texts when I next get the chance and learn all about perturbations. I should probably also mention I incorrectly said Mars takes twice as long to orbit the sun as the Earth, when in fact the reverse is true.