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Just a few hours ago the moon-bound spacecraft Chandrayaan-3 was launched.

While it will orbit Earth for a few days, it is accelerating/changing its orbit often to prepare for the transfer to a lunar orbit, so its coordinates (especially from a specific location on Earth's surface) are very unpredictable.

Neither an orbital element approach nor TLEs will work here reliably unless they are updated very frequently (the latter only seem to work for earth-orbiting satellites anyway).

In the future, there will probably exist more moon-orbiting spacecraft like the Lunar Gateway which will also change its orbit often. Does a publicly accessible website/API exist that provides the current coordinates for such objects?

In this case it seems ESA's Estrack network is supporting the tracking of this probe, but it doesn't seem like they have a public API: https://www.esa.int/Enabling_Support/Operations/ESA_ground_stations_support_Chandrayaan-3_Moon_mission

Edit: Permalink to the code I adapted from PM 2Ring below, to color observed orbit segments

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    $\begingroup$ JPL have a pre-launch planning trajectory ssd.jpl.nasa.gov/api/… Let me see what it looks like... $\endgroup$
    – PM 2Ring
    Jul 14 at 15:10
  • $\begingroup$ NASA also sometimes publishes SPICE kernels with the trajectory. $\endgroup$
    – Greg Miller
    Jul 14 at 15:50
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    $\begingroup$ Chandrayaan-3 has a NORAD ID: 57320 and you can track the live location of it here n2yo.com/?s=57320&live=1 $\endgroup$
    – Dima Chubarov
    Jul 15 at 15:31
  • $\begingroup$ @DimaChubarov This doesn't seem to match up with the JPL Horizons data - with which I apparently just managed to image it - what is their data source? $\endgroup$
    – 2080
    Jul 16 at 11:12
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    $\begingroup$ Hmmm. I don't think TLE's will work here at least in the long term because they are only intended for Earth-orbiting spacecraft. Also, since it is often accelerating to raise its orbit, the TLE is probably out of date because of this $\endgroup$
    – 2080
    Jul 16 at 13:28

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Does a publicly accessible website/API exist that provides the current coordinates for such objects?

Yes! There's a pre-launch planning trajectory from ISRO/JPLNAV in the Horizons system. Chandrayaan-3 has ID number -158. It's classed as a major body, so we can use it as an observation centre, not just a target. There's some info here.

This preliminary trajectory covers from 2023-Jul-14 09:23 to 2023-Sep-13 09:00. The data on Horizons will be updated as the mission proceeds, but not in real time.

Here's a view looking from above (north) of the ecliptic plane, from 2023-Jul-15 0:00 UTC, using a 1 hour time step. Earth is blue, the Moon is yellow, the spacecraft is red. The grey line is the X axis, which points towards the First Point of Aries (the equinox point). The plotted points are connected with cubic Bézier curves, using the normalised velocity vectors to compute Bézier control points. 

Earth, Moon, Chandrayaan-3

This trajectory has a significant component in the north-south axis:

Side-on view showing N-S component

These are screenshots from this interactive 3D plot. There's some info on how to use that plotting script here.

Note that you can set the Moon (ID 301) as the center. I recommend a start time of Aug-10, and you should probably toggle off the curve plotting.

FWIW, here's a query URL which returns the position & velocity vectors (in the J2000.0 ecliptic frame), using a 1 day time step.

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    $\begingroup$ @uhoh Ah, right. :) BTW, vector tables use TDB by default, but you can put UTC or TT after the start time to request a different time scale. $\endgroup$
    – PM 2Ring
    Jul 15 at 3:55
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    $\begingroup$ Thanks to you, we now have this: youtube.com/watch?v=F7LAFiUXLMo :) $\endgroup$
    – 2080
    Jul 16 at 12:36
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    $\begingroup$ Uploaded here: deeprandomsurvey.org/static/img/Chandrayaan-3.gif In the meantime I have found this SkyTrack software which can continuously track from JPL Horizons Ephemerides as well: heavenscape.com/videos.html $\endgroup$
    – 2080
    Jul 17 at 8:24
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    $\begingroup$ We observed it two more times, last just now on its lunar transfer trajectory: deeprandomsurvey.org - thank you very much for your answer and for the code that helps us visualize the orbits! $\endgroup$
    – 2080
    Aug 1 at 12:23
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    $\begingroup$ Here is my adapted code that colors a segment: sagecell.sagemath.org/?q=exuezf $\endgroup$
    – 2080
    Aug 1 at 12:25
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SPICE kernels are available for many NASA (and other missions). A large collection is available from NAIF. As well as some archived datasets. These can be processed using the SPICE toolkit, which is available for several programming languages directly from NAIF. Additional 3rd party libraries like SpiceyPy are also available.

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