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Radar-like Solar System

You know how all the planets around the Sun move at different speed and distances from the Sun? Would it have been possible, by luck or extension of how the solar system was made, that all the planets would always be at the same angular position? Would it be possible that all the planets would always be aligned perfectly?

 

In the previous equation, the velocity of an object is its angular velocity times the radius. If we want all the planets to be aligned, T (how long it takes to do a complete revolution) must then be constant.

r (the radius, or the distance between the Sun and the body) is the variable here, which gives us the body’s speed through space.

Is that all there is to it?

 

Kepler’s Third Law of Planetary Motion indicates that

meaning that the time taken for one orbital period, squared, is proportional to the distance from the sun, cubed.

For the Earth, (149,598,261,000m)^3 / (31,556,736s)^2 = 3.362E9. For Mars, (227,939,100,000m)^3 / (59,354,294.4s)^2 = 3.362E9. Same thing for the other planets.

And that means that, for a given orbital period (say, one julian year), a planet can only be at a specific distance from the Sun.

 

So, no, a planetary system can’t have all its planets constantly aligned. But that would be eerily cool!

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