What is the speed of light?

Nicely done.

Nit..."He noticed that the eclipses appeared to lag the most when Jupiter and Earth were moving away from one another, ..."

As soon as Jupiter moves past opposition, then the Earth is moving away from Jupiter. But it was the extra distance not just the "moving away" that created the time delay for Io's orbit. I doubt he was working on any Doppler-like model.

"In order to accurately describe the universe, Einstein's elegant equation requires the speed of light to be an immutable constant."

Yes, but it might help some to see that it was the brilliant insight he had that the immutable constant speed of light that was the key to Relativity, which brought forth his E = mc^2.

Because it was becoming clear that motions of galaxies and our planet, and our cluster all would make physics very difficult such that one's inertial frame would require knowledge of all these motions, then something else must be needed. It was getting messy and the top physicists understood this, including Eddington. Fixing c as a constant solved this problem. Einstein called his theory, the Invariant Theory since inertial frames weren't varying after all when it came to the laws of physics. But, this is only my limited understanding of this. A deeper dive would be interesting and important.

It may be worth noting that by fixing c as a constant then, at very high velocities, either the time or the distance to another star system is altered, so much so that at 0.8c, for example, the traveler would cut the time by 40% (or distance). No one knows, AFAIK, whether it is time or distance that is altered. There is much evidence, however, favoring time (atomic clock experiments), and perhaps only one hint of evidence (flattening profile of relativistic particles) that favors distance shrinking.
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Oct 22, 2019
The article states "Although the speed of light is often referred to as the universe's speed limit, the universe actually expands even faster. The universe expands at a little more than 42 miles (68 kilometers) per second for each megaparsec of distance from the observer, wrote astrophysicist Paul Sutter in a previous article for Space.com. (A megaparsec is 3.26 million light-years — a really long way.) In other words, a galaxy 1 megaparsec away appears to be traveling away from the Milky Way at a speed of 42 miles per second (68 km/s), while a galaxy two megaparsecs away recedes at nearly 86 miles per second (136 km/s), and so on. "At some point, at some obscene distance, the speed tips over the scales and exceeds the speed of light, all from the natural, regular expansion of space," Sutter explained. "It seems like it should be illegal, doesn't it?"

This is critical to BB cosmology that 3D space can expands >> c, inflation uses this too. Objects in the universe today with redshifts => 1.4 are moving faster than c because 3D space is expanding faster than c. The cosmology calculators will show this, Cosmology Calculators (caltech.edu) or Cosmology calculator | kempner.net

The light-time distance is the look back time, the comoving radial distance is where the object is calculated to exist, thus z => 1.4, the objects are moving away in 3D space faster than c. The universe today is said to be some 93 billion light years in diameter because the CMBR z ~ 1100 today. The radius is then some 42-43 billion light years away from Earth yet expanded that distance in 13.8 billion years :) In December 2013, Alan Guth published the scale factor for inflation. Inflation starts 10^-36 s after BB where 10^-53 m size maps to 1 m size today. Space expands > 10^20 c in inflation. It should be point out. Direct measurements in labs has not verified 3D space expanding at velocities like this or 3D space expanding faster than c or even at c velocity. My point. 3D space expanding faster than c lacks experimental verification in the lab.
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Jul 30, 2021
How long would it take us to get to this or that place in space if we were traveling at the speed of light?

• 1.28 seconds to fly to the moon
• 4 minutes and 36 seconds to get to Mars
• 8 minutes and 20 seconds to get to the Sun
• 1 hour 18 minutes to fly to Saturn
• 5 hours and 35 minutes to get to Pluto
• 4 years and 3 months to reach the nearest star (other than the Sun) Proxima Centauri
• 30,000 years to fly to the center of our Galaxy - the Milky Way
• 2.5 million years to get to the closest to the Milky Way large Galaxy Andromeda (Andromeda Fog)
• 340 million years to fly to large galaxy cluster Coma Cluster (Coma Cluster)
• it would take us 46.5 billion years.
How long would it take us to get to this or that place in space if we were traveling at the speed of light?
Neutrinos (that likely have some slight mass) have been found to travel from supernovae at very, very close to the speed of light. For instance, the 1987 SN emitted neutrinos that arrived on Earth shortly before the light arrived. This is because the light event happens after neutrinos are formed internally during the explosion.

The travel time, as experienced by the neutrinos, to go 2.3 million lightyears was only a matter of minutes on their clock.

At some point, we could be capable of traveling at relativistic speeds, allowing us to reach distant places quickly. The technological will likely be far more challenging than one might imagine.
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