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Let us assume Ho = 71 1 / s

In order for our solar system to stay in orbit around the milky way, the escape velocity must be greater than the recessional.

Resc > Rrec

(2GM / R)^1/2 > HoR

Now lets refer to Kepler's third law to substitute in for the mass.

T^2 = 4π^2R^3 / GM

M = 4π^2R^3 / GT^2

((2G / R) * (4π^2R^3 / GT^2))^1/2 > HoR

(8π^2R^2 / T^2)^1/2 > HoR

πR√(8) / T > HoR

π√(8) / T > Ho <------------------------- FINAL EQUATION!

What do you think? the units are dimensionally correct. If the inequality is satisfied, the object will stay in orbit forever by the means of the expanding universe. We can actually rearrange this even more to give..

π√(8) / Ho > T

0.125 s > T <-------------- This must be satisfied! Given Ho = 71 1 / s

Obviously, our solar system doesn't take 0.125 s to orbit the galactic center. Therefore, we should be moving away from it.

In order for our solar system to stay in orbit around the milky way, the escape velocity must be greater than the recessional.

Resc > Rrec

(2GM / R)^1/2 > HoR

Now lets refer to Kepler's third law to substitute in for the mass.

T^2 = 4π^2R^3 / GM

M = 4π^2R^3 / GT^2

((2G / R) * (4π^2R^3 / GT^2))^1/2 > HoR

(8π^2R^2 / T^2)^1/2 > HoR

πR√(8) / T > HoR

π√(8) / T > Ho <------------------------- FINAL EQUATION!

What do you think? the units are dimensionally correct. If the inequality is satisfied, the object will stay in orbit forever by the means of the expanding universe. We can actually rearrange this even more to give..

π√(8) / Ho > T

0.125 s > T <-------------- This must be satisfied! Given Ho = 71 1 / s

Obviously, our solar system doesn't take 0.125 s to orbit the galactic center. Therefore, we should be moving away from it.

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