Are my planets too close together?

Question

I have four similarly-sized planets (5000-6000km radii) all in circular orbits 10 million km apart (i.e. 300M, 310M, 320M and 335M km from the sun respectively). They are 0.37, 0.61, 0.64 and 0.83 earth masses, respectively. I can alter these masses if need be, all I need is for them to large and massive enough that they could sustain atmospheres, oceans, and, by extension, life as we would recognise it. They have moons, most of which can be captured asteroids but I need one to be lunar sized.

The system also has two smaller Mercury-sized inner planets at 50m and 150m km, and a couple of gas giants beyond 600m km (but these could be further away if that made things easier), then some Kuiper belt sized objects at around 1200-1350m. The star was originally to be larger than ours but orange (but am prepared to change that to make sure the Goldilocks zone centres on my four close planets).

Are the four planets too close together? If they are, what is the closest their orbits can be to each other?

Answer 1

Earth's semimajor axis is 149,598,023 kilometers. Thus the orbits of your planets are about 2.005, 2.072, 2.139, and 2.239 times the semi-major axis of Earth's orbit, the Astronomical Unit (AU).

Note that your outermost planet orbits 1.116666 times as far from the star as your innermost planet.

And to be more precise, your second planet would have 1.03333 times the semi-major axis of your inner planet, your third planet would have 1.0322 times the semi-major axis of your third planet, and your fourth planet would have 1.0468 times the semi-major axis of your third planet.

I think that decades ago astronomers would have said that such close orbital grouping would be dynamically unstable, but recent exoplanet discoveries make it seem much more plausible.

According to this list:

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes1

The smallest difference between the orbits of two exoplanets is only 0.0016 AU or 240,000 kilometers, less than the distance from Earth to the Moon, between Kepler-70b and Kepler-70c. Kepler-70c orbits at 1.26666 times the orbital distance of Kepler-70b. Another planet is suspected to orbit between their obits but is unconfirmed.

And the smallest ratio between the orbits of two exoplanets is 11 percent. Keplar-36c orbits 1,944,700 kilometers farther out than Keplar-36b, or about 11 percent. Keplar-36c orbits 1.1127 times farther out than Keplar-36b,

According to the list of potentially habitable exoplanets that orbit within the habitable zones of their stars:

https://en.wikipedia.org/wiki/List_of_potentially_habitable_exoplanets2

The four exoplanets of TRAPPIST-1 in its habitable zone have years ranging from 12.4 Earth days down to 4.05 Earth days. That shows that they must orbit very close to their star TRAPPIST-1 and to each other.

The difference between the orbits of TRAPPIST-1d, the innermost planet in the habitable zone, and TRAPPIST-1g, the outermost planet in the habitable zone, is only 0.0245966 AU or 3,680,000 kilometers. The orbit of TRAPPIST-1g has 2.9578 times the radius of the orbit of TRAPPIST-1d.

And to be more precise, TRAPPIST-1e has 1.3153 times the semi-major axis of TRAPPIST-1d, TRAPPIST-1f has 1.3150 times the semi-major axis of TRAPPIST-1e, and TRAPPIST-1g has 1.2170 times the semi-major axis of TRAPPIST-1f.

https://en.wikipedia.org/wiki/TRAPPIST-13

Of course the planets of TRAPPIST-1 are all expected to be tidally locked to their star, making it less likely to support life. That would not be a problem in your solar system where the planets would orbit many times farther away from their brighter star.

It may be noted that Keplar-70 has already been a red giant and is shrinking to becaome a white dwarf, while TRAPPIST-1 is estimated to be about 7,600,000,000 years old, much older than the sun. Thus the orbits of their planets should be stable.

Nobody has discovered a stars system like yours yet, but some of the ones that have been discovered give hope that a system like yours might be stable.

I believe that calculations indicate that the outer limit of the habitable zone of a spectral class F star could be over three AU out. Thus the orbits you specify are possible for a class F star much brighter than the Sun.

But there is a problem. The brighter a main sequence star is, the faster it will burn up its nuclear fuel and become a red giant and then a white dwarf, and in the process probably killing all life on its inner planets - and probably absorbing some of them as a red giant.

The Earth is about 4,600,000,000 years old and only developed such interesting for story purposes aspects as an oxygen rich atmosphere and other things needed to be habitable for humans, advanced multi celled lifeforms, and intelligent life, comparatively recently geologically speaking. The planets in your solar system would probably be significantly younger than Earth, and thus would have to develop faster to be as interesting as Earth.

It is more or less arbitrarily assumed that no planet could possibly be habitable until it is at least 3,000,000,000 years old, and I think that class F2 stars are the brightest stars that spend as much as 3,000,000,000 years on the main sequence.

Of course only a small minority of F2 stars will be as old as 3,000,000,000 years, and only a small minority of the Earth like planets of those stars will have advanced a lot faster than Earth did and so be habitable for humans.

Your star will probably be somewhat dimmer than a F2 and have a longer lifespan, and thus having habitable planets will be a lot more likely.

As for the stability of orbits that close, planets tend to interfere with each other's orbits and eject nearby planets from their obits. The strength of that effect seems to depend on the distances and masses of the planets and the distance and mass of their star.

I think that having a more massive star will reduce the degree to which nearby planets interfere with each other's orbits.

Answer 2

Venus is orbiting the Sun at 108 MKm. Terra is at 149.6 Mkm. Mars is at 228 MKm. That's 41 Mkm and 78 Mkm difference from Terra's orbit. If you don't want to do the math perhaps sticking close to the Venus/Terra difference would be best. So orbits 35-45 MKm apart should work. Next you need to figure out how fast they are orbiting the star. That is what will keep them in orbit. It takes Mars just about 2 Tyears (Terran years) to complete and orbit. Venus is about .6 Tyears.

I hope this helps.

Edit: How long does this configuration need to last? If it is for a few million years then you are golden do what you want. These distances are huge and your planets small.