Cosmic Dynamics - Cosmological Constant

[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_$\Lambda$ = E_T / V
E_T = 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*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*10²²)*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.

 

[phyzguy]

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