Gravity Simulator
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Message started by Tony on 05/05/07 at 01:45:50

Title: Sources of error
Post by Tony on 05/05/07 at 01:45:50

Gravity Simulator only takes into account Newtonian point-mass physics. These equations alone are extremely accurate. For example. when given accurate starting conditions, the asteroid Apophis can be propogated in orbit from the present epoch to 2029, when it will pass close to Earth, and miss its JPL-predicted close approach distance by only a few hundred kilometers. This is like driving a golf ball 500 miles, and missing your target by less than a centimeter.

But why isn't it perfect? What causes this small descrepancy? From:

Parameter Relative Along-track Effect
----------------------------------------------- -----------------------------------
Solar particle wind 0.001
Galilean satellites -0.333
Galactic tide -0.833
Numerical integration error (128-bit vs. 64-bit) -1.000 (9900 km, 12 min)
Solar mass loss +1.333
Poynting-Robertson drag -2.333
Solar oblateness [ +4.08, +1.75]
Sun-barycenter relativistic shift +81.0 (inc. in nominal)
61 most perturbing "other" asteroids -144
Planetary mass uncertainty [ +132, -156]
Solar radiation pressure -1092
Yarkovsky effect [+1152, -6924]

I'm not quite sure what the numbers mean. But at least it gives a relative difference between the sources. I'm surprised that the Yarkovsky effect is the strongest.

Title: Re: Sources of error
Post by frankuitaalst on 05/05/07 at 02:05:25

I think they set the numerical integration (128 vs. 64) at 1.000 and defined the other errors relative to this error .
So the Yarowski may have an influence of 1000 ( haven't they omitted a . ? ) more than the numerical integration error .

Title: Re: Sources of error
Post by frankuitaalst on 05/05/07 at 04:56:25

Heres a link that gives more information about uncertainties . Haven't read it yet .
It's funny : the first time i got through . From this link here the acces is limited . I made a copy of a part of the content ...

Table 3. Trajectory propagation factors and their individual and combined effect on our prediction of the along-track position of 1950 DA, on 16.0 March 2880, just before the time of nominal orbit intersection with Earth. Differences are expressed relative to the reference trajectory. Bracketed quantities indicate the bounding value found by varying the parameter over the intervals described in the text.


Trajectory propagation factor Along-track effect

Distance (km) Time


(A) Galactic tide  8400  10 min
(B) Numerical integration error  9900  12 min
(C) Solar mass loss +13300 +16 min
(D) Solar oblateness (J2) (+42100, +17600) (+49, +21) min
(E) 61 additional asteroids  1.5 106  1.2 days
(F) Planetary mass uncertainty (+1.38, 1.54) 106 (+1.1, 1.3) days
(G) Solar radiation pressure  11.2 106  9.1 days
Combined (A-G) (11.0, 17.6) 106 (9.0, 14.3) days
Yarkovsky effect only (+11.9, 71.0) 106 (+9.6, 57.7) days

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