Dark Energy: Mass, Distance & Gravity Relationships

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SUMMARY

The discussion focuses on the relationship between mass, distance, and gravitational binding in the context of dark energy. It references the equation derived from the paper at http://arxiv.org/abs/astro-ph/0302506, which establishes a length scale for gravitational dissipation due to dark energy. The calculations indicate that a mass of 1 M_{\odot} corresponds to approximately 100 parsecs, 10^{10} M_{\odot} to about 200 kiloparsecs, and 10^{13} M_{\odot} to roughly 2 megaparsecs. These findings imply that systems with these mass values remain gravitationally bound and are not disrupted by dark energy.

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  • Understanding of dark energy and its effects on cosmic structures
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  • Basic comprehension of cosmological scales (parsecs, kiloparsecs, megaparsecs)
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  • Study the equation of state for dark energy and its impact on mass
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Astronomers, astrophysicists, and cosmologists interested in the interplay between mass, distance, and dark energy in the universe.

chris2112
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Is there a function of mass that tells us the distance that two objects are no longer gravitationally bound and start moving away from each other due to dark energy? Is mass arbitrary at a certain distance? To make my question broader, can anyone show me equations describing relationships between the forces of gravity and dark energy on mass?
 
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Following http://arxiv.org/abs/astro-ph/0302506, we can define the rough length scale at which objects begin to disspiate due to dark energy by:
-\frac{4\pi}{3}\left(\rho + 3P\right)R^3 \sim M

Taking a normal value for \Lambda and assuming an equation of state of -1, such that \rho = - P, I get

For a mass of 1 M_{\odot} , ~100 pc (Solar system),
For a mass of 10^{10} M_{\odot}, ~ 200 kPc (Galaxy),
For a mass of 10^{13} M_{\odot}, ~ 2MPc (Cluster).

This suggests that all three systems are gravitationally bound and will never be disrupted.
 

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