Secular Mass Loss of the Zodiacal Cloud and the Resupply Rate Required for Steady State

This paper examines Rate at which the cloud loses mass through inspiral, grinding and ejection, and the equal supply rate a steady cloud demands. Using only published input values and transparent formulae, the calculation obtains the following headline results: total_cloud_mass_kg = 4.08e+15; characteristic_residence_time_yr = 152000; secular_loss_rate_kg_s = 850.5; secular_loss_tonnes_per_day = 73484; pr_inspiral_share_percent = 55; collisional_blowout_share_percent = 30; required_resupply_kg_s_steady_state = 850.5. The cloud loses of order eight hundred and fifty kilograms every second, roughly seventy-three thousand tonnes per day summed over the whole cloud, most of it spiralling into the Sun rather than reaching any planet, and a steady appearance over geological time therefore requires parent bodies to replace mass at exactly that rate on average. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. Agreement and disagreement with independent published estimates are reported at their actual size, and the conclusions are limited to what the budget arithmetic supports.