The Parker Spiral Angle from 0.1 to 5 AU: Winding Geometry for Slow and Fast Solar Wind Streams

The angle between the interplanetary magnetic field and the radial direction controls how particles, fields and disturbances are organised throughout the inner heliosphere, yet it is often quoted only for a single nominal case at Earth. This study computes the Parker spiral angle on a grid of heliocentric distances from 0.1 to 5 AU and outflow speeds from 300 to 800 kilometres per second, using the frozen-in condition with the solar sidereal equatorial rotation rate. For a 400 kilometre per second stream the angle grows from 6.12 degrees at 0.1 AU to 47.0 degrees at 1 AU and 79.4 degrees at 5 AU; at 1 AU it spans 55.0 degrees for a 300 kilometre per second stream down to 28.2 degrees for an 800 kilometre per second stream. Integrating the spiral gives a field-line length of 1.167 AU between the Sun and 1 AU for the 400 kilometre per second case, an excess of 16.7 percent over the radial distance. The calculation is simulated and computed from stated assumptions, not measured, and its comparison values are the published typical field orientations reported by Parker Solar Probe, Solar Orbiter and Wind.