Today I learned that the Sun’s magnetic field is ‘only’ about twice that of Earth’s - with a pile of caveats like the local magnetic fields in sunspots are about 10,000 times that of Earth’s.
Doesn’t the magnetic field strength of a dipole fall off as the cube of distance? So if the magnetic field of the Sun is twice that of Earth, but measured at some particular radius from the Sun’s center - like the Earth’s field is measured at the surface - what does that mean? If you measured Earth’s magnetic field strength 430 odd thousand miles from its center, it would be a lot less than 0.3 Gauss, right?
So is there some other measure of overall magnetic, I dunno, ‘power’? The magnetic field of the Sun pushes measurably out beyond all the planets, while that of Earth does not, as far as I know. It would seem that twice the field strength at 100 times the distance would make the Sun’s field a lot more than twice as strong by some other kind of measurement.
It feels like saying that the Sun (10,000F) is less than three times as hot as my propane torch (3,600F) while ignoring that the Sun is radiating multiple orders of magnitude more energy. What am I missing?
I have in my hand a magnet from the refrigerator. In my other hand is a magnetic compass. Within six inches of the magnet, the compass deflects and points to the magnet. Further than six inches away, the compass points north. Clearly, within six inches, the magnetic field of the fridge magnet is stronger, but that’s only true over a very short distance. The Earth’s magnetic field is weaker than that of the magnet, but over a much larger volume. What does the Earth’s field have more of than the fridge magnet’s field? Oomph?
It’s easy to get confused between the units of Gauss & Tesla and the micro & nano versions of Tesla. The various values here and there throughout both articles don’t all use common units. But I agree with your big picture that the bog-standard polar field of the Sun is real weak compared to that of Earth.
Reading through the Sun article magnetic section more deeply, a lot of the Sun-caused magnetic field out here among & beyond the planets is generated locally by the interaction of the charged solar wind with existing gas particles in the interplanetary medium. It’s mostly not a result of the Sun’s internally generated polar field being all that intense umpteen hundred million miles out despite the inverse-cube law.
Without getting well past even my nodding acquaintance with the facts and my marginal interest in digging further, I’m going to bet that that explains most of the discrepancy you cite in the OP.
With luck the real astronomers & physicists will be shortly to laugh at my fumbling.