- #1

r731

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A complete graph K6 of six planets (of different masses) has 15 edges, why don't the planets collapse to the center?

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In summary: Newton in his second law of motion. It is the resistance of a body to change its state of motion.In summary, the planets in a K6 graph do not collapse to the center because there is a negligible force between each planet and the sun. This is because the force between each planet and the sun is what primarily determines the orbit of each planet.

- #1

r731

- 40

- 6

A complete graph K6 of six planets (of different masses) has 15 edges, why don't the planets collapse to the center?

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- #2

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What's the connection with physics?

- #3

Ibix

Science Advisor

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Planets aren't arranged like that, for a start.

Essentially, orbits work because the objects are moving fast enough that their paths curve towards the Sun at the exact rate they need to move in a circle (or ellipse, more usually). Newton provided a plausibility argument (nice explanation and animations at Wikipedia), and developed the detailed maths.

Essentially, orbits work because the objects are moving fast enough that their paths curve towards the Sun at the exact rate they need to move in a circle (or ellipse, more usually). Newton provided a plausibility argument (nice explanation and animations at Wikipedia), and developed the detailed maths.

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- #4

Delta2

Gold Member

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Well the forces between planets are considered "kind of" negligible (because their mass isn't so big in relation to the vast distance that separates the planets) and they don't affect a lot the orbit of the planets, it isr731 said:

A complete graph K6 of six planets (of different masses) has 15 edges, why don't the planets collapse to the center?

- #5

DrStupid

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r731 said:A complete graph K6 of six planets (of different masses) has 15 edges, why don't the planets collapse to the center?

Let's say "planet" means planet-like object. If you arrange them this way, then they need to have a tangential velocity in order to prevent them from collapsing into the center. If you have n "planets" with the identical mass m at the positions

##r_i = R \cdot \left( {\begin{array}{*{20}c} {\cos \varphi _i } \\ {\sin \varphi _i } \\ \end{array}} \right)##

with

##\varphi _i = 2 \cdot \pi \cdot \frac{i}{n}##

they would be accelerated with

##\ddot r_i = G \cdot m \cdot \sum\limits_{j \ne i} {\frac{{r_j - r_i }}{{\left| {r_j - r_i } \right|^3 }}} ##

towards the center and would need to move with the speed

##\left| {\dot r} \right| = \sqrt {R \cdot \left| {\ddot r} \right|} ##

to remain on a circular path.

However, such a configuration is not stable. This example with 6 Jupiter-like objects in a common orbit of 1 AU turns into chaos after 5 revolutions:

https://tinyurl.com/ybw8kyhv

- #6

artis

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In fact centrifugal force is a way by which one can produce "artificial gravity" because the force that pushes on clothes that rotates within a centrifuge washing machine is identical to gravity.

http://www.mso.anu.edu.au/~pfrancis/roleplay/MysteryPlanet/Orbits/

- #7

weirdoguy

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artis said:because of centrifugal force

Which exists only in non-inertial frames. I find it risky to explain things by using inertial forces because people usually don't understand them properly.

- #8

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artis said:@r731 planets/objects generally don't fall into the sun while orbiting it because of centrifugal force which counteracts gravity and keeps them in balance.

Newton's second law applies to planetary orbits with the gravitational force only; there is no counterbalancing centrifugal force. In Newtonian physics, gravity acts as a

If we apply general relativity, then there are no forces acting on the planets, gravitational, centrifugal or otherwise.

- #9

artis

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Ok I agree , not the best explanation one could give. Pardon.

Gravity being the invisible "string" that provides centripetal force to keep planets in circular orbits should of have sufficed.

- #10

SpaceJacob

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- #11

weirdoguy

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SpaceJacob said:Gravity and inertia are two major forces

Since when inertia is a force?

The force that keeps the planets orbiting normally is called centripetal force. This is the force that pulls an object towards the center of its circular path.

Centripetal force works by continuously pulling the planets towards the center of their orbit, preventing them from flying off into space.

The centripetal force that keeps the planets orbiting normally is caused by the gravitational pull of the sun. The sun's massive size and gravitational force keeps the planets in their orbits.

If centripetal force stopped working, the planets would no longer be held in their orbits and would fly off into space in a straight line. This would result in chaos and the destruction of the solar system as we know it.

No, the amount of centripetal force required for a planet to maintain its orbit depends on its mass and distance from the sun. The larger the mass of the planet, the greater the centripetal force needed to keep it in orbit. Similarly, the farther a planet is from the sun, the weaker the centripetal force needed to keep it in orbit.

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