How would one go about calculating (as a first-order approximation) the gravitational time dilation generated by multiple point sources?(adsbygoogle = window.adsbygoogle || []).push({});

When generated by one point source ([itex]M = 1\cdot10^{25}, r = 1, t = 1[/itex]), I've got it down to:

[tex]

\tau = t \cdot \sqrt{1 - \frac{2GM}{rc^2}} \approx 0.992546\;\;(eq.1)

[/tex]

For two bodies equidistant from the test particle (each contains half the total mass), I've tried the following:

[tex]

\tau = t \cdot \sqrt{1 - \frac{2G(M/2)}{rc^2}} \cdot \sqrt{1 - \frac{2G(M/2)}{rc^2}} = t \cdot \left(1 - \frac{2G(M/2)}{rc^2} \right) \approx 0.992574\;\;(eq.2)

[/tex]

For four:

[tex]

\tau = t \cdot \left(1 - \frac{2G(M/4)}{rc^2} \right)^2 \approx 0.992588\;\;(eq.3)

[/tex]

For six:

[tex]

\tau = t \cdot \left(1 - \frac{2G(M/6)}{rc^2} \right)^3 \approx 0.992592\;\;(eq.4)

[/tex]

Is this correct, or should [itex]\tau[/itex] be constant regardless if the mass is split into 1, 2, 4 or 6 equidistant bodies? Ex:

[tex]

\tau = t \cdot \sqrt{1 - \frac{2G({\rm Total\;Mass})}{({\rm Average\;Distance})c^2}} \approx 0.992546\;\;(eq.5)

[/tex]

I've always wondered about this.

The reason I wonder is because I know that in between two points of equal mass (or inside of a thin homogeneous ring or shell) it is found that [itex]\frac{d\tau}{dr} = 0[/itex] (no acceleration), and I was curious to know if [itex]\tau = \rm constant[/itex] if the total mass for the points and shell and ring are equal. If that is the case, then [itex](eq.5)[/itex] is correct.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Gravitational time dilation from two or four bodies

Loading...

Similar Threads - Gravitational dilation four | Date |
---|---|

B How does time behave in overlapping gravitational fields? | Sep 24, 2017 |

I Gravitational time dilation, proper time and spacetime interval | Aug 18, 2017 |

B Uniform-gravitational time dilation -- exact or approximate | Jul 24, 2017 |

**Physics Forums - The Fusion of Science and Community**