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How big will the Sun be once it becomes a red giant? How much of the solar system will it engulf?

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This is answered in How fast will the sun become a red giant?. I'm just adding a note here because it's not answered directly in a form a non-expert might spot.

The maximum size of the sun is estimated to be 256 times it's current radius, the Earth's orbit is 215 times the sun's radius - so it will consume Mercury, Venus, Earth and a bit of the way toward mars.

It's a little complicated because as the Sun expands it losses mass - large stars blow off their outer atmosphere. With the Sun having less mass it's gravity is weaker and Earth's orbit moves further out. The linked paper says (if I read it correctly) that the Sun will expand first, passing the Earth, before it has lost enough mass for the Earth to move far enough away.

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    $\begingroup$ I would add that the point of the paper cited in that answer is that the Earth would move out far enough to avoid engulfment (since the Sun will lose mass and have less of a gravitational hold on us), as was known for some time, but they predict tidal drag will pull the Earth into the bloated Sun anyway. In any event, the planets' orbits are certainly subject to change during such a time. $\endgroup$
    – user10851
    Commented Nov 28, 2012 at 2:44
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    $\begingroup$ I read the abstract as saying that there wasn't signficant mass loss during RGB to shift the earth, and the peak radius would be 1.15au. The large, 0.3Msol, mass loss was only later in the AGB phase $\endgroup$ Commented Nov 28, 2012 at 20:08
  • $\begingroup$ This is slightly scary... :P $\endgroup$
    – Alenanno
    Commented Nov 29, 2012 at 13:26
  • $\begingroup$ @Alenanno - don't worry, you have about 5-7 Gyr to stock up on really heavy duty sun tan lotion $\endgroup$ Commented Nov 29, 2012 at 15:54
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    $\begingroup$ @Thriveth - that's only an issue for you feeble humans $\endgroup$ Commented Jun 6, 2013 at 18:52

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