Metrics for the Sun & Earth: Rs & Assumptions

In summary, the conversation discusses the possibility of a metric other than the Schwarzschild metric for the Sun and Earth, and the assumptions that would turn it from general relativity to Newtonian mechanics. It is noted that the Schwarzschild radius is always inside the body for objects less massive than black holes, but this is not a problem as the exterior Schwarzschild solution applies to any spherically symmetric static spacetime. It is also mentioned that under certain conditions, one can recover the Newtonian equations from the Schwarzschild metric.
  • #1
Philosophaie
462
0
Is there a Metric for the Sun and Earth other than the Schwarzschild Metric who has the Schwarzschild Radius on the interior of the body?

What are the assumptions that turn that from GR to Newtonian?

Rs(Earth)=8.87*10^-3m
Rs(Sun)=2954m
 
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  • #2
The Schwarzschild radius is outside the body pretty much by definition... though you can see where the Schwarzschild radius would be if all the matter were concentrated at the center ... but that is always inside the body for objects less massive than black holes. So I think you need to be a bit more precise about what you mean.

It is probably possible to produce a metric which has a coordinate singularity anywhere you like.
 
  • #3
Philosophaie said:
Is there a Metric for the Sun and Earth other than the Schwarzschild Metric who has the Schwarzschild Radius on the interior of the body?

What are the assumptions that turn that from GR to Newtonian?

Rs(Earth)=8.87*10^-3m
Rs(Sun)=2954m
As you point out, the Schwarzschild radii for the Earth and Sun are inside the physical bodies. But that is not a problem because the exterior Schwarzschild solution applies to any spherically symmetric static( stationary?) spacetime.

If the spatial curvature is ignored and all velocities << c, and r>>m one can recover the Newtonian equations.
 
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Related to Metrics for the Sun & Earth: Rs & Assumptions

What are metrics for the Sun & Earth?

The metrics for the Sun & Earth are quantitative measurements used to describe and analyze various aspects of these celestial bodies. These metrics can include size, mass, distance from each other, and other characteristics.

What are Rs & Assumptions in relation to the Sun & Earth metrics?

Rs refers to the radius of the Sun, while assumptions refer to the scientific assumptions and models used to calculate and understand the metrics for the Sun & Earth.

Why is it important to have metrics for the Sun & Earth?

Having metrics for the Sun & Earth allows scientists to better understand and study these celestial bodies. By quantifying their characteristics, we can gain insights into their behavior and interactions with each other.

What are some challenges in measuring and analyzing metrics for the Sun & Earth?

One challenge is the vast distances involved, which can make it difficult to accurately measure certain metrics. Additionally, the dynamic nature of these bodies means that metrics may change over time and require constant monitoring and updates.

How do scientists ensure the accuracy and reliability of metrics for the Sun & Earth?

Scientists use a variety of methods, including advanced technology and mathematical models, to collect and analyze data and make accurate measurements. These methods are constantly being refined and improved to ensure the accuracy and reliability of metrics for the Sun & Earth.

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