Question 3 25 TitusBode Rule Law Whilst we are thinking abou

Question 3 (25%) Titus-Bode Rule (Law) Whilst we are thinking about orbital mechanics, I want to comment that there is an interesting relationship between the Solar System planet\'s semi-major axis and a simple numerical series. The relationship states that the semi-major axis of planets in our Solar System conforms to (where 10 AU 4 n Where a semi-major axis n 0, 3, 6, 12, 24, 48 n, with the exception of the first step, has each value is twice the previous value. Thus the 3rd planet from the Sun (Earth) has a semi-major axis (a) 4+6 10, or 1AU. B. It is unclear if this is a rule, law, or perhaps even coincidence. What could be an explanation for this to be a rule/law? How could we test this (in the real Universe)?

Solution

It is neither a law or rule it was just a coincidence and this rule fails for neptune i.e is n= 128 it gives 39Au as answer but neptune is at 30 Au but later it was found that pluto was at 39.52 Au

Orbital resonance from major orbiting bodies creates regions around the Sun that are free of long-term stable orbits. Results from simulations of planetary formation support the idea that a randomly chosen stable planetary system will likely satisfy a Titius–Bode law

there is no real way to test this in universe it was just a hypothesis at the time of mentioning and later it was dicredited at its went wrong at neptune and There is a decidedly limited number of systems on which Bode\'s law can presently be tested but the number of planets found with Titius–Bode law predictions were still lower than expected