Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Alan McDougall on 23/06/2008 08:37:22
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Hi
Imagine waking up in a universe completely void and empty except for three planets. Your own and two others nearby. Pretend you are able to observe each other in the absence of sunlight. You have at your disposal all the present tools for examining the other two nearby planets Telescopes etc etc.
Scenario 1) is, all the planets are moving relative to each other?
Scenario 2) if not which are moving relative to the other?
Scenario 3) calculate the Mass of the three planets
Scenario 4) can you determine the relative velocity of each, with the vague information at hand.
Scenario 5) are they all relatively stationary to the other.
Scenario 6) ...............................................100)?
Would it be impossible given the vague information I gave you?
Alan
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Some of your scenarios describe states and some are questions, so I'm finding it difficult to understand what you what to find out.
Scenarios 1 & 5 are identical in that they describe the two possible outcomes from the same situation - either the planets are moving relative to each other (Sc1) or they're not (Sc5) - they aren't questions but answers.
You wouldn't need to calculate relative velocities (Sc2/4), if they are present, because if you have all the tools for examining the two nearby planets you'd probably just use radar to establish both the distances and velocities, and with the info thus gained it would be possible to calculate the masses (Sc3).
The final answer would therefore seem to be No.
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Under the conditions you describe radial and relative transverse velocities are measurable. I am of course assuming there are no distant stars to act as a reference point and that the knowledge of gravitation and the physical laws are available as well as all the measuring instruments.
The measurement of mass depends on the initial relative velocities. If it is initially zero and there is no net angular momentum the planets will accelerate towards their common centre of gravity and collide. With a bit of luck you may be able to calculate the relative masses before you are destroyed in the collision. If there is enough angular momentum in the three planet system they will all be in orbit around their common centre of gravity and this gives a fourth and static reference point which can be determined over time and will allow the mass of the three planets to be determined. However in general the orbits will not have long term stability if placed at random. This means that one of the three will be ejected leaving a pair and a single planet. There are however some long term stable conditions If the planets are paced in an equilateral triangle and have the correct velocities they can be stable indefinitely. Also if one is a pair orbiting closely about their common centere of gravity with a third orbiting some distance away about the centre of gravity of the pair and the more distant one it will also be stable for quite a long time but not indefinitely.
There is a third and extremely peculiar stable orbit if all the planets have exactly the same mass it is in the form of a figure of eight but is very easily disturbed.
If of course the relative angular momenta of the planets is too great they will just move in hyperbolic orbits around their common centre of gravity and move away from each other
It is important to remember that the general gravitational interaction between two bodies approaching each other and not on a collision course is an open hyperbolic orbit around their common centre of gravity. That is they deflect and pass each other but cannot go into orbit around each other, It requires the addition of some other force another body or gaseous drag to decelerate one of the bodies to create a stable orbit
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The problem with this 'thought model' is that, according to Mach's principle, the way things behave depends upon the sum total of the stuff in the Universe. So everything would be different - possibly too different to have a clue about what would happen using what we know here and now.
Perhaps you could take your experiment and set it in a particularly empty part of our Universe and have a huge cloud of dust around you so you couldn't see any stars.
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The problem with this 'thought model' is that, according to Mach's principle, the way things behave depends upon the sum total of the stuff in the Universe. So everything would be different - possibly too different to have a clue about what would happen using what we know here and now.
Perhaps you could take your experiment and set it in a particularly empty part of our Universe and have a huge cloud of dust around you so you couldn't see any stars.
This hypothetical thought experiment assumes that although there in no star the beings on each planet can observe on another.
We could change the experiment to Venus Earth and Mars suddenly finding them selves in an empty universe.
QUESTIONS 1 AND 5 are not identicle