For those into astronomy, is there a trend to when or by how much Neptune varies from its predicted orbit? Call me simplistic, but could the variation in its orbit be maximized when both Saturn and Jupiter are opposite Neptune? Or, does the mysterious “tug” appear to be from something beyond Neptune?

Where do you find descriptions of Neptune straying from its predicted orbit?

Maury had a whole show about it. Larissa’s got a big mouth.

I didn’t even know it did stray, but I don’t understand your questions - if there was a trend, that would *be* a factor in the predicted orbit.

You’d better keep an eye on Uranus!

If it’s this kind of phenomenon Jinx is asking about the answer is that anyone discussing surprise tugs on Neptune have accounted for and eliminated the influence of all the known bodies in the Solar System.

And I assume the focus on Saturn in the linked article is that the presence of Cassini gives us more accurate data on Saturn’s orbit than we get from Earth based observation.

Interesting.

Can someone verify this:

Would it be 16 times as bright if twice as close? I think the inverse-square law of light intensity operates twice — once Sun to Nine, once Nine to us.

But it would be smaller if closer. Assuming Nine is at distance d, has radius r and is of some fixed density, to get equivalent pull on Saturn, r[sup]3[/sup] ∝ d[sup]2[/sup], right? With this I get 6.35 times as bright, not 16 times.

Where did I go wrong?

My area of expertise is logic rather than math, and history rather than astronomy, but wouldn’t an objects brightness depend more on it’s reflectivity than anything else? Or what it’s composed of?

And gravitational effects on the other planets would be affected by distance, yes, but also mass. The further it is from Neptune or Saturn, the more massive it would have to be to have the same effect on their orbits.

I think both webpage and myself approached it from the “all else (including density and albedo) being equal” standpoint. Given such assumptions I’m curious who’s wrong: webpage, me, or (my guess :)) *both*!

Start with I[sub]0[/sub] at the Sun and assume a distance of A = 600 AU.

I(A) = 1/A[sup]2[/sup]

I(earth) = I(A)*1/A[sup]2[/sup]= 1/A[sup4[/sup]

I(2A)= 1/(2A)[sup]2[/sup]

I(earth)=I(2A)*1/(2A)[sup]2[/sup]=1/4A[sup]2[/sup]*1/4A[sup]2[/sup]=1/16A[sup]4[/su]

The moral of the story is that you have to be very careful when saying “all else being equal”, because it can’t all be equal at once. The author of that webpage was assuming “equal size”, but **septimus** was assuming “equal gravitational influence”, and they can’t both be equal.

I had a really difficult time learning partial derivatives, because far too often, issues like this are glossed over, and my intuition of what should be kept equal was often different from the teacher’s. I didn’t really get them until statistical mechanics, where it’s *always* ambiguous, and thus everyone’s always forced to make it clear.