Replacing Jupiter with a brown dwarf?

Question

This is a purely hypothetical question but I can't find a satisfactory answer to it.

Let's say somehow Jupiter collects enough mass to be considered a brown dwarf. Let's assume Jupiter achieves a maximum of 75 Jupiter Mass, which will be large brown dwarf in the solar system.

What would happen to Earth if this were to happen? I mean more in terms of Earth's orbit and radiation output. Would life still exist on Earth?

Further, what would the solar system even look like if Juptier were to become a brown dwarf? Would the planets and Jupiter still orbit around the Sun? Or would sheer mass of Jupiter catapult some planets out of the solar system altogether?

Answer 1

This is the formula for how much force gravity exerts between any two masses in space:

$$ G \frac{m_{1} m_{2}}{r^2} $$

Where:

• G is a constant: $$ G = 6.674×10^{-11} N (\frac{m}{kg})^2 $$
• m₁ and m₂ are the masses involved
• r is the distance between the masses

Let's calculate how strongly Jupiter attracts the Earth. We need some background first:

• Distance on closest approach ~= 5.88 x 10¹¹ meters
• Earth's mass ~= 6 x 10²⁴ kg
• Jupiter's current mass ~= 1.9 x 10²⁷ kg

At their closest approach, for all practical purposes, Jupiter attracts the Earth with a force of...

$$ 6.674×10^{-11}N(\frac{m}{kg})^2×\frac{(6×10^{24}kg)×(1.9×10^{27}kg)}{(5.88×10^{11}m)^2} ~= aprox. 2.2×10^{18}N $$

2.2x10¹⁸ Newtons may seems like a heck of a force, but it is only enough to accelerate the Earth at a rate of 3.6676x10^-7 meters per second towards Jupiter. That is close to a tenth of a millionth of a meter per second. By the time any significant pull is done, the Earth will have gone further away from Jupiter, lessening the pull.

Now let's run the same calculation with 75 Jupiter masses:

$$ 6.674×10^{-11}N(\frac{m}{kg})^2×\frac{(6×10^{24}kg)×(1.425×10^{29}kg)}{(5.88×10^{11}m)^2} ~= aprox. 1.65×10^{20}N $$

That is enough to accellerate the Earth towards Jupiter at 0.0000275 meters per second. It is almost the same pull that the Moon has on Earth. Running the same equation for the pull between the Earth and the Moon (mass = 7.34x10²² kg, distance 384.400 km):

$$ 6.674×10^{-11}N(\frac{m}{kg})^2×\frac{(6×10^{24}kg)×(7.34×10^{22}kg)}{(3.844×10^8m)^2} ~= aprox. 1.989×10^{20}N $$

Which is comparable to the previous calculation. However, since Jupiter is much farther away, the difference in the forces it would exert on the near and far sides of Earth would be very small: varying the distance by six thousand kilometers more or less in the formula above gives a variation in newtons within the 12^th negative power of ten. Not enough to cause tides (contrary to what I said in a previous version of this post).

Saturn's closest approach distance to Jupiter is very close to Earth's closest approach distance. Saturn's mass is close to a hundred Earth masses, so the pull between Saturn and brown dwarf Jupiter would be around 100x the pull between brown dwarf Jupiter and Earth. Not enough to fling Saturn out of its orbit... Maybe some rings would be rearranged.

Other bodies in the solar system would be similarly affected. Perturbations in the asteroid belt could fling some towards the sun over millenia, which could put us at risk, but we shouldn't have much cause for immediate worry.

Answer 2

First, I am going to assume that the question is, "What would have happened to Earth if, during the formation of the Solar System, Jupiter had grown to be a large brown dwarf rather than a moderate-sized gas giant."

This is a difficult question for two reasons. First, while we've made excellent progress in understanding the formation of planets, we still have a lot to learn. Secondly, the process is usually chaotic in the technical sense, where small changes at early times can produce arbitrarily large changes in the final results.

So one point right off the bat: Possible outcomes include the Earth and other small planets being ejected from the solar system or impacting the Sun or UberJup. Based on what I recall from reports on detailed modelling, I'm pretty sure that most of the asteroid belt would be ejected and possibly Mars as well. There a paper at http://iopscience.iop.org/article/10.1086/300695/fulltext/ which presents simulations of planets in various binary system to determine orbital stability. (Note that it doesn't actually look at the brown dwarf case, but the lowest mass case it does consider gives us hints. Also, note that it only looks at 10,000 "years", and that we know from other work that instabilities can happen much later.)

However, given those caveats it looks like stable orbits can exist inside about half UberJup's distance from the Sun. Since UberJup is at about 5 AU, we can reasonably expect all of the inner planets (including Mars at about 1.5 AU) to have stable orbits.

This is for the case of a low-eccentricity orbit for UberJup, since a higher eccentricity makes the inner planets less stable.

Bottom line so far: The inner plants could survive in stable orbits, but there is a non-trivial chance they wouldn't.

There's a lot of cutting-edge work on planetary migration, which I've not considered and which probably decreases Earth's survival chances. Basically, once you're not looking at ultra-close approaches -- cosmic billiards -- resonance effects become important. Resonance effects don't even require huge masses. Basically, if, say, Earth and Venus had orbits whose periods were in a small integer ratio: 2:3, 1:2, 3:4, etc., they occupy the same relative positions again and again and again and even very small gravitational effects can build up and, slowly over time, planets can exchange surprisingly large amounts of energy and momentum.

It appears that in the actual history of the Solar System, Jupiter and Saturn did just that and moved first in to perhaps half their current orbital distances and then out before settling down where they are today. I have no idea how replacing Jupiter with UberJup would affect this. It could be simulated, but it's beyond my ability and I know of no one who has considered this problem. (Which is not to say no one has -- the literature is very large.)

So let's forget all that and look at the minimum changes case: UberJup sits where Jupiter sits. The inner planets are basically unaffected in their orbits. The asteroid belt is probably nearly empty. Outside UberJup's orbit there are probably some gas giants and neptunes, but their arrangement and number is probably different than the Solar System's. The arrangement has a reasonable chance of being stable.

One potentially big change is that the clearing of the asteroid belt would probably have resulted an an increased very early bombardment of Earth, so the Earth might be a few percent more massive than it is today. It might also have a second natural satellite, though much smaller than the Moon.

Finally -- here's where chaos comes in -- there's a good chance the Moon would not exist at all. It appears that the formation of the Moon happened due to a glancing strike of one of the last planetary embryos on a nearly complete Earth. This splashed a lot of matter into orbit, some of which coalesced into our massive Moon. It appears this is a fairly low probability event, so the presence of UberJup might well have erased our giant Moon.

Answer 3

(Not a scientist, just using locigal thinking. And I do excuse for my grammer misstakes.)

I think, if Jupiter gathers enough mass most of the closer objects (the asteriod belt between Jupiter and Mars) might be pulled towards the planet, now a brown dwarf, and start to orbit it. Planets close enough like Satern and Mars might see change in their orbit pattern. Mars might even become a "moon" of Jupiter. Jupiter will probably have stronger and more extreme effect on weather conditions on Earth. Like a bigger version of the moon. The eco system of Earth will probably be highly effected.

Maybe in time the sun and Jupiter enter a binary star realationship, as the sun and Jupiter might be pulled together because of their gravitatinal pull. And some of the smaller planets might be swung out of the solar system because of changing gravitatinal pulls.