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This answer on Space Exploration to a question about Mars says that one reason Mars has such a thin atmosphere is because it lacks a magnetic field to protect it from the effect of double solar winds.

Here MBR explains that Venus does not have a magnetic field.

Venus-atmopshere

Image credit: ESA

If this is the case, then why has Venus's atmosphere not been stripped away by solar wind like that of Mars?

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Venus has a strong ionosphere that protects it against violent solar winds. So, even though Venus has no intrisic magnetic field, it has an effective, induced magnetic field due to the interaction between the solar winds and the atmosphere, that protects it against solar winds.

Venus atmosphere is thick enough to have a consequent ionosphere, that would be the difference between Mars and Venus (and Venus was able to keep a thicker atmosphere due to its greater mass, contrary to Mars).

Sources:

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    $\begingroup$ I believe I read somewhere that the character of Venus's atmosphere has been changed over the eons. Water in the atmosphere was split into separate hydrogen and oxygen atoms, with the hydrogen being blown into space by the solar winds. This makes Venus not only hot, but dry. I wonder if Earth might have benefited by capturing some of the hydrogen and matching it up with free oxygen in our atmosphere. $\endgroup$ – Howard Miller Jun 19 '16 at 23:27
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A major factor, is that Venus' volcanoes are still active. Mars's died millions of years ago. If they were still erupting, then Mars' atmosphere would be much thicker today.

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Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.

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    $\begingroup$ Sounds about right, but can you expand this answer a little? Now it is more of a comment. $\endgroup$ – Hohmannfan Sep 15 '16 at 4:07
  • $\begingroup$ Still, it's a pretty cool comment! :) $\endgroup$ – Fattie Oct 24 '16 at 10:07
  • $\begingroup$ Downvote: This is not known. There are indications that the surface might be young (~30 million yrs) but except for counting of large craters there is no data available on the age of the surface. $\endgroup$ – AtmosphericPrisonEscape Nov 10 '18 at 19:12

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