Question

So, I chose this question for my chemistry assignment which is "How many moles of photons will it take to fill up the volume of the photon sphere around Sagittarius A". I realized there is no actual question or solution as to how to calculate the volume for the photon sphere, so my theory is to find the Schwarzschild Radius of the Event Horizon from the point of Singularity (Rs[s-ev]) then calculate Schwarzschild Radius from the point of Singularity to the Photon Sphere. We can identify the size difference in them. Then we calculate the volume of the event horizon. Now we know the radius and volume of the event horizon, and radius of the photon sphere. To find volume, we can use size difference to calculate volume (for example: an apple has a volume of 2 cubic feet, 2 inches in radius, a banana has a radius of 4, so what's volume --> well, from radius of 2 to 4, volume must go from 2 to 4).

I spoke to my physics teacher and he mentioned how I would need to find the size of an actual photon. So my question is, would the calculation to find the photon sphere work and does it make sense? Also, any theories on the size of a photon.

Answer 1

The proposed calculation using the Schwarzschild radius and comparing sizes between the event horizon and photon sphere does not work. The size of a photon cannot be measured because photons are massless particles. Therefore, it is not possible to calculate the number of moles of photons that would fill the photon sphere around Sagittarius A*.

Step-by-step explanation:

The calculation you proposed to find the size of the photon sphere around Sagittarius A* using the Schwarzschild radius of the event horizon is not directly applicable. The size of the photon sphere is determined by the distance from the black hole where photons can maintain a stable orbit. It is not simply a matter of comparing sizes between the event horizon and photon sphere.

The size of a photon cannot be accurately measured because photons are massless particles that do not have a defined size. They only possess energy and momentum. Therefore, it is not possible to calculate the number of moles of photons that would fill the volume of the photon sphere.