Gravitational radiation galaxy lifetime...

[Orion1]

Radial decrease rate between two bodies versus time: (ref. 1, pg. 20), (ref. 2)

[math]\frac{dr}{dt} = - \frac{64 G^3 (m_1 m_2)(m_1 + m_2)}{5 c^5 r^3}[/math]

 

Time decrease rate between two bodies versus radius: (ref. 1, pg. 20), (ref. 2)

[math]\boxed{\frac{dt}{dr} = - \frac{5 c^5 r^3}{64 G^3 (m_1 m_2)(m_1 + m_2)}}[/math]

 

Integration for total inspiral time from total radius [math]R[/math] to zero.

[math]\tau = - \frac{5 c^5}{64 G^3 (m_1 m_2)(m_1 + m_2)} \int_R^0 r^3 dr = \frac{5 c^5 R^4}{256 G^3 (m_1 m_2)(m_1 + m_2)}[/math]

 

Two-body total orbit inspiral lifetime: (ref. 3)

[math]\boxed{\tau = \frac{5 c^5 R^4}{256 G^3 (m_1 m_2)(m_1 + m_2)}}[/math]

 

Milky Way galaxy mass: (ref. 4, pg. 1)

[math]M_{g} = 1.26 \cdot 10^{12} \cdot M_{\odot} = 2.506 \cdot 10^{42} \; \text{kg}[/math]

 

[math]\boxed{M_{g} = 2.506 \cdot 10^{42} \; \text{kg}}[/math]

 

Milky Way galaxy radius: (ref. 5), (ref. 6)

[math]R_g = 8.515 \cdot 10^{20} \; \text{m} \; \; \; (90 \; \text{kly})[/math]

 

Milky Way galaxy total orbit inspiral lifetime:

[math]\boxed{\tau_g = \frac{5 c^5 R_g^4}{256 G^3 (M_g M_{\odot})(M_g + M_{\odot})}}[/math]

 

[math]\boxed{\tau_g = 6.697 \cdot 10^{39} \; \text{s}} \; \; \; (2.122 \cdot 10^{32} \; \text{y})[/math]

 

Any discussions and/or peer reviews about this specific topic thread?

 

Reference:

Orbital decay from gravitational radiation: (ref. 1)

http://www.eftaylor.com/exploringblackholes/GravWaves150909v1.pdf

 

Wikipedia - Orbital decay from gravitational radiation: (ref. 2)

https://en.wikipedia.org/wiki/Gravitational_wave#Orbital_decay_from_gravitational_radiation

 

Wikipedia - Orbital lifetime limits from gravitational radiation: (ref. 3)

https://en.wikipedia.org/wiki/Gravitational_wave#Orbital_lifetime_limits_from_gravitational_radiation

 

Mass models of the Milky Way: (ref. 4)

http://arxiv.org/pdf/1102.4340v1

 

Space.com - Milky Way galaxy size: (ref. 5)

http://www.space.com/29270-milky-way-size-larger-than-thought.html

 

Wikipedia - Milky Way galaxy: (ref. 6)

https://en.wikipedia.org/wiki/Milky_Way

Edited February 12, 2016 by Orion1