Suppose the energy density of the cosmological constant is equal to the present critical density ε(adsbygoogle = window.adsbygoogle || []).push({}); _{[itex]\Lambda[/itex]}= ε_{[itex]c,0[/itex]}= 5200 MeV m^{-3}. What is the total energy of the cosmological constant within a sphere 1 AU in radius?

My answer:

ε_{[itex]\Lambda[/itex]}= E_{T}/ V

E_{T}= ε_{[itex]\Lambda[/itex]}* V = (8.33 * 10^{-10}J)*4∏/3*(1.5*10^{11}m^{3})^{3}= 1.2*10^{35}J

What is the rest energy of the Sun ?

My answer:

E = (2*10^{30}kg)(3*10^{8}m/s)^{2}≈ 1.8*10^{47 J}

Comparing these two numbers, do you expect the cosmological constant to have a significant effect on the motion of planets within the solar system?

My answer:

E_{solar}≈ (1.5*10^{22})*E_{T}

So the total amount of energy from the Sun is much much greater than the total energy of the cosmological constant within a sphere of 1 AU radius.

According to Einstein, mass/energy curves spaces around it. Thus, the immense curvature of space by the sun will control the motion of the planets.

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# Cosmic Dynamics - Cosmological Constant

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