Areal velocity is constant: r² θ’ =h Kepler’s Law
h = 2π a b/T; b=a√ (1-ε²); a = mean distance value; ε = eccentricity
r² θ’= h = S² w’
Replace r with S = r exp (ỉ wt); h = [r² Exp (2iwt)] w’
w’ = (h/r²) exp [-2(i wt)]
w’= (h/r²) [cosine 2(wt) - ỉ sine 2(wt)] = (h/r²) [1- 2sine² (wt) - ỉ sin 2(wt)]
w’ = w’(x) + ỉ w’(y) ; w’(x) = (h/r²) [ 1- 2sine² (wt)]
w’(x) – (h/r²) = – 2(h/r²)sine²(wt) = – 2(h/r²)(v/c)² v/c=sine wt
(h/ r²)(Perihelion/Periastron)= [2πa.a√ (1-ε²)]/Ta² (1-ε) ²= [2π√ (1-ε²)]/T (1-ε) ²

Δ w’ = (d w/d t – h/r²] = -4π {[√ (1-ε²)]/T (1-ε) ²} (v/c) ² radian per second
Δ w’ = (- 4π /T) {[√ (1-ε²)]/ (1-ε) ²} (v/c) ² radians
Δ w’ = (-720/T) {[√ (1-ε²)]/ (1-ε) ²} (v/c) ² degrees; Multiplication by 180/π
Δ w’ = (-720×36526/T) {[√ (1-ε²)]/(1-ε)²} (v/c)² degrees/100 years
Δ w” = (-720×3600/T) {[√ (1-ε²)]/ (1-ε) ²} (v/c) ² seconds of arc by 3600

Δ w” = (-720x36526x3600/T) {[√ (1-ε²]/(1-ε)²} (v/c)² seconds of arc per century
This Kepler’s Equation solves all the problems Einstein and all physicists could not solve

The circumference of an ellipse: 2πa (1 – ε²/4 + 3/16(ε²)²- –.) ≈ 2πa (1-ε²/4); R =a (1-ε²/4) v=√ [G m M / (m + M) a (1-ε²/4)] ≈ √ [GM/a (1-ε²/4)]; m< Advance of Perihelion of mercury.

G=6.673×10^-11; M=2×10^30kg; m=.32×10^24kg
ε = 0.206; T=88days; c = 299792.458 km/sec; a = 58.2km/sec
Calculations yields:
v =48.14km/sec; [√ (1- ε²)] (1-ε) ² = 1.552
Δ w”= (-720x36526x3600/88) x (1.552) (48.14/299792)²=43.0”/century

Conclusions: The 43″ seconds of arc of advance of perihelion of Planet Mercury (General relativity) is given by Kepler’s equation better than all of Published papers of Einstein. Kepler’s Equation can solve Einstein’s nemesis DI Her Binary stars motion and all the other dozens of stars motions posted for past 40 years on NASA website SAO/NASA as unsolved by any physics

Anyone dare to prove me wrong?

“Update : Tonight MESSENGER is again flying by Mercury for the second time in its October 2008 fly-past. This thread is linked to that and now if youclick my name the link should take you back to the latest Bad Astronomy ‘MESSENGER-flies-by-Mercury’ thread. Providing it works … lets see ..”

Well I’ve just checked &, yes, the links working so you can click there to come here and click my name here to go back there folks.

Hope that is okay netiqutte-wise. Am trying to make things easier for fellow posters here. Please let me know if this is considered bad form or anything like that – don’t think it is, obviously, but not really too sure ..

Actually thinking netiquette is there a problem with acronymic names like MESEENGER which, being in all-capps, is like SHOUTING in net-ese? Would it be more polite or less (certainly less accurate I ‘spose) to have MESSENGER written in lower-case ie. Messenger instead? Oh, & then if it is lower case there’s always the risk of confusing the spaceprobes name with the word ‘messenger’ itself .. Hmmm …

Tongue-twister potential here :

The MESSENGER team’s messenger came with the message that mercury had been discovered on Mercury and also that because saying MESSENGER not messenger sounds like shouting on-line the MESSENGER teams’ messenger wanted us to use ‘messenger’ instead of ‘MESSENGER’ – except for when also mentioning the MESSENGER’s teams messenger!

This thread is linked to that and now if youclick my name the link should take you back to the latest Bad Astronomy ‘MESSENGER-flies-by-Mercury’ thread.

Providing it works … lets see ..

PS. Oh & more good news – Huckabee didn’t make McCain’s Vice-Presidential choice or Republican nomineee and looks like fading away with his 15 minutes of fame (too long IMHO) well and truly over … The bad news o’course being that Sara Palin seems like a female Huckabee clone.

I don’t know of any specifically on the 14th, but we are coming up on “hell week” for NASA. All of the loss-of-life mission accidents in its history have occurred within the seven day stretch at the end of January:

Apollo 1 fire – 27 January 1967
Challenger – 28 January 1986
Columbia – 1 February 2003

This does not include deaths in training accidents, etc.

- Jack

That tiny crater you pointed out, I would hazard a guess that it would have been made by something fairly brittle and of low mass? As opposed to a heavier object whose ejecta wouldn’t travel as far and may appear more uniform. Total guess though, I’m no astronomer, just a total amateur. It is an interesting one, I wouldn’t have spotted it otherwise.

(Hmmm, maybe Bill needs to register “eightplanets.org” to keep up with the IAU…?)

On the gas-giant-core-thing, would a naked core not look substantially different than the not-quite-Luna that Mercury presents? Setting aside the issues of the distance at which the atmosphere would be stripped, and the probable mass of the core, I mean. I assume much of the cratering we see on other airless bodies in the solar system was inflicted shortly after the planets coalesced, when potential impactors were more numerous. If Mercury was a giant, wouldn’t its core have escaped much of the cratering, due to potential impactors exploding in the atmosphere, or have seen it erased due to atmospheric erosion?

(Plus, if core accretion is correct, the minimum size of a gas giant’s core should be somewhere around 6-10 Earth masses, which is a LOT bigger than Mercury)

I’m picking at nits here, but from a planetary formation standpoint, how is this possible? When the planet was young, there were few craters, so the number of craters destroyed by the average impact would have been close to zero. As the number of craters increased, the number of craters destroyed on average would also increase until it approached the number of craters created on average; at which point the crater system would be in equilibrium, and the total number of craters would be approximately constant. But your statement implies that the crater system has actually gone past equilibrium, which makes no sense.