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Suppose that a planet whose size was somewhere between the sizes of Mercury and Jupiter impacted the Sun. Would such an event change local stellar activity sufficiently enough and for long enough that Earth's climate would be affected?

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    $\begingroup$ Just an extension to this question, but Should Jupiter's magnetosphere be considered? Since the sun could fit comfortably inside of it, I'd wonder if strong magnetic forces from Jupiter would affect the sun. $\endgroup$ – Sidney Nov 5 '14 at 18:47
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    $\begingroup$ I like to think about the scene from Hitchiker's Guide to the Galaxy where the contractor asked Arthur how much damage he thought his bulldozer would take if it ran Arthur over. The answer to this question is most likely the same as the one posed to Arthur: "None at all." $\endgroup$ – Cort Ammon Nov 6 '14 at 1:46
  • $\begingroup$ Similar question on Space Exploration: What would happen if an Earth-sized body encountered Jupiter? $\endgroup$ – a CVn Apr 23 '16 at 16:42
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Mercury vs. the Sun

  • Mass: Mercury - $3.3022×10^{23} \text{ kg}$; Sun - $1.98855×10^{30} \text{ kg}$. Mercury clearly won't so much as jostle the Sun. There should be no major changes in the Sun's orbit around the galactic center.
  • Composition: Mercury - oxygen, sodium, hydrogen, and iron; Sun - hydrogen and helium. The extra elements shouldn't affect the Sun's fusion process, especially given how scarce they are.

Jupiter vs. the Sun

  • Mass: Jupiter - $1.8986×10^{27} \text{ kg}$; Sun - $1.98855×10^{30} \text{ kg}$. Jupiter could perhaps perturb the Sun a little if it hit it right on.

  • Composition: Jupiter - hydrogen and helium; Sun - hydrogen and helium. The Sun would gain a little fuel, but not enough to cause a substantial change in the Sun's fusion.

In both cases, the Earth should be fine. Sure, there could be a solar flare or two, but not anything substantial enough to severely impact the Earth.

There are two interesting side effects of such a collision, and while they wouldn't impact Earth, they're still worthy of mention. First, the collision of a gas giant with a star would increase the lithium-6 concentration in the star (see Israelian et al. (2001) and Melendez et al. (2016), who studied HD 82943 and HIP 68468, respectively). Second, if the planet (again, assuming it's a gas giant) was a victim of orbital decay, then it could be torn apart when it reached the Roche limit. The resulting angular momentum transfer could drastically increase the star's rotation rate (see Hellier et al. (2009)).

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    $\begingroup$ Something that might impact earth more is Jupiter passing through the earths orbit on it's way to the sun, or even what event that caused Jupiter to change orbit so drastically. $\endgroup$ – bowlturner Nov 5 '14 at 17:19
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    $\begingroup$ "Jupiter ... The Sun would gain a little fuel" You've just given me a brilliant idea to extend the life of our star by a few minutes! $\endgroup$ – Michael Nov 5 '14 at 22:32
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    $\begingroup$ @Michael Not for biological life in our solar system - if that life is on Jupiter. . . :-) $\endgroup$ – HDE 226868 Nov 5 '14 at 22:33
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    $\begingroup$ @Michael Adding fuel to a star shortens it's lifespan. $\endgroup$ – Taemyr Nov 6 '14 at 10:45
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    $\begingroup$ @HDE226868 - the additional mass will compact the core very soon and make it burn hotter to compensate, as soon as it is no longer 'in orbit' of the sun. This faster burn means shorter life. $\endgroup$ – Oldcat Dec 5 '14 at 22:38
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Neither the Sun nor Jupiter are "solid" masses.

Speed of impact will make a huge difference. In a very slow impact, the Sun absorbs Jupiter with little more than a hiccup.

Though I could see the sun having some flares and CMEs. If they are pointed at the Earth, the effects will range anywhere from a mild increase in the ionization of the ionosphere (better short wave communications) to a game over blast of high energy particles (kills all ungrounded/shielded electronics and electrical systems).

In a high speed impact will likely eject some mass, again the direction of this is everything.

I think @bowlturner has a serious point. Jupiter passing the Earth (with its intense magnetic field) could be a huge problem in its own right. Fortunately, space, even in the inner system, is BIG. Lots of room to slip Jupiter past us.

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Yes and no. Jupiter is 317 times more massive than the Earth and 1000 times less massive than the Sun. That's big and small. This would likely cause a solar flare due to disruption of the magnetic field which could potentially increase Earth's temperature resulting in climate change, cause damage to the ozone and wipe out electronic technology.

Mercury on the other hand at 0.05 the mass of Earth would have little effect.

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Given that Jupiter is mostly gas, surely it would both be pulled apart tidally and evaporate as it approached the sun.

If that is the case then there would be no impact at all merely a diffuse addition to the Sun's mass.

I suspect the same might be true of almost any planet - gaseous or not.

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