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Guessing the Chang’e-3 trajectory [Where is Chang'e-3 now]

Our Chinese colleagues launched a lander to the Moon on December first, but unfortunately they have chosen not to publicly share where their spacecraft is.  A few days ago there were several TLEs in Spacetrack associated with the Chang’e 3 launch, all of which didn’t appear to be associated with it at first glance (wrong plane, etc.) .  So, given we don’t have any real ephemeris available, let’s see if we can create a reasonable guess on our own with a bit of Astrodynamics detective work.

First, let’s start off with some information we do know from their live broadcast.

We know the launch time: 1 Dec 2013 17:30 UTC.

We know the launch site is the LC2 Launch Complex at the Xichang Satellite Launch Center (XSLC).  I have 28.2455 deg N Latitude, and 102.027 E Longitude for that site.

Next question is, what direction do they launch, and to what altitude?

Robert Christy’s excellent site Zarya.info provides us with a decent first guess here:

Chang’e 3 Launch Events

Robert did a lot of our work for us by nailing the separation events, and approximate latitude and longitude positions of events based on the video stream.  It may seem rough to try to calculate a trajectory from this information, but actually it tells us quite a bit.  We know the launch site, and we know the approximate perigee altitude of the transfer trajectory (~210 km) .  We also have a pretty good idea of the TLI time: 6 Dec 2013 09:30 UTC from a tweet by Robert Christie (@Zarya_Info) and we know the landing site from the same source.  So let’s make a few simplifications:

Impulsive maneuvers.  I’m going to use these for TLI and LOI for now, just because I’m lazy and don’t feel like digging out the parameters of the spacecraft (and it makes my setup a bit more complicated).

From Robert’s link about, I can eyeball the center of TLI at about 17:45:36 UTC on Dec 1, 2013.  That’s where I’m going to put my TLI.  I don’t know the exact launch azimuth they flew, so I’m going to guess 97.5 and then let it float a bit (i.e. use the burnout Lat, Lon and Alt as controls).  I don’t know their exact burnout altitude, so I’m going to guess 210.  Normally I’d know all of this stuff exactly.  If I were planning the mission (as I did on LADEE) I knew my launch site, azimuth etc. and the exact burnout state of the Mintoaur V.  I could figure out from this what my launch time ought to be, and when TLI was etc.  In this case, I’m having to guess things from parameters I DO know. It’s  detective work, but my peers in China have to work with the same physics and math as me, so it’s going to be pretty close.

So I have to fix the launch time and the TLI time, let the burnout conditions float a bit for my controls, and then vary my TLI Delta-V to hit an LOI at the proper time and get into the proper orbit (I’m going to use a 100 km altitude, 90 deg inclination orbit).

So what does that give us?

First off, it makes our launch ground track look like this:

 

Estimated Chang'e 3 Ground track (click to zoom)

Estimated Chang’e 3 Ground track (click to zoom)

 

TLI occurs at the end of the yellow segment, burnout of stage 2 at the end of the red segment.

So assuming a 90 deg inclination, 100 km altitude insertion (impulsive still) on 6 Dec 2013 9:30 UTC, we get a trajectory that looks like this:

 

Earth-Centered View, C-3 at 5 Dec 2013 17:32 UTC (Click to zoom)

Earth-Centered View, C-3 at 5 Dec 2013 17:32 UTC (Click to zoom)

 

Earth-Centered View, C-3 at 5 Dec 2013 17:32 UTC (Click to zoom)

Earth-Centered View, C-3 at 5 Dec 2013 17:32 UTC (Click to zoom)

 

This gives us a good idea where C-3 is now, but what does the rest of the trajectory look like?  First let’s look at the LOI geometry.

 

Chang'e 3 LOI Geometry (Click to zoom)

Chang’e 3 LOI Geometry (Click to zoom)

 

Note that with a 5 day transfer(4.8 really, 116 hrs) the approach to the Moon comes from the side, with respect to the Earth.  This is a nice geometry for visibility at LOI, especially for a polar orbit, because it lets the LOI burn happen in full view of the ground.   With equatorial spacecraft (LADEE) getting the LOI in view of the Earth can require a bit more work.  It’s not a great geometry for watching the maneuver, given that there won’t be much radial-rate component, but it’ll do.

Now let’s take a closer look at the Earth to see what is visible.

 

View of Earth at LOI (click to zoom)

View of Earth from Moon at LOI (click to zoom)

 

Without digging up the locations of the ground stations, it’s pretty clear that major portions of China are visible, as is Australia.  Since we know Chang’e 3 is using some ESA stations, this is set up for a multiple ground stations to see LOI.  Nice geometry for Orbit determination and real-time tracking of the event.

After one rev in Lunar orbit, we can see what the orbit looks like here:

 

Lunar Orbit 1 Rev past LOI (click to zoom)

Lunar Orbit 1 Rev past LOI (click to zoom)

 

The next question is, how does this set us up for landing?  We have approximated the landing site at the Sinus Iridum region, with a Lunar Latitude of 43 deg N, and a Lunar Longitude of 31 Deg W.  Note the lighting of that site at LOI:

 

Sinus Iridum landing site lighting at LOI (click to zoom)

Sinus Iridum landing site lighting at LOI (click to zoom)

 

Let’s look at the first day’s worth of ground tracks on the Moon, which will help us see what we’re waiting for, both in terms of lighting and geometry:

 

Chang'e 3 Ground track 1 day after LOI (click to zoom)

Chang’e 3 Ground track 1 day after LOI (click to zoom)

 

Note that the light blue line shows the incoming trajectory and the subsequent lines show the progression of ground tracks (which move from right to left).  Further note that part of our ground track is in shadow (blue) as is the landing site, and part is in sunlight.  Obviously, for landing we’d like sunlight both on the site and on our ground track.  Here are the tracks a day later:

 

Chang'e 3 Ground track 2 days after LOI (click to zoom)

Chang’e 3 Ground track 2 days after LOI (click to zoom)

 

Our sunlit ground track on the right is moving closer to the landing site, and the shadow is drifting in the right direction as well.  The trick here is to just wait in orbit while the Moon rotates under us.  Looking at this in 3D gives a better geometrical perspective:

 

Chang'e 3 landing site and shadow geometry 2 days after LOI (click to zoom)

Chang’e 3 landing site and shadow geometry 2 days after LOI (click to zoom)

 

The orbit is pretty much fixed in inertial space, and we just have to wait while the Moon rotates.  If we wait until Dec 15th we get this:

 

Dec 15 Lunar Ground Tracks (click to zoom)

Dec 15 Lunar Ground Tracks (click to zoom)

Dec 15 Lunar Ground Tracks Zoomed (click to zoom)

Dec 15 Lunar Ground Tracks Zoomed (click to zoom)

 

 

 

 

 

 

 

At this point we’ve all but gotten lined up with the landing site, and it’s time to start the descent.  Now we have to do a bit of guessing.  We know that the descent profile goes from a 100 km circular orbit to a 100 x 15 km orbit (altitudes).  We know that the vehicle lowers to periselene and then lowers from there.  We’re going to assume that we won’t go a full rev in the 100 x 15 km orbit, but will instead just execute one half rev and descend.  If so, it looks like this:

 

Descent Orbit Initiation to Peri (click to zoom)

Descent Orbit Initiation to Peri (click to zoom)

 

It’s hard to show on this scale, but if you zoom and look closely at the left, you can see the orbit starts at 100 km (yellow) and then descends to 15 km on the right.  Let’s look from the landing site perspective.  Note we can see the approach hyperbola still (blue) the 100 km parking orbit (yellow) and the spacecraft at Periapsis just peeking over the limb at the top.  You can see that the parking orbit isn’t completely locked inertially, it’s got a bit of drift in it from the Lunar gravity field.

 

Descent to Periapsis from Landing Site (click to zoom)

Descent to Periapsis from Landing Site (click to zoom)

 

Now I have to really fake it.  According to the superb site Spaceflight101, the landing engine actively throttles all the way down:

 

Spaceflight101 Chang’e 3 Flight description

 

While I can model an engine that throttles, it’s way too much work (if I was working on the mission, I’d have the lander controls people do this) so I’m going to fake it with 2 constant thrust finite burns and a coast segment.  I won’t bother trying to get masses and engine masses right either, I just want to show the basic idea:

C-3 Landing

C-3 Landing (click to zoom)

 

Of course the real profile won’t be exactly like this, but this is a reasonable facsimile.  Let’s check out the geometry with respect to the Earth:

 

Earth Vector at Landing (click to zoom)

Earth Vector at Landing (click to zoom)

 

And finally let’s see what’s visible from Earth at the landing time:

 

View of Earth from Moon at Landing time

View of Earth from Moon at Landing time

 

Which looks pretty darn good if you want to get coverage from Chinese ground stations.  (Note: I lit the Earth up a bit in this picture to show what was visible, but this half of the Earth is in darkness at the landing.)

Pretty fun stuff.  We welcome any updates, if anyone has better data than we do, it’s real easy to change the assumptions and re-run.

-Astrogator_Mike

 

  • Jonathan McDowell

    Nice, but what actual numbers did you end up with for the TLI conditions? I haven’t done the proper job you have to match to a lunar arrival, I just used the quoted 380000 km apogee and boosted from the usual 190 km 29 deg Long March 3 parking orbit, with an impulsive burn at 1745 UTC over 145E 15N at inertial azimuth 115.0 deg to a MECO-2 Vi = 10.924 km/s. Would be interested to see your estimate and work up a TLE!

  • http://www.astrogatorsguild.com/ Astrogator_mike

    My TLI orbit is 192 x 369362 km with an inclination of 28.5. My TLI occurs at 1 Dec 2013 17:45:36.100, but this is just a midpoint from the Zarya site’s report of the start and stop of that burn. My Latitude is: 11.34 deg N, Longitude is 152.74 deg. Inertial Az is 116.36 deg. MECO Vi = 10.908 km/sec. I totally eyeballed the burnout state, and it sounds like your numbers are a bit better than that being based on previous launches. I’m also targeting a LOI state at the Moon that I’m not sure of. While the 100 km altitude is right, I don’t know what the inclination is. Everything I’ve seen says “Polar” which I’ve assumed is 90 deg, but it’s likely not exactly 90 (and this affects everything). If I knew the inclination (the inclination of Chang’e 2 might give us a clue), we could nail it down even better. When I look at trying to land on the 14th (the currently official landing day) I can’t hit that unless I change the inclination. It’s all a matter of getting the ground track to fly over the site, and if I change the lunar inclination to 82 deg or so, I can start to get the ground track over the site on the 14th.

  • Jonathan McDowell

    Thanks – my attempt to extrapolate from CZ-3 comsat launches may be pretyt inaccurate too. I’ll take a look at your model and compare when I get a chance.
    The quoted numbers from a Chinese source were 210.3 x 389109.2 km x 28.5
    but of course it’s not clear what Earth model those altitudes are relative to, or whether
    that is osculating els or whatever. I agree it’s not clear what the real LOI inclination is
    and I doubt we’ll be told even after the event, so your results are very interesting!

  • http://www.astrogatorsguild.com/ Astrogator_mike

    I’m trying to locate the inclination for Chang’e 2. I’m guessing that this mission is flying a very similar trajectory, based on what they’ve said so far. If so, they may break LOI up into 3 capture burns, which would also affect the ground track.

  • Jonathan McDowell

    My notes claim that the end-of-primary mission orbit was 100 x 100 km x 86 deg
    on 2011 Apr 1. The LOI was to a 119 x 8599 km orbit; LOI-2 changed inclination by 3.2 degrees (from what to what I dunno). I don’t have the technology to figure out how the inclination might have changed between 2010 Oct and 2011 Apr.

  • reddog694uk .

    We don’t need to know where it is, we need to be able to access the images it sends back to earth, get to work geeks !