Interplanetary background measurements can be used to derive the solar flux that is illuminating the atoms in the interplanetary medium. We present a new algorithm combining measurements from the SWAN‐SOHO Lyman α photometer with Earth‐based solar flux measurements to derive the solar illuminating flux at Lyman α in any direction along the ecliptic plane. The modulations of the solar flux and the interplanetary background intensity are proportional. The proportionality coefficient is a direct measurement of the fraction of the interplanetary brightness that is due to single scattering in the interplanetary medium. We find that for an observer at 1 AU from the Sun, single scattering photons represent roughly 70% of the total brightness. This new algorithm is tested by a comparison with actual measurements from the EUVM‐MAVEN solar monitor in orbit around Mars since 2014.