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How does the semi-major axis of Mercury's orbit compare to that of the innermost planet of other exosystems? What about the semi-major of Neptune compared to that of the outmost planet of a system? I'm trying to get a sense for whether our solar system is relatively tightly clustered around the Sun? Relatively loose? Very average?

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    $\begingroup$ I don't think our list of exoplanets is a fair sample of the actual objects out there. We suffer from observational bias in the various methods used to detect them. Planet size and orbital distances are mentioned in this article: exoplanetscience.org/the-bias-of-large-exoplanets $\endgroup$ Nov 25, 2023 at 13:22

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This is several questions - and not all can be confidently answerd at the time of writing due to observation bias which makes detection of far-out planets less likely with the most successful current methods, thus radial velocity and transits.

There is an interesting paper The Mass Budgets and Spatial Scales of Exoplanet Systems and Protoplanetary Disks by Mulders and collegues (2021) who try to answer exactly your question, though.

Earlier they make an assessment of the sensitivity of the methods and assessing the observation bias (published in Fernandes et al (2019)). This hints that the frequency of finding Jupiter-sized planets might decline again after the snow line. In the summary of this paper they say

(...)In a recent study, Wittenmyer et al. (2016) used their Anglo-Australian Planet Search survey to estimate that only $6.2$% of solar-type stars have a Jupiter analog, i.e., a giant planet with masses between $0.3$ and $13 M_J$ located between 3 and 7 au. In the same planet-mass and semimajor-axis range, we derive an occurrence of $3.8%±0.8%$ from the epos best-fit symmetric power law, in agreement with Wittenmyer et al. (2016) within the quoted uncertainties. Thus, it appears that Jupiter analogs are rather rare. Using the same best-fit model, we also calculate an integrated frequency for planets between 0.1 and 100 au of $26.6 %$ for $0.1–20 M_J$ and $6.2%$ for planets more massive than Jupiter ($1–20 M_J$).

In the 2021 paper they

calculate the mass and spatial scale of solid material around Sun-like stars probed by transit and radial velocity exoplanet surveys and compare those to the observed dust masses and sizes of Class II disks in the same stellar-mass regime.

Taking the observations and the analysed biases into account, they come up with a distance to mass plot for typical systems (figure 9), and the different detection methods:

system mass as function of semi major axis, Mulders et al, ApJ 920 (2021)

They conclude

We have calculated the mass and spatial distribution of heavy elements contained in exoplanets around Sun-like stars from the Kepler and radial velocity surveys and compared those to the solids detected in Class II protoplanetary disks in the Lupus and Chamaeleon I star-forming regions. The solid mass reservoirs of exoplanets and protoplanetary disks appear to be of similar magnitude, consistent with previous results (Najita & Kenyon 2014). We find that roughly half of Sun-like stars have disks and exoplanets, with a median solid mass of $≈10–20 M⊕$.

If we follow this analysis, then the Solar system has an above-average mass, and is larger than an average planetary system - however this is still to be taken with at least some grains of salt as large uncertainties especially regarding size and masses in the outer planetary systems remain.

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Short Answer:

Our solar system may be at or new the record for one or two qualities of a planetary system, but seems to be somewhere between the extremes in all other qualities of planetary system. And probably it would be better to wait for hundreds and thousands of other multiplanetary systems to be discovered before calculating averages and seeing how the solar system compares to the average.

Long Answer:

I may add to other answers that there are considerable differences between various known planetary systems around other stars.

Most methods of detecting exoplanets have an easier time detecting planets closer to their stars, and most methods of detecting exoplanets favor detecting larger and/or more massive planets. So planets with closer orbits, and larger and/or more massive planets, are more likely to be discovered and should be over represented among known planets.

Thus is considered likely that many or most known planetary systems around other stars are not known completely and that some planets are still undiscovered in those systems.

So if a star is known to have one planet at this time, in many cases it is unknown whether the star actually has only one planet, or whether it has some more planets which may be discovered in the future. In some cases astronomers have been able to rule out additional planets within a specific size range, and/or within a specific range or orbital distances.

You write:

How does the semi-major axis of Mercury's orbit compare to that of the innermost planet of other exosystems? What about the semi-major of Neptune compared to that of the outmost planet of a system? I'm trying to get a sense for whether our solar system is relatively tightly clustered around the Sun? Relatively loose? Very average?

And I think that it is safe to say that, going by the known variations between the comparatively few known extrasolar planetary systems, planetary systems where the outermost planet, equivalent to Neptune, Pluto, or the hypothetical Planet Nine in our solar system, orbit the star closer than Mercury orbits the Sun, should exist.

And I think that is safe to say that, going by the known variations between the comparatively few known extrasolar planetary systems, planetary systems where the innermost planet, equivalent to Mercury in our solar system, orbits farther than Neptune and Pluto orbit the Sun in our solar system, should exist.

But even though a few thousand exoplanets are now known, and hundreds of examples of two or more known planets orbiting a star, I don't think that there are enough examples of extrasolar planetary systems to decide what an average system is like and to compare our solar system with it.

Wikipedia has a list of exoplanet extremes. And that list cautions:

The following are lists of extremes among the known exoplanets. The properties listed here are those for which values are known reliably. It is important to note that the study of exoplanets is one of the most dynamic emerging fields of science, and these values may change wildly as new discoveries are made.

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

for example, the exoplanet COCONUTS-2b has the longest orbital period, about 1.1 million years.

2MASS J2126–8140 previously held this record at ~900,000 years.

SWIFT J1756.9-2508 b, which orbits a pulsar, is listed as having the shortest orbital period, 48 minutes 56.5 seconds.

K2-137b has the shortest orbit around a main-sequence star (an M dwarf) at 4.31 hours.[25]

The largest orbit around a single star is held by COCONUTS-2b at about 7,506 Astronomical Units (AU).

Projected separation of 6,471 AU.[23] Next largest are 2MASS J2126–8140 with 6,900 AU and HD 106906 b[29] with ~738 AU.

The smallest orbit is that of WD 1202-024 B, at about 0.0021 AU. However, WD 1202-024 Bis not technically a planet, but a brown dwarf, intermediate in mass between a planet and a star, and orbits very close to a white dwarf star.

https://www.syfy.com/syfy-wire/wd-1202-is-a-weird-binary-one-of-the-stars-used-to-be-inside-the-other-one

So some other object, not listed there, should be the true exoplanet with the shortest orbital distance from its star.

The record for "Smallest semi-major-axis difference between consecutive planets" is given to Kepler-70b and Kepler-70c. The distances between the semi-major axis of their orbits is only 0.0016 AU (240,000 km).

During closest approach, Kepler-70c would appear 5 times the size of the Moon in Kepler-70b's sky.[needs update]

But the Wikipedia article on Kepler-70 says:

However, later research[7] suggested that what had been detected was not in fact the reflection of light from exoplanets, but star pulsation "visible beyond the cut-off frequency of the star." Further research[8] indicated that star pulsation modes were indeed the more likely explanation for the signals found in 2011, and that the two exoplanets probably did not exist.

So maybe they should lists planets which are more confirmed.

The record for "Smallest semi-major axis ratio between consecutive planets" is held by Kepler-36 b & c, a ratio of about 11 percent.

Kepler-36b and c have semi-major axes of 0.1153 AU and 0.1283 AU, respectively, c is 11% further from star than b.

Mercury's orbit has a semi-major axis of 0.387098 AU, 3.017 times that of Kepler-36c. So until and unless planets orbiting beyond Kepler-36c are discovered, the Kepler-36 system will remain an example of a system where the planets orbit closer to their star than Mercury orbits the Sun.

The records for "Multiplanetary system with smallest mean semi-major axis (planets are nearest to their star)" and "Multiplanetary system with smallest range of semi-major axis (smallest difference between the star's nearest planet and its farthest planet)" are held by Kepler-42:

Kepler-42 b, c and d have a semi-major axis of only 0.0116, 0.006 and 0.0154 AU, respectively. The separation between closest and furthest is only 0.0094 AU.

Kepler-70 b, c and d (all unconfirmed and disputed) have a semi-major axis of only 0.006, 0.0076 and ~0.0065 AU, respectively. The separation between closest and furthest is only 0.0016 AU.

So Kepler-42 is an example of a system where the known planets are all closer to their star than Mercury to the Sun. And if the disputed Kepler-70 planets are confirmed, they will be another example.

The records for: "Multiplanetary system with largest mean semi-major axis (planets are farthest from their star)" and "Multiplanetary system with largest range of semi-major axis (largest difference between the star's nearest planet and its farthest planet)" are held by TYC 8998-760-1.

TYC 8998-760-1 b and c have a semi-major axis of 162 and 320 AU, respectively.3 The separation between closest and furthest is 158 AU.

The semi major axis of the orbit of TYC 8998-760-1 b is 5.387 times the semi-major axis of the orbit of Neptune (30.07 AU). So until and unless a planet orbiting TYC 8998-760 is discovered it will be an example of a system where the innermost planet orbits farther than any planet in our solar system.

The system with the most planets is listed as Kepler-90, with 8.

Tau Ceti may have up to 8, 9, or even 10 planets if all proposed candidates are counted.[50] However, only four of these planets are considered confirmed, and even they have been disputed by one study.[51]

https://arxiv.org/abs/2010.14675

https://arxiv.org/abs/1901.03294

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

So the Sun seems to be near or at the upper limit for known planets, but possibly the difficulties in detecting smaller and more distant planets skew the results.

The record for: "Exo-multiplanetary system with largest range in planetary mass, log scale (largest proportional difference between the most and least massive planets)" is held by Kepler 37.

Mercury and Jupiter have a mass ratio of 5,750 to 1. Kepler-37 d and b may have a mass ratio between 500 and 1,000, and Gliese 676 c and d have a mass ratio of 491.

So the solar system holds the record for the mass ratio between planets, but possibly the difficulties in detecting smaller and more distant planets skew the results.

Thus our solar system may be at or new the record for one or two qualities of a planetary system, but seems to be somewhere between the extremes in all other qualities of planetary system. And probably it would be better to wait for hundreds and thousands of other multiplanetary systems to be discovered before calculating averages and seeing how the solar system compares to the average.

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