# Cosmic Dynamics - Cosmological Constant

1. May 20, 2014

### johnnnyboy92

Suppose the energy density of the cosmological constant is equal to the present critical density ε$\Lambda$ = ε$c,0$ = 5200 MeV m-3. What is the total energy of the cosmological constant within a sphere 1 AU in radius?

My answer:
ε$\Lambda$ = ET / V
ET = ε$\Lambda$ * V = (8.33 * 10-10 J)*4∏/3*(1.5*1011m3)3 = 1.2*1035 J

What is the rest energy of the Sun ?

My answer:
E = (2*1030kg)(3*108 m/s)2 ≈ 1.8*1047 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:
Esolar ≈ (1.5*1022)*ET

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.

2. May 20, 2014

### phyzguy

You've made an error in the first line. ET should be about ((10^11)^3)*10^(-10) = 10^23, not 10^35.

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