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Suppose there’s a planet in the habitable zone of a class F star, a bit smaller than Earth and about the same density, with 80% of earth’s gravity. How far away from the planet would a brown dwarf orbiting the same star have to be in order to act like Jupiter does in our system, shielding the planet from extinction-level impacts for a long enough time for complex life to develop?

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    $\begingroup$ Welcome to worldbuilding. Note that you are asking too many questions and all of them are ill defined. We are not going to do a complete study of all the possibilities for you (how far is the brown darf? how far is the planet? are there other bodies in the system? etc.). Please specify more the problem you want to be solved. $\endgroup$ – L.Dutch Apr 12 '18 at 12:33
  • $\begingroup$ Yes it will protect the planet. Its Jupiter's gravitation that deflects comets, asteroids and meteors. A brown dwarf has more gravity. At a minimum as far away as Saturn to be visible. Probably, if they were both in the habitable zone. Perhaps not, as the brown dwarf acts an attractor for incoming impactors. $\endgroup$ – a4android Apr 12 '18 at 12:36
  • $\begingroup$ To be clear, the Earth is not safe from asteroid impacts. The end of the Cretaceous period, with an asteroid effectively wiping out the dinosaurs proved that. Jupiter makes us safer but it's risk mitigation, not risk elimination. On the same basis, a brown dwarf would also afford a measure of protection but based on its mass and orbit, it may well let through some threats Jupiter has protected us from and removed some that Jupiter didn't catch. Based on that, we could have easily turned out to be intelligent bird like creatures descended from velociraptors. $\endgroup$ – Tim B II Apr 12 '18 at 12:38
  • $\begingroup$ Also, Jupiter has a small influence on Earth orbit. A brown dwarf in its place could disrupt the Earth orbit. One more reason for you to better specify masses and distances. $\endgroup$ – L.Dutch Apr 12 '18 at 13:47
  • $\begingroup$ Apologies for the broadness, I’ve re-written the question in an attempt to remove this issue. $\endgroup$ – Brimstoned Apr 12 '18 at 17:09
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Let me try to answer this.

Assumptions:

  1. Star stats $\approx$ 1.2 solar masses, 7,000 K surface temperature, 4 solar luminosity units
  2. Planet stats $\approx$ 2 AU from star (well inside conservative Goldilocks zone), radius about 5,100 kilometers.

Now, for the brown dwarf. It needs to be big enough to deflect comets coming in from the outer solar system (>200 year orbits) that are going pretty fast. They probably originate in a 'Oort cloud' of sorts, given they exist. The 'Oort cloud' would be further than the 1 light-year away ours is, so assuming comets are going at ~1.8 km/s, the amount of velocity change the brown dwarf would have to give is about 0.75 km/s (from that astronomy answer). Given $\frac{G m_1m_2}{d^2}$, with a mass of about $30$ Jupiters, such a brown dwarf could guard about $30$ times as much area as our Jupiter. Since diameter is proportional to circumference, this could guard as many comets as Jupiter does at about $30$ times the distance away (my math may be wrong, please check). Even factoring in the effect of Saturn on comets, I think it could be safe to consider putting your brown dwarf at 50 AU (4 AU times 12.5).

However, it isn't for certain this is the function of Jupiter. See this study.

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