AbstractA summary of the long‐term, 1974–2018, measurements of the line‐of‐sight velocity of the solar photosphere, performed at the Crimean Astrophysical Observatory, is presented. The work shows that the Sun is pulsating with two periods: P0 = 9,600.606(12) s and P1 = 9,597.924(13) s. The new measurements, 1996–2018, confirm the remarkable phase stability of the second period. The true origin of both pulsations is unknown, but their beatings are noted to have occurred with a period of 397.7(2.6) days, coinciding well with the synodic period of Jupiter, 398.9 days. A hypothesis is advanced that the shift from P0 to P1 is induced by the gravity field of Jupiter.