How much does the Solar System weigh, minus the Sun? Menichella (arXiv:2603.17561) compiles the answer: 462 Earth masses, with a 90% credible interval stretching from 449 to 642 Earth masses.
The giant planets are 96.2% of the total. Jupiter alone is most of it. The rocky planets, moons, asteroids, comets, and dust contribute the rest — a few percent, known to much higher precision than the whole.
The uncertainty is dominated by a single component: the inner Oort cloud, a hypothesized reservoir of trillions of icy bodies between roughly 2,000 and 20,000 AU from the Sun. No survey has directly observed the inner Oort cloud. Its mass is inferred from models of Solar System formation and the observed flux of long-period comets. This single unseen population contributes 98.2% of the uncertainty in the total mass budget.
Everything else is well-constrained. Spacecraft have measured planetary masses to 8+ significant figures. Asteroid surveys catalog millions of objects. Trans-Neptunian objects are counted and sized from occultations and thermal measurements. The knowledge is precise where we can look and almost completely absent where we cannot.
The Solar System's mass is known to within a factor of 1.4 at 90% confidence. That factor is not the accumulated error of measuring many things badly — it is the total ignorance of one thing we have never seen. The inner Oort cloud is the dark matter of the Solar System: gravitationally significant, observationally absent, and responsible for nearly all of what we don't know about the mass of our own neighborhood.