Yes, let's make the same mistake as Terra's dominant calendar and not have a year zero
I once created the Heliocentric Yurian Date system (☉ЮD), a word play on the Julian Date system astronomers use, and named after Yuri Gagarin, who requires no further introduction. It is a simple decimal system that counts the number of seconds elapsed since 00:00 UTC on April 12, 1961, corrected by the ~ 8m20s OWLT to the Sun at that moment, to make it a solar-centred clock.
On that clock 1,710,997,312 seconds have passed at the time of typing this. A Yurian "day" has 100,000 seconds, the ☉ЮD is thus 17109.97312 (in Star Trek tradition it could be referred to as "Stardate 17109.9"). This makes a Yurian Day slightly longer than a Terran one (100,000 seconds v 86,400), 27.777 hours. In the blackness of space, that wouldn't matter. I, for one, would actually love to have a few extra hours for my "daily" routines