…Compared With Spacecraft Measurements
Series III Test 3B
Introduction
This test (Test 3B) examines the three–dimensional geometry of the Parker spiral and compares the predicted magnetic field orientation with spacecraft observations obtained throughout the heliosphere. This test extends the investigation of Series III by examining whether the large-scale spiral structure of the solar magnetic field behaves in a manner consistent with the geometric framework explored in the Möbius Solar Constitution.
Background
The Parker spiral describes the geometry formed when the solar magnetic field is carried outward by the solar wind while the Sun continues to rotate. Because the solar wind expands radially and the Sun rotates beneath the field lines, the resulting magnetic structure forms an Archimedean spiral that extends throughout the heliosphere.
The heliospheric current sheet described in Test 3A is embedded within this spiral structure. Together these two elements define the large-scale magnetic architecture of the solar wind environment.
Spacecraft Measurements
Multiple spacecraft have measured the direction and magnitude of the solar magnetic field across a wide range of heliocentric distances. These measurements allow the predicted Parker spiral orientation to be compared with actual magnetic field vectors.
Relevant missions include:
• Ulysses: high-latitude measurements of the heliospheric magnetic field
• Voyager 1 and Voyager 2: measurements in the outer heliosphere approaching the heliopause
• Parker Solar Probe: close-in measurements near the Sun
• ACE and WIND: near-Earth solar wind monitoring missions
These spacecraft provide a distributed observational network for testing the predicted spiral geometry.
Method
1. The Parker spiral model is used to calculate the expected magnetic field direction at various heliocentric distances based on solar rotation rate and solar wind speed.
2. Magnetic field vectors measured by spacecraft are compared with the predicted Parker spiral orientation.
3. Deviations between the model and observations are examined to determine whether the structure behaves as a coherent rotating geometry or exhibits additional structural features.
Interpretation
If spacecraft measurements consistently follow the Parker spiral orientation, this supports the interpretation of the heliosphere as a structured rotating magnetic environment anchored to the Sun.
Within the framework of the Möbius Solar Constitution, the Parker spiral represents the rotational extension of the solar magnetic field through the heliosphere. When combined with the oscillating heliospheric current sheet examined in Test 3A, the resulting structure resembles a large-scale twisted surface whose orientation evolves through the solar cycle.
Significance
This test strengthens the connection between solar magnetic dynamics and heliospheric geometry by comparing theoretical spiral structure with observational data.
The results of this comparison help determine whether the heliosphere behaves as a coherent geometric system capable of supporting the topological framework proposed in the Constitution.
Next Step
Th following test (Test 3C) will examine the behavior of the heliospheric magnetic structure near the heliopause, where the solar wind interacts with the interstellar medium. This final test in this series will explore whether the structural relationships identified in the inner heliosphere persist at the outer boundary of the solar system.
Produced by The Lilborn Equation Team:
Michael Lilborn-Williams
Daniel Thomas Rouse
Thomas Jackson Barnard
Audrey Williams