- #1

r731

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- 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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- Thread starter r731
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- #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?

- #2

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What's the connection with physics?

- #3

- 10,067

- 10,618

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

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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 is

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

- #5

DrStupid

- 2,167

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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?

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

- 915

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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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@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

- 915

- 822

Gravity and inertia are two major forces

Since when inertia is a force?

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