## Friday, January 19, 2018

### Tisserand's Parameter

One topic that comes up frequently in orbital dynamics is the Tisserand parameter. So as an interested layman, I'm curious about it, and have several questions about it, like "what is the Tisserand parameter?" or "how is it useful?". Well, first, here is it's definition:

${T}_{p}=\frac{{a}_{p}}{a}+2\sqrt{\frac{a}{{a}_{p}}\left(1-{e}^{2}\right)}cosi$

As you can see, it relates the orbital parameters semimajor axis a, eccentricity e and inclination i of a perturbed body (i.e. a small body encountering a larger body) to each other and to the semimajor axis of the perturber ap, like, say, Jupiter, or any larger body in the Solar System. The result is the dimensionless value called the Tisserand parameter Tp, or Tisserand's criterion.

The nice thing about it is that it is a quasi-conserved quantity that stays more or less the same before and after a close encounter of an asteroid, a comet or a space probe with a large body. That makes it a useful tool to identify prior visits of periodic comets, whose orbital parameters may have changed in the mean time, but since the Tiserand parameter stays about the same, old observations can be searched for a similar value.

Another use is the shaping of spacecraft trajectories, since each of the orbital parameters changes through a flyby in a predictable way. It is in fact this property of the Tisserand parameter that made achievements like the Voyager's Grand Tour or Cassini's epic tour of the Saturn system, possible. The former through flybys of all the giant planets, the latter case through regular flybys of Saturn's largest moon Titan.

OK, that's what it does, but I had a hard time visualizing how it behaves for each of the parameters. So I made the formula interactive:

As you can see, the graph lets you select each parameter a, e, and i separately, and chose a value for the other two. Select any kind of trajectory and see how it's Tisserand parameter changes relative to each of the outer planets, which are represented by a red circle. The currently selected parameters are indicated in the resulting formula at the lower right.

For asteroids the value relative to Jupiter is normally Tj < 3 and for comets within 2 < Tj < 3. If you select semimajor axis, you'll see that Tj only gets close to these values if the bodies' orbit goes anywhere close to Jupiter, and if you plat areound with e or i, the higher you chose them /(i.e. more comet-like) the lower Tj gets.

Maybe this helps somebody else as well.

Check out the source code on GitHub

## Sunday, January 14, 2018

### New IAU Star Names for D3-Celestial

As the IAU has recently approved a lot of official star names, so I updated d3-celestial to reflect these. Some are comletely new, others now have an officially approved spelling. I changed all those I previously spelled differently.

Here are those that have completely new names I didn't have before:

Name         Designation  ID    Con #    Vmag    HIP#    HD#  RA(J2000) Dec(J2000)
Alkarab      HR 8905      ups   Peg -    4.42  115623 220657 351.344931  23.404100
Athebyne     HR 6132      eta   Dra A    2.73   80331 148387 245.997858  61.514214
Beemim       HR 1393      ups03 Eri -    3.97   20535  28028  66.009239 -34.016848
Brachium     HR 5603      sig   Lib A    3.25   73714 133216 226.017567 -25.281961
Castula      HR 265       ups02 Cas -    4.62    4422   5395  14.166271  59.181055
Chamukuy     HR 1412      tet02 Tau Aa   3.73   20894  28319  67.165586  15.870882
Dalim        HR 963       alf   For A    3.86   14879  20010  48.018864 -28.987620
Fang         HR 5944      pi    Sco Aa   2.89   78265 143018 239.712972 -26.114108
Fulu         HR 153       zet   Cas -    3.69    2920   3360   9.242851  53.896908
Fuyue        HR 6630      -     Sco -    3.19   87261 161892 267.464503 -37.043305
Ginan        HR 4700      eps   Cru -    3.59   60260 107446 185.340039 -60.401147
Iklil        HR 5928      rho   Sco Aa   3.87   78104 142669 239.221151 -29.214073
Jishui       HR 2930      omi   Gem -    4.89   37265  61110 114.791387  34.584346
Kang         HR 5315      kap   Vir -    4.18   69427 124294 213.223939 -10.273704
Larawag      HR 6241      eps   Sco -    2.29   82396 151680 252.540878 -34.293232
Lilii Borea  HR 824       39    Ari -    4.52   13061  17361  41.977256  29.247115
Mahasim      HR 2095      tet   Aur A    2.65   28380  40312  89.930292  37.212585
Nembus       HR 464       51    And -    3.59    7607   9927  24.498154  48.628214
Pipirima     HR 6252      mu02  Sco A    3.56   82545 151985 253.083939 -38.017535
Revati       HR 361       zet   Psc A    5.21    5737   7344  18.432864   7.575354
Saclateni    HR 1612      zet   Aur A    3.69   23453  32068  75.619531  41.075839
Taiyangshou  HR 4518      chi   UMa -    3.69   57399 102224 176.512559  47.779406
Tianguan     HR 1910      zet   Tau A    2.97   26451  37202  84.411189  21.142544
Tiaki        HR 8636      bet   Gru -    2.12  112122 214952 340.666876 -46.884576
Tianyi       HR 4863      7     Dra -    5.43   62423 111335 191.893099  66.790305
Unurgunite   HR 2646      sig   CMa -    3.49   33856  52877 105.429782 -27.934830
Wurren       HR 338       zet   Phe Aa   4.02    5348   6882  17.096173 -55.245758
Xamidimura   HR 6247      mu01  Sco Aa   3.00   82514 151890 252.967630 -38.047380
Xuange       HR 5351      lam   Boo -    4.18   69732 125162 214.095912  46.088306
Zhang        HR 3903      ups01 Hya A    4.11   48356  85444 147.869558 -14.846603


See some more d3-celestial examples here, play with it here or check out the documentation and/or fork/download the source from the GitHub repository.

## Thursday, January 4, 2018

### Planetary Elongation 2018

All the planetary elongations from the Sun for this year, plus eclipses, full moons and solar transits, in one graph.

## Monday, January 1, 2018

### Space Observatories Update 01/2018

There were no new missions launched but with several telescopes entering planning and the usual delays it is time for an update to the Space Observatories page. Especially in the X-ray range the new appeaances in the list are IXPE, the Imaging X-Ray Polarimetry Explorer by NASA, the Indian XPoSat or X-ray Polariation Satellite, and the follow.on reimplementation of the Japanese ASTRO-H mission, ASTRO-H2 or XARM (X-ray Astronomy Recovery Mission)

The source data are now available on my space exploration history github repository, together with the included infographics.

## Sunday, December 31, 2017

### Solar System Missions Update 01/2018

Here's my map of all active and future Solar System Missions as of January 1st 2018.

I know somebody is going to try to throw a car at Mars, but sorry, that dosn't count as "Space Eploration" in my book.

Data, images and documentation are available on my space exploration history GitHub repository and the associated website.

## Thursday, November 30, 2017

### Solar System Missions Update 12/2017

Here's my map of all active and future Solar System Missions as of December 1st 2017.

No changes again this time apart from those mandated by the never ending dance of gravity...

Data, images and documentation are available on my space exploration history GitHub repository and the associated website.

## Tuesday, October 31, 2017

### Solar System Missions Update 11/2017

Here's my map of all active and future Solar System Missions as of November 1st 2017.

No changes this time apart from those mandated by the never ending dance of gravity...

Data, images and documentation are available on my space exploration history GitHub repository and the associated website.