Hypothetical question: If there were astronomers on a planet, say, 100 light years away, could they detect enough wobble in the Sun's position to infer the existence of Jupiter? Or maybe Jupiter and Saturn?

With what instruments? Over how much time of measurement?

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Probably a better question would be: What kind of instruments and observations would an astronomer 100 light years from here need to detect planets around the Sun?

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The best radial velocity measurements these days have a precision of about 1 m/s. Jupiter creates a periodic signal of 12 m/s in the Sun's motion. So, if aliens 100 light years away have instruments like ours, and if they happen to be located in the plane of the ecliptic, and if they measure the Sun's radial velocity for a decade or two ... yes, they would detect Jupiter's presence.

Would they detect Saturn's? Go look up the relative masses of Jupiter and Saturn.

So if Saturn is ~1/3 the mass of Jupiter, does that mean that it induces a ~4 m/s signal in the Sun?

No, not exactly. There are two factors involved: the mass of a planet, and its distance from the Sun. The more distant a planet is from the Sun, the larger the distance between the Sun and the center-of-mass of the system ... and so the larger the orbit of the Sun around that center-of-mass. That's good for creating a larger radial velocity signal. But the more distant a planet is from the Sun, the longer its period ... which means the longer the Sun's orbital period around the center-of-mass .... which means the smaller its radial velocity signal. Which effect is more important? You can use Kepler's Third Law to figure it out.

You can compute these by multiplying the circular orbital velocity of the planet around the star * the ratio of the planet mass / star mass. So for Jupiter:
sqr(6.673e-11*1.989e30/778000000000) * (1/1047) = 12.48 meters/second

where:
6.67ee-11 is the Gravitational Constant G
1.989e30 is the Sun's mass in kg
778000000000 is Jupiter's semi-major axis in meters
1/1047 is the Jupiter/Sun mass ratio

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Here's a quick approximation to the solar reflex (Doppler) if seen in the ecliptic plane. Circular orbits, fictitious starting longitudes, but it captures the way the signals from Jupiter and Saturn beat against each other over decades. The thin curves are Jupiter and Saturn by themselves - the thick line includes all major planets and shows just-discernible wiggles from Venus and Earth.

Attached Images

sunwobble.jpg (73.6 KB, 22 views)

Thanks, great answers, Stupendousman and ngc. to antisoneb and 0110etc.

Here's a page I put together showing a "top-down" view of how the Sun moves in response to the planets. http://www.orbitsimulator.com/gravit...arycenter.html In each successive image, I delete the planet with the largest effect to showcase the effects of the less massive planets. Of course in real life, a top-down view would not yield any results.

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Fantastic, Tony! Thanks.

I thought the OP would ask about us detecting planets further out in our system. Since the actual question seems answered, I am curious about whether or not we can see a planet say 10,000 a.u. or further? A Jupiter-sized planet would be too dim for Hubble ( < mag. 30), but could Spitzer detect one that far out?

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I wonder if the people engaged various programs for detecting planets could usefully tell us which of the Solar planets can be detected at what range with the techonology available, as it progresses. It's the sort of information that would provide an illuminating insight into the process for the non-specialist.

If the aliens had similar technology and looked long enough I think these aliens would find evidence of a planetary system, the big question you should be asking is are these aliens are funding their space programs or do they have dumbo alien politicans that keep cutting their space agency's budgets. As you probably know the most common way of finding planets is RadialVelocity or checking the Doppler shift in the Stars specturm but getting record breaking distances would be difficult. If they had NASA's TPF, the TPF is a design for an orbiting flotilla of infrared telescope systems each more powerful than Hubble I'm sure they could find something. Or if the aliens had something like ESA's Gaia craft an Astrometry mission looking at measuring positions of 200 microarcsecs at stars of 20 mag they might be able to do it

Seeing an exoplanet 9,000+ light years away requires a bit of luck, it usually requires a chance view of a transit. The planet passing in front of the parent star where it usually gets a name like "Ogle 23456" or Gravitational lensing where you just happen to be sitting in the right view point and these distances can number into the 10s of thousands of light years. Kepler will launch in 2009, it will add huge advances to exoplanetary science and maybe even detect world in similar size and mass to our Earth but it is no TPF, the Kepler telescope does have limitations. It can find something 6 times the mass of Earth in a 1 year orbit around its star that is about 30 light years from the Earth, the Terrestrial Planet Finder which the short sighted politicians gutted would have been a far more productive mission.

Whatever happened to Terrestrial Planet Finder?

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The problem with planets that far out might not be so much "detecting" them as detecting the movement that gives them away as planets. Even as close as 300 AU, that's ~arc minute/year!

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That's a good point. But I am still surprised that even the HST is incapable of detecting any light from a Jupiter-sized object at 10,000 au, while hundreds of planets have been "seen" lightyears away. [Of course, these are indirect observations that are quite credible.]

BTW, is it "AU" or "au"? Since it is not a proper name like "K" in temperature for Lord Kelvin, should it not be lower case? I seem to be the only lower case guy here.

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The project has been deferred indefinitely!

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I believe the convention is to use upper case for the astronomical unit to differentiate from au = atomic units.

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I use upper case to distinguish it as an abbreviation and not a word.

ETA: Plus what AndreasJ said!

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Ah, yes.


Hmmmm.... o.k., I mean, OK.

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So, is "nm" nautical miles or nanometers?

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Yes!

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You can eschew obfuscation if you use C (angstrom) for Prof. Angstrom.

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