If your fancy computer model doesn’t approximately equal your back of the envelope calculation, that’s generally a knock against the computer model rather than the napkin math. Exceptions exist, but for a system as linear as this you should be able to separate out gravity and look at it on its own no problem.

Do you have a link to a paper, I couldn't find one on google

The one linked in the article? https://advances.sciencemag.org/content/1/11/e1500679