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Comets Halley and Hale-BoppAsteroid Trajectories

Comet Shoemaker-Levy 9

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Collision with Jupiter July 16-22, 1994

[Artist impression above by David Seal, JPL]

Between 16 and 22 July 1994 comet P/Shoemaker-Levy 9 collided with Jupiter. On the comet's previous pass around Jupiter in July, 1992 it came so close that it moved within the Roche limit and subsequently shattered into many fragments. Those fragments, numbering 21 major bodies, range in size between 1 to 5 kilometres and all eventually impacted on Jupiter. This was the first major collision between any two solar system bodies that has ever been predicted in advance. Seven spacecraft and a large proportion of Earth-based observatories watched the events, both before and after they occurred.

The 21 fragments are labeled A through W, and they all impacted on Jupiter at a point just out of direct view of Earth, but near the edge on the far side of Jupiter. Within 10 or 15 minutes after impact, however, the impact region rotated into view of Earth.

In this notebook I have produced a simple animation to illustrate the K=12 impact. The animation was produced using the Scientific Astronomer package for Mathematica, and it will give you an idea of the timescale of the impact, and also things to look out for during the event. With good binoculars you can see the four Galilean moons orbiting Jupiter, and with a good telescope you can see the cloud features on Jupiter including the Great Red Spot.

Impact Times

Impact times have been calculated in advance by Paul Chodas et al. There is still some uncertainly in the precise times, so a colunm of uncertainty is also given. In general the smaller the uncertainty, the bigger the fragment.

-----------------------------------------------

Fragment Impact Uncert- Jovian Angle

Date/Time ainty Latitide E-J-F

July (UT) (min) (deg) (deg)

---------------h--m--s-------------------------

A = 21 16 19:59:40 5.5 -43.08 99.04

B = 20 17 02:54:13 4.1 -43.04 99.40

C = 19 17 07:02:14 3.7 -43.22 98.42

D = 18 17 11:47:00 4.7 -43.45 98.08

E = 17 17 15:05:31 3.1 -43.42 97.72

F = 16 18 00:29:21 4.0 -43.52 98.61

G = 15 18 07:28:32 3.1 -43.58 97.09

H = 14 18 19:25:53 3.1 -43.70 96.86

K = 12 19 10:18:32 3.1 -43.77 96.21

L = 11 19 22:08:53 3.4 -43.88 95.93

N = 9 20 10:20:02 4.9 -44.19 96.09

P2= 8b 20 15:11:55 4.6 -44.51 97.01

Q2= 7b 20 19:31:43 -44.31 95.32

Q1= 7a 20 19:59:10 4.5 -44.02 95.07

R = 6 21 05:25:56 4.6 -44.05 95.06

S = 5 21 15:10:22 4.4 -44.13 94.73

T = 4 21 18:03:45 11.5 -44.99 96.23

U = 3 21 21:48:30 12.8 -44.47 95.41

V = 2 22 04:16:53 8.1 -44.31 95.60

W = 1 22 07:57:36 5.2 -44.17 94.36

-----------------------------------------------

In the table the angle E-J-F is the Earth-Jupiter-Fragment angle at impact. Values greater than 90? indicate a farside impact. All impacts will be just on the farside as viewed from Earth, but later impacts will be closer to the limb. Each impact will however rotate into sight of Earth after about 15 minutes though.

The labelling system looks a bit chaotic because the letters I and O were never used, and also because the J and M fragments have faded from view. The initially named P and Q fragments have also subsequently split into two smaller fragments each.

Earth Viewpoint

The K=12 impact occurs at about 1994 July 19 10:18:00 (Universal Time), which in Mathematica Date notation could be written as {1994,7,19,10+TimeZone[],18,0}. This is equivlavent to 8:18pm Melbourne time (Melbourne, Australia is 10 hours ahead of GMT or Universal Time).

SetLocation[GeoLongitudeRule145. Degree,
GeoLatitudeRule-37.8 Degree,
TimeZoneRule10];

Using the function PlanetPlot3D, we can see a view of Earth as seen from Jupiter during the K=12 impact:

PlanetPlot3D[Earth,
{1994,7,19,10+10,18,0},
ViewPointRuleJupiter];

The image shows that Australia is best placed to view the event because not only is it facing Jupiter during the K=12 impact, but also because it is in darkness at that time. Local sunset occurs at the following time.

SunSet[{1994,7,19}]

which is about 5:20pm. It is winter in Melbourne during July, hence the Sun sets early.

From Melbourne, at the time of the K=12 impact, Jupiter will be well placed in the sky.

HorizonCoordinates[Jupiter,
{1994,7,19,10+10,18,0}]

The above says that Jupiter will be about 57? above the horizon at 8:18pm. What's more the position of the Moon will not be too close.

Separation[Jupiter, Moon,
{1994,7,19,10+10,18,0}]

Although the next full moon will be four days away:

FullMoon[{1994,7,19}]

so the Moon will be quite bright.

The K=12 impact has one special property. It will accur when the moon Europa is visible from Earth, but eclipsed from the Sun. A reflected flash might therefore be visible. Of the 21 impacts it is the only one that is certain to happen during a Jovian lunar eclipse.

Comet Impact Animation

To produce an animation of the K=12 impact I have used the standard PlanetPlot3D function to show a graphic of Jupiter along with its moons and cloud features (the Great Red Spot and the three lesser known White Spots). Labeling and comet trajectory were added as an after thought by using the Epilog option. Additional options such as PlotRange and PlotRegion were used to get a slightly bigger field of view centred just to the left of Jupiter where all the impacts occur.

So here is the animation of Jupiter, with a frame every 15 minutes, from 6pm on 1994 July 19 until 4am the next morning (Melbourne time):

Do[PlanetPlot3D[Jupiter,
{1994,7,19,10+10,15+m,0},
ViewPointRuleEarth,
PlotRangeRule{{-1,1},{-1,1},
{-1,1}} 72000 3.,
PlotRegionRule{{-0.5,2},{-1,2}},
EpilogRuleannotate[m]],
{m,-135,450,15}]

The position of the Great Red Spot and also the three lesser known White Spots are shown correctly. The two moons visible during the animation are Io and Europa. Both are shown as green dots, but Europa is the dot appearing from behind Jupiter. Due to the Sun being at an angle - slightly towards the right but behind the viewpoint above - the moon Europa will be in eclipse (and shaded as a darker green in the graphic) for about two hours or so. During that eclipse the K=12 impact will occur. Later the shadow of Io can be seen passing across the Jovian disk. In the animation the blue comet trajectory line, as well as the blue impact dots were added with the Epilog option. Local clock time is shown with white text, which was also added with the Epilog option.

At the time of impact, I have used yellow lines to indicate the flash that will occur. In the first version of this animation I used a Rectangle[mins, maxs, soundgraphic] function to generate a crashing sound when the impact frame appeared - but this got annoying after a while so I took it out.

Finally the reason I chose the duration of the animation to be 10 hours, was that the Great Red Spot approximately repeats one full revolution around Jupiter in that time, and so if you run the animation in a loop it will appear to repeat without a glitch.

Here's the definition of annotate[m_] as passed to Epilog

Based on some orbital elements I found for the Q=7 fragment of the comet, I was able to add a new object to the package:

SetOrbitalElements[Q, ViewPoint -> Jupiter, Date -> {1994, 7, 15, 10, 0, 0},
OrbitalMeanMotion -> Revs/(930.*Day),
OrbitalSemiMajorAxis ->
(34776.7*AU)/((1 - 0.9987338)*149579000),
OrbitalEccentricity -> 0.9987338,
OrbitalInclination -> 94.2333*Degree,
MeanLongitude -> (43.47999 - (360*(20.7846 - 15))/930.)*Degree,
PerigeeLongitude -> 43.47999*Degree,
AscendingLongitude -> (290.8745 + 55.1908)*Degree];

From the above elements I worked out the final impact trajectory and hence found the comet's position relative to Jupiter in 5 minute intervals to be:

comet={{0.451195,0.269150},{0.450219,0.283792},{0.448266,0.298433},{0.445338,0.314051},{0.443386,0.329669},{0.44241,0.346263},{0.441434,0.362856},{0.440457,0.381402},{0.440457,0.400925},{0.440457,0.420447}};

I then used the above to add the blue annotations to the PlanetPlot3D animation.

annotate[m_] :=
Block[{d, h, m0 = (10 + 10)*60 + 15 + m},
d = Floor[m0/(60*24)]; h = Floor[1/60*(m0 - 24*60*d)];
m0 = Floor[m0 - 24*60*d - 60*h];
{{RGBColor[0, 0, 1], Thickness[0], Line[comet], PointSize[0.01],
Which[m == 0, {RGBColor[1, 1, 0], Line[{{0.425, 0.44}, {0.4, 0.44}}],
Line[{{0.435, 0.432}, {0.42, 0.412}}],
Line[{{0.446, 0.42}, {0.45, 0.4}}]},
Inequality[-50, LessEqual, m, Less, 0], Point[comet[[m/5]]],
300 > m > 10, Point[{0.5 - 0.07*Cos[0.01*(m + 10)], 0.437}], True, {}]
}, {GrayLevel[1], Text["K=12 Impact", {0.4, 0.7}]},
{GrayLevel[1], Text[{1994, 7, 19 + d, PaddedForm[h, 2],
PaddedForm[m0, 2], 0}, {0.4, 0.67}]}}]

Galilean Moons

During the period over which the comet fragments will impact, the inner moons of Jupiter will make several orbits. The following chart shows the position of the four Galilean moons during the period July 17 until July 23. Time is shown down the right side, and is measured in hours after local midnight Melbourne time.

JupiterMoonChart[{1994,7,17},
{1994,7,23}];

The black, red, green and blue lines represent the positions, as seen from Earth, of the Galilean moons Io, Europa, Ganymede and Callisto respectively. And the white line wrapping round the purple coloured Jovian disk represents the position of the Great Red Spot.

Comets Halley and Hale-BoppAsteroid Trajectories



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