I Dawn dead in Ceres orbit, ran out of fuel Oct 2018

[mfb]

16:21 UTC, 14 hours or 5/3 orbits later, Dawn will cross the equator soon (going south, extrapolated from your post). 645.1 km, close to the value it had over the south pole. 528 mph or 236m/s.

 

[marcus]

Thanks for making a projection, did you notice how closely it turned out? If it was right, it represented progress. Altitude over the equator is a rough estimator of the average altitude, in the simplified picture I have in mind. Currently altitude over the equator is about 640 km.

I see Earth (the tiny dot in the box over Ceres' northwest horizon) and Orion's belt to the southeast.
I suppose in about 4 hours---5pm pacific on 19 Nov, or 1 h UTC on 20 Nov---Dawn will be crossing equator going south on the day side. By then the average alt. should be slightly less than 640. This is all just guesses and rough estimates, but seems to be working out for now, more or less.

Getting to be time to re-calculate the approximate orbital period, though. It keeps shrinking. : ^)

 

[mfb]

640.93 km, halfway on the way to the equator as of 0:08 UTC. Dawn stopped thrusting.
527 mph or 235.6 m/s.

 

[marcus]

I was away from computer and didn't check but just now 1:21 UTC simview said 633 km. Dawn was shown bit less than halfway from equator to S pole.
We could split the difference and guess it was about (641+633)/2 = 636 when it crossed equator
So that would be our new guess as to the average altitude.
average radius of Ceres 473 km
mass 938e18 kg
average altitude about 636 km today
so orbit radius currently about 1109 km
2 pi ((1109 km)^3/(G*938e18 kg))^(1/2) gives 8.15 hours for the new orbital period.

Update: crossing equator northwards at 5 h UTC (or 9pm pacific 19 Nov) with altitude given as 639 km.
Engine still off. Roughly onsistent with what mfb said which suggested the southward crossing was around 1 h UTC, or 4 hours earlier at much the same altitude (because the ion engine was off--average alt. shouldn't change). DSN shows Canberra antenna #43 talking with Dawn.

Update: Simview 20 Nov 17:18 UTC shows Dawn crossing equator southwards at altitude 629 km and speed 238 m/s

 

[marcus]

Rayman update:
==quote==

November 20, 2015 -Dawn Reaching Ever Closer to Ceres

Dawn's average altitude today is about ... (635 kilometers). The spaceship is orbiting Ceres at ...[237 m/s]

Once a week during its spiral descent, Dawn stops ion thrusting so it can point its main antenna at Earth. When it did so on Nov. 19, the JPL flight team transmitted the latest flight plan, which incorporated updates using the navigation data collected one week earlier. (See the Nov. 13 status update.)
==endquote==

as of 19 h UTC simview Dawn is passing over S pole at altitude 618 km
Update: now crossing S pole again, alt. 611 km 21 Nov 3 h UTC, speed put at 240 m/s

So orbital period is currently about 8 hours, as we thought.

Update: later I happened to see simview for 21 Nov 6:50 hours, altitude given was 628 km

 

[marcus]

Simview for 21 November 15:47 hours UTC showed Dawn just having passed over N pole, at altitude 619 km.
N pole crossing is what I've been taking for apoapsis---this can change but seems to be working well so far at least as a rough approximation.
I'll hazard a guess that around 19:30 UTC it will show passage over S pole at about altitude 605 km.
Would be surprised if the probe doesn't get below altitude 600 km sometime on 22 November.
Update: Simview Dawn crossed equator on dayside at altitude 609 km, 21 Nov 17:30 UTC.
Altitude over equator has proven reasonable indicator of average altitude, for the time being.

average radius of Ceres 473 km
mass 938e18 kg
average altitude about 609 km today
so avg. orbit radius currently about 1082 km
2 pi ((1082 km)^3/(G*938e18 kg))^(1/2) gives 7.9 hours for the new orbital period.

Update: alt = 600 km as probe approaches S pole at 18:40 hours UTC.
My guess was wrong, off by 5 km. It was too conservative.

598.44 km at 19:30 hours UTC

Further update, at 22 Nov 1:15 hours UTC, altitude over dayside equator 602 km.
So avg. altitude for now is estimated at that 602 km.
Currently, it seems to go down about 6 km each time around.

 

[marcus]

Simview updates
Passing over S pole at alt. 579 km, on 22 Nov at 18:48 hours UTC
Crossing S pole with alt. 574 km, on 23 Nov at 02:34 hours UTC
Crossing N pole with alt. 588 km, on 23 Nov at 06:40 hours UTC

So the orbit period is still just bit less than 8 hours. The spread between lowest and highest altitude is about 15 km (?). The descent each time around tends to be around 5 km. Periapsis (closest approach) still seems coincide with passage over the S pole.

Crossing S pole with alt. 562 km, on 23 Nov at 17:42 hours UTC (note orb. period diminished slightly)
Crossing S pole with alt. 556 km, on 24 Nov at 1:03 hours UTC

 

[marcus]

Rayman (mission director) update:
==quote==

November 23, 2015 -Dawn's Maneuvering Proceeding Well

As Dawn continues to lower its orbit, today its average altitude is about ... (570 kilometers). At this height, each revolution around Ceres takes about 7.5 hours.
==endquote==
So Simview is still staying reasonably consistent with the less frequent real world updates from JPL.
E.g. he could have been talking about the S pole low point (periapsis) of 562 km, because the average alt. has tended to be about 7 or 8 km higher than the lowest. That would put the average right around 570 km, as per Rayman.

Simview "Crossing S pole with alt. 562 km, on 23 Nov at 17:42 hours UTC" is not too bad a match.

BTW at the moment I see Simview saying alt 547 km, Dawn recently having passed over S pole. (16:36 hours UTC on 24 Nov) Speed = 246 m/s

An interesting commentary on the efficiency of solar powered xenon ion drive, from the October 2015 Dawn Journal:
==quote==
In its eight years of interplanetary travels, the spacecraft has thrust for a total of 1,976 days, or 68 percent of the time ... While for most spacecraft , firing a thruster to change course is a special event, it is Dawn’s wont. All this thrusting has cost the spacecraft only...(396 kilograms) of its supply of xenon propellant, which was ... (425 kilograms) on Sep. 27, 2007. The spacecraft has used 66 of the 71 gallons (252 of the 270 liters) of xenon it carried when it rode its rocket from Earth into space.

The thrusting since then has achieved the equivalent of accelerating the probe by ...(39,200 kilometers per hour). ... Having accomplished 98 percent of the thrust time planned for its entire mission, Dawn has far exceeded the velocity change achieved by any other spacecraft under its own power. (For a comparison with probes that enter orbit around Mars, refer to this earlier log.) The principal ion thrusting that remains is to maneuver from the present orbit to the final one from late October to mid-December.
...
==endquote==

 

[marcus]

So there's less than 200 km more to descend, to reach the target 375 km altitude! Orbit radius will then be 473+375 = 848 km.
And orbit period will be 2 pi ((848 km)^3/(G*938e18 kg))^(1/2) or around 5.45 hours. Something to compare with Rayman's current figure of 7.5 hours : ^)

 

[anorlunda]

So there's less than 200 km more to descend, to reach the target 375 km altitude! Orbit radius will then be 473+375 = 848 km.
And orbit period will be 2 pi ((848 km)^3/(G*938e18 kg))^(1/2) or around 5.45 hours. Something to compare with Rayman's current figure of 7.5 hours : ^)

How elliptical is the orbit?

Thanks for sharing Marcus, this stuff is way cool.

 

[marcus]

How elliptical is the orbit? To make a rough guess, judging from Simview, I've noticed that periapsis and apoapsis seem to come while the spacecraft is crossing the S and N poles. and the difference seems to be around 14 or 15 km.

That can vary. The actual trajectory is an elliptical spiral, not a closed ellipse. I don't know the current ellipticity, just have a rough idea, and it can change. Final orbit (alt. ≈ 375 km) will be circular.

We could be using the polar radius of Ceres, rather than the average radius of 473 km. Out of laziness I just use 473. Easier to remember one number and not distinguish between polar and equatorial radii.
So r_a in km is about 473+altitude over N pole
and r_p in km is about 473+altitude over S pole

 

[marcus]

How elliptical is the orbit?

...

You can estimate the ellipticity by looking at http://neo.jpl.nasa.gov/orbits/fullview2.jpg
At the moment I see it showing altitude 540 km as of 24 Nov 22:42 hours. It has about 45 minutes UTC to reach the S pole. So we can come back at 23:30 UTC and see it over the pole. That will be 15:30 pacific, or 3:30 pm my time. So if I'm not busy I'll check back here and get the S pole altitude.
Then we just need the next N pole altitude and we can estimate the eccentricity.

S pole alt. tends to be the low point and N pole the high.

OK I happened to catch it going over S pole at 23:30 UTC on 24 Nov.

Altitude was 539 km.
To learn the ellipticity we need a similar reading at the N pole about 3 and 1/2 hours from now or about 7:30 pm pacific time (it's 4 pm my time)

 

[OmCheeto]

...
the difference seems to be around 14 or 15 km.
...

At least it's not as wobbly as it was this last May. It looks like it was >1000 km back then.

First posted on page 23, btw. Good god, this is a long thread!

 

[marcus]

You're right, on several counts That was the descent from initial "RC3" orbit to "survey" orbit.

Orbit    dates      altitude(km)  pixelsize(m) res/HST  period  soccerball at
RC3    April 23–May 9    (13,600)    (1,300)    24     15 days    (3.0 meters)
Survey    June 6-30      (4,400)      (410)     73     3.1 days    (1.0 meters)
HAMO    Aug 17–Oct 23    (1,470)      (140)     217    19 hours    (33 cm)
LAMO Dec 15–end of mission (375)      (35)      850    5.5 hours    (8.5 cm)

Also IIRC the descent from survey to HAMO was a lot more elliptical than the present trip from HAMO to LAMO. The current trajectory seems like a fairly trim orderly spiral. At least if we go by Simview (and it has proven reasonably reliable so far.)

Thanks for finding that wavy plot of the earlier descent.
=================
Anorlunda, it looks like 15 or 16 km is the current separation between lowest and highest altitudes. I just checked simview at 7:15 pm pacific and probe was approaching N pole at altitude 555 km. Remember the S pole altitude was 540 km---so the difference is 15 km.

Or more exactly the lower figure was 539, I rounded
So the two altitudes min and max were 539 and 555. And the difference was 16 km. That was for 24 Nov.

That, together with the average radius of the body, 473 km, should be enough to calculate a measure of the ellipticity or eccentricity---the departure from perfect circularity--rotational symmetry---of the spiral. I'm not sure what a good measure would be, you could make up one that seems to make sense and define it.
or use the conventional "e" number I posted earlier.

 

[marcus]

An update from Marc Rayman:
==quote==
November 25, 2015 -Dawn Making Good Progress to Lower Altitude

During this spiral descent from the third mapping orbit to the final one, Dawn has paused ion thrusting on Thursdays so JPL mission controllers can transmit an updated flight plan. To give the flight team time off for Thanksgiving, the operations schedule has an update today instead of tomorrow. So this afternoon Dawn will stop thrusting and rotate to point its main antenna to Earth.

The tireless explorer will not take the holiday off. It will spend Thanksgiving using its ion propulsion system to reduce its orbital altitude. It will be thankful that on Nov. 26, its average altitude will be ... (537 kilometers), so it will only have to lower its orbit by about ... (160 kilometers) more.
==endquote==

Going by Simview, for 24 Nov we had min and max altitudes 539 and 555 km, with average 547.
So the semi major axis, or average orbit radius was 473+547 = 1020 km.
2 pi ((1020 km)^3/(G*938e18 kg))^(1/2)
approximate orbit period= 7.2 hours.

Today, 25 Nov, at 18:00 hours UTC the probe passed over N pole with alt. 540 km. The speed indicated was 246 m/s. Thruster was still on. The fact that the thruster will be turned off (for navigation and communication) later today could change what we should expect. Peri and apo may have shifted.

Update, crossing S pole with alt. 524 km, so the spread is still 16 km. Average comes out 532 km.

 

[OmCheeto]

I knew I should not have started this latest project...

I title this graph; "How not to do science, unless you are REALLY dedicated enough to take measurements for more than 24 hours every 30 minutes..."

x-axis: hours since Nov 24 2332 utc
y-axis: altitude in km
black vertical bars: period

Conclusion: Science was much simpler, in the olden days, when it took Dawn two weeks to get around Ceres.

 

[marcus]

Heh heh,
to me it reads as a tongue-in-cheek comment on my own efforts the past few days.

 

[marcus]

DSN does not show any antenna talking with Dawn, as yet. Simview shows thruster off and Dawn oriented for communication. So I guess what Rayman was talking about as planned for today is in progress. Since we've turned a page I'll bring forward a couple of images that encapsulate what this is all about.

Because of its density (2 g/cc) Ceres is assumed to have a large component which is water, making it similar to a number of outer solar system bodies, but unique in the inner solar system. It's shape indicates some degree of differentiation---with a denser core and a less dense outer layer (mantel) covered by some type of crust. The outer mantel may be a rock+ice mixture---could vary in consistency---a 60%-40% mix was conjectured recently and reported by Lakdawalla. I don't know of a cutaway diagram for Ceres that reflects current thinking. The less oblate the more differentiated, and Ceres is comparatively UN-oblate.

The next image is a reminder of the analysis of surface chemistry (down to depth of one meter) that is planned for the final stage, starting in a little over 2 weeks. This involves neutron and gamma ray spectroscopy.

Optical and IR spectroscopy have already indicated some stuff about the surface material, reported at a recent conference (Lakdawalla's account). Ammonia-bearing clays.

Update: Now, 3:12 pm pacific, DSN shows Goldstone antenna #14 assigned to Dawn, but not transmitting or receiving yet. So that business is presumably just getting started.

I can't use the N and S pole crossing to estimate max and min altitudes now. They were good markers but the apsides have shifted. I'll try 30 degrees before you get to the N pole, for max, and 30 degrees before you get to S pole, for min.

 

[marcus]

...
I can't use the N and S pole crossing to estimate max and min altitudes now. They were good markers but the apsides have shifted. I'll try 30 degrees before you get to the N pole, for max, and 30 degrees before you get to S pole, for min.

That's right, apsides have shifted (could have something to do with shutting off thrust Wednesday for navigation etc.)
Altitude got a max (around 535 km) at some 30 degrees before getting to N pole. So I'm expecting min to come about 30 degrees before S pole.

 

[OmCheeto]

That's right, apsides have shifted (could have something to do with shutting off thrust Wednesday for navigation etc.)
Altitude got a max (around 535 km) at some 30 degrees before getting to N pole. So I'm expecting min to come about 30 degrees before S pole.

I should be in full relax, data collecting mode by 6 am tomorrow.
I'll see if I can't capture the new apsides.

But I'm off to dinner now.
Happy Thanksgiving, Marcus!

 

[marcus]

Happy Thanksgiving to you, Om! I was just helping in the kitchen---somehow the mashed potatoes were boiling over. Slowly and slurpily.

514 km at 60 degrees before S pole, (27Nov 0012?? UTC)
512.66 km at 45 degrees before S pole 27 Nov 0036 UTC

529 km at 90 degrees before N pole 27 Nov 0327 UTC
526 km at 30 degrees before N pole 27 Nov 0442 UTC507 km at 45 deg before S pole 27 Nov 0732 UTC
506.81 km at 30 deg before S pole 27 Nov 0759 UTC

 

[mfb]

509.26 at 16:07:28 UTC.
The coordinate system is in the shadow right now, but Dawn is at ~45 degrees after crossing the South pole.

 

[marcus]

Mfb, thanks for helping with this! A figure of 509 or 510 could be a reasonable estimate for the average altitude this time around.

I suspect that periapsis (min) is about 45 deg before S pole, and apoapsis (max) is about 45 deg before N pole. So that halfway between the apsides would be somewhere around 45 deg after crossing S pole. Or after crossing N pole (where the coordinate system would be more visible).

 

[marcus]

Just noted:
27Nov17:36 519.31 at what looks like 65 deg before NP
27Nov18:10 517.8 at what looks like 50 deg before NP

That suggests I underestimated the shift in apsides. Doesn't it seem more likely that apoapsis is now closer to 60 degrees before NP
and periapsis more like 60 deg before SP?

 

[OmCheeto]

Sorry for not paying attention, but are the latitude lines 30° apart?

 

[marcus]

I think so, Om.
Moreover it may be a sign of your astute good judgement that you have not been paying attention
For the better part of a month the apsides were approximately stable (or so it seemed) at or around the poles. But now they seem to be adrift and it may be a wild goose chase trying to keep track of them.

Even a slight change of the angle of thrust could do that. Make them differ day by day. The navigation team may be trying now to circularize the spiral.
27Nov20:38 500.16 at what looks like 80 deg before SP
27Nov21:02 498.03 at what looks like 60 deg before SP (that might be as close an estimate of the periapsis that we can get for now)
27Nov21:26 496.67 at what looks like between 40 and 45 deg before SP (so it's not 60 deg anyway)
27Nov22:15 498.41 right on the SP (I got absorbed with something else and neglected to check earlier.)

 

[OmCheeto]

I think so, Om.
27Nov20:38 500.16 at what looks like 80 deg before SP

Yay!

I'm in full nerd mode this morning, and very happy to see that our eyeballs are calibrated.

Doh! I'm a minute late for my next reading...

an: after north
bn: before north
np: north pole
as: after south
bs: before south

 

[mfb]

500.61 at 60° after S pole, 13:00:24 UTC, 564 mph.
Ceres doesn't fit into the picture any more.
Om, do you have that table in a format that allows to copy it?

 

[OmCheeto]

500.61 at 60° after S pole, 13:00:24 UTC, 564 mph.
Ceres doesn't fit into the picture any more.
Om, do you have that table in a format that allows to copy it?

Let me know if this doesn't work for you.
You should be able to import this as a csv file.
If not, I can export it as csv, excel, or numbers, and upload the file.

eyeballer, eyeballed °, dir, mo, day, hr, min, , km, m/s, mph, time
, , , Nov , 27, 15, 43, utc, 505.46, 251, 562, 71.12
mfb, 45, as, Nov , 27, 16, 7, utc, 509.26, 251, 561, 71.52
, , , Nov , 27, 16, 34, utc, 513.85, 250, 560, 71.97
, , , Nov , 27, 16, 58, utc, 517.26, 250, 559, 72.37
, , , Nov , 27, 17, 22, utc, 519.19, 249, 558, 72.77
marcus, 65, bn, Nov , 27, 17, 46, utc, 519.31, 249, 557, 73.17
om+marcus, 47.5, bn, Nov , 27, 18, 10, utc, 517.80, 249, 556, 73.57
om, 10, bn, Nov , 27, 18, 34, utc, 515.17, 249, 556, 73.97
om, 0, np, Nov , 27, 19, 1, utc, 511.66, 249, 557, 74.42
om, 25, an, Nov , 27, 19, 25, utc, 508.53, 250, 560, 74.82
om, 50, an, Nov , 27, 19, 49, utc, 505.62, 252, 563, 75.22
om, 70, an, Nov , 27, 20, 12, utc, 502.94, 253, 566, 75.60
om+marcus, 80, bs, Nov , 27, 20, 39, utc, 500.16, 254, 569, 76.05
om, 60, bs, Nov , 27, 21, 3, utc, 498.03, 254, 569, 76.45
om, 40, bs, Nov , 27, 21, 26, utc, 496.67, 254, 568, 76.83
om, 20, bs, Nov , 27, 21, 52, utc, 496.68, 253, 566, 77.27
om, 0, sp, Nov , 27, 22, 16, utc, 498.41, 252, 564, 77.67
om, 20, as, Nov , 27, 22, 40, utc, 501.71, 252, 563, 78.07
om, 40, as, Nov , 27, 23, 6, utc, 506.47, 251, 562, 78.50
om, 60, as, Nov , 27, 23, 30, utc, 510.69, 251, 561, 78.90
om, 80, as, Nov , 27, 23, 54, utc, 513.79, 250, 560, 79.30
om, 80, bn, Nov , 28, 0, 18, utc, 515.11, 250, 559, 79.70
om, 50, bn, Nov , 28, 0, 42, utc, 514.51, 249, 558, 80.10
om, 30, bn, Nov , 28, 1, 9, utc, 512.03, 249, 557, 80.55
om, 10, bn, Nov , 28, 1, 33, utc, 508.92, 249, 558, 80.95
om, 5, an, Nov , 28, 1, 57, utc, 505.61, 250, 560, 81.35
om, 30, an, Nov , 28, 2, 21, utc, 502.52, 251, 562, 81.75
om, 50, an, Nov , 28, 2, 45, utc, 499.81, 253, 566, 82.15
om, 80, an, Nov , 28, 3, 11, utc, 497.13, 254, 569, 82.58
om, 80, bs, Nov , 28, 3, 35, utc, 494.95, 255, 570, 82.98
om, 55, bs, Nov , 28, 3, 59, utc, 493.12, 255, 570, 83.38
om, 35, bs, Nov , 28, 4, 25, utc, 492.04, 254, 569, 83.82
om, 10, bs, Nov , 28, 4, 49, utc, 492.51, 253, 567, 84.22
om, 10, as, Nov , 28, 5, 13, utc, 494.62, 253, 565, 84.62
om, 30, as, Nov , 28, 5, 37, utc, 498.14, 252, 564, 85.02

It looks like this when graphed:

x-axis: hours
y-axis: km, altitude

My eyes were getting exhausted last night, so I took a break.
I decided to collect two full cycles to see what the overall descent rate was.

I also plotted back to Nov 24th, to see if I could remove the descent from the graph and see if the ellipticity has been changing.

upper graph is actual altitude vs time
lower graph has the slope removed

 

[mfb]

Thanks. Looks like a sine and a smooth slope fit quite well.

Just crossing a pole again (maybe 5-10° later), S I guess. 485.13 km, 568 mph, 18:42 UTC.

70° after crossing the pole: 497.37 km, 565 mph, 19:56:46 UTC.

That is a very fast increase in height.

Right at the equator: 499.72km, 564 mph at 20:20:53 UTC.