How would one calculate the minimum mass required for the earth to retain an atmosphere?

If we could hypothetically start removing mass from the earth with a star-trek style transporter, how much mass would the earth have to lose before its atmosphere would no longer cling to its surface?

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    $\begingroup$ I'm glad you want to participate, but you should edit your question to show the results of your initial research. You may find there is no single answer -- it may depend on the planet's chemical composition, magnetic field, and its environment (i.e. solar wind) relative to its star. $\endgroup$ – Spencer Jan 17 '18 at 1:17
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    $\begingroup$ We've had quite a few discussions about retention of planetary atmospheres over at astronomy. Take this simplified answer for example: astronomy.stackexchange.com/questions/10256/… . But keep in mind, that this simplified picture presented there is only a very rough rule of thumb and cannot explain differences between the atmospheres of Mars, Venus, Earth and Titan. $\endgroup$ – AtmosphericPrisonEscape Jan 17 '18 at 16:51
  • $\begingroup$ please update the question to clarify what atmosphere means to you,is it composition or density,if you change earths mass the atmosphere will change a lot in both density and composision,if you look at mars only the heaviest gasses are left now. $\endgroup$ – trond hansen Jan 18 '18 at 14:41
  • $\begingroup$ The atmosphere is at greater risk from the solar wind than mass per se. The Van Allen belts are the primary protection against solar wind erosion. Mars lost its atmosphere when its internal dynamo cooled diminishing its protective radiation fields. $\endgroup$ – TomO Jan 19 '18 at 23:01
  • $\begingroup$ Already asked, and nicely answered, over at Worldbuilding. $\endgroup$ – Pont Jan 25 '18 at 7:08

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