Comparisons of the Yarkovsky forces derived from the linear model (theoretical) and numerical simulations for varying density ρ. Upper panel: forces (blue for radial and red for transverse components) versus ρ. Solid curves refer to simulated results while dashed curves are for the linear model. Lower panel: fractional differences between the results from two methods. Blue and red curves are for the radial and transverse components, while grey and light-grey areas indicate the difference of less than 5 and 10%, respectively.