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Just curious how these two magnets are spatially related to?

enter image description here

And in case there is no any special preferred particular orientation, what is anyway their spatial orientation relation (relative angles)? Possible varying with seasons or year cycles. There must be a record of these measurements? I cannot find anything about this on the internet?

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    $\begingroup$ I hope someone comes along with a nice put together answer but of course it's not really one or the other most of the time, as even from our point of view it doesn't (anti)align with Earth's dipole moment over the course of a few days. $\endgroup$
    – Triatticus
    Commented Jun 1, 2023 at 12:47
  • $\begingroup$ Of course in the picture above, cases a&b, there could be additional combinations like NS-SN instead of NS-NS in case (a) or NS-NS instead NS-SN in case (b). This is because at that macroscopic distances gravitational forces prevail over the much weaker magnetic forces. $\endgroup$
    – Markoul11
    Commented Jun 2, 2023 at 12:25
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    $\begingroup$ I mean because they can be oriented in a direction that is neither parallel nor antiparallel and in general are not either. $\endgroup$
    – Triatticus
    Commented Jun 2, 2023 at 17:37
  • $\begingroup$ @Triatticus Right. So what is anyway their spatial orientation relation (relative angles)? Possible varying with seasons or year cycles. There must be a record of these measurements? I cannot find anything about this on the internet? $\endgroup$
    – Markoul11
    Commented Jun 5, 2023 at 9:31
  • $\begingroup$ Judging by the illustration in this article here colorado.edu/today/2020/03/17/… , seems to me by observing the magnetic flux pattern of the Earth that their relation in general is repulsive. Therefore, magnetic polarity of Earth and sun should face towards the same or opposite more or less direction in space. Something like NS-NS side-by-side or NS-SN or SN-NS head on. $\endgroup$
    – Markoul11
    Commented Jun 5, 2023 at 9:59

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The Sun's magnetic field reverses polarity approximately every 11 years, defining the solar cycle. This results from the dynamics of the solar dynamo. A similar process causes Earth's magnetic field to reverse over much longer timescales. Therefore the magnetic moment of the Sun and Earth do not maintain a fixed orientation with respect to one another. They do tend to be parallel or antiparallel to the bodies' axes of rotation, though.

It's worth noting that the Sun's magnetic field deviates significantly from a simple magnetic dipole. "Open" magnetic field lines of opposite polarity are separated by the heliospheric current sheet, which rotates with the sun ($\approx27$ day period). The planets regularly pass through this current sheet. Thus the solar magnetic field does not have a consistent direction with respect to Earth, even on timescales shorter than the solar cycle.

Heliospheric magnetic field

Solar wind plasma carries a frozen in magnetic field with it. This is not necessarily aligned with the Sun's overall magnetic moment. However, the alignment of the solar wind with Earth's magnetic moment does determine how it impacts the geomagnetic field. Strong geomagnetic storms tend to be triggered by coronal mass ejections with magnetic field of opposite alignment to Earth's.

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  • $\begingroup$ "They do tend to be parallel or antiparallel to the bodies' axes of rotation, though." By that you mean using the right-hand rule to find the angular momentum vector, say for ccw physical spin the angular momentum vector is pointing up and the magnetic moment vector can therefore point in the same general direction thus parallel or in opposite direction thus pointing down and antiparallel? $\endgroup$
    – Markoul11
    Commented Jun 5, 2023 at 14:13
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    $\begingroup$ Yes, the magnetic moment vector and angular momentum vector are usually close to parallel or antiparallel (they make an angle of $\theta \approx 0^{\circ}$ or $180^{\circ}$). Currently the Earth's magnetic moment vector is $169^{\circ}$ from its angular momentum vector. $\endgroup$
    – FTT
    Commented Jun 5, 2023 at 22:15
  • $\begingroup$ oh! that's very interesting! You have said "currently". Is there a link towards a table of the recorded values over time or a calculation of this angle? I assume it would also take into account the 23.4 degrees precession angle. $\endgroup$
    – Markoul11
    Commented Jun 6, 2023 at 8:14
  • $\begingroup$ Also, which is the crux of my PSE question here, taking as reference z-axis, the spin angular momentum axis of the sun and plotting in a graph the corresponding relative angular momentum vector of the Earth and relative magnetic moment vectors of both Earth ( $169^\circ$ antiparallel to Earth' spin axis) and sun (?) then, what is currently the relative angle between the magnetic moment of the Earth to the sun's magnetic moment vector? $\endgroup$
    – Markoul11
    Commented Jun 6, 2023 at 8:43
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    $\begingroup$ @Markoul11 My previous comment only considered the alignment of Earth's magnetic moment and its axis of rotation (assuming the latter aligns with angular momentum). Therefore the axial tilt was not taken into account there. However, it would certainly need to be considered in order to comparing Earth's magnetic moment to that of another body (which requires transformation to a common coordinate system). In answer to your question about how Earth's magnetic field changes with time, the IGRF model tracks this: earth-planets-space.springeropen.com/articles/10.1186/…. $\endgroup$
    – FTT
    Commented Jun 6, 2023 at 13:38

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