Are tiny black holes zipping through our solar system? Scientists hope to find out.

[Jim__]

6. They're not looking at single encounters, but rather at simulations of cumulative effects over years.

And, they don't talk about it in terms of feet, but rather in terms of (delta ⁢r) / r(t) where r is the approximate distance between earth and another solar system object.


From the paper:

Finally, Figure 3 presents the results from 500 simulations performed over a longer time span of 20 years for M_PBH=10²⁰ g. In the left panel we display the perturbation |delta ⁢𝕣|/r of the vector between Earth and Mars. A notable difference to Figure 1 is that the perturbations oscillate with a period of roughly two years which corresponds to the synodic orbital period of Mars and is thus simply a result of the change of r. We add an estimate for a 3⁢σ detection limit by assuming that sigma r≈70 cm for the Earth-Mars distance (Park et al., 2021). Out of all 500 simulation runs only 4 exceed this limit at least once within 20 yrs, implying a ∼1% chance of detection with a confidence level of 3sigma.

In the right panel of Figure 3 we show the mean perturbation strength |delta ⁢𝕣|/r of all simulation runs for several planets. In our analysis we focus on the Earth-Mars pair for the reasons outlined in Section 2. The results shown here demonstrate that this does not limit the generality of our statements as the observed perturbations are very similar for other planets in the solar system.



Figure 3: Left: Perturbation of the vector between Earth and Mars induced by PBHs for M_PBH=10²⁰ g as a function of time. Each blue line corresponds to one simulation run. We only show 100 simulation runs to improve readability. The black dashed/dotted line indicates the median/mean value obtained from all 500 simulations. The analytical result of the impulse model is displayed as an orange line. The green line shows a model for the median perturbation strength, given by Equation 15. The red line is an estimate of the 3⁢ sigma observational detection limit. Right: Mean perturbation strength |delta ⁢𝕣|/r as a function of time for the vector between Earth and various planets.