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

[mfb]

21:10 UTC, 390.63 km, 45° past N pole, 601 mph. Another 4 km of periapsis in a single orbit. Two days left to lower the periapsis a tiny bit more and to make the orbit a bit more circular.

 

[marcus]

!

 

[OmCheeto]

!

??​

 

[marcus]

What Mfb said, Om
Less than 6 km left to descend, and the last orbit reduced periapsis by ~4 km.

BTW last time around I found min and max were 395 and 412
Then this time around we found they were 391 and 408
So the orbit knocked 4 km off both the min and the max.
Mfb found the min:

21:10 UTC, 390.63 km, 45° past N pole, 601 mph. Another 4 km of periapsis in a single orbit. Two days left to lower the periapsis a tiny bit more and to make the orbit a bit more circular.

I rounded his 390.63 to 391. We both reported the same "45º past N pole" for the min position.
And I just checked and found the max
6 Dec 00:25 UTC, 407.78 km, 65º after S
(So the extrema came at essentially the same latitudes as last time round. and they were each less by 4 km.)

Update: again the min came at essentially the same place. Within 1 km of target!
6 Dec 02:52 UTC, 386.29 km, 40º past N

 

[marcus]

Mystic simulator has been shut off---the last view was dated 6 December 7:22 UTC. That was Saturday 5 December at 11:22 PM pacific time.

So here it is 10 PM pacific Sunday the 6th, almost a full 24 hours that the simulation has been off. I have no idea why. Maybe at this point getting into the final orbit is too complicated for the person running Mystic to want to simulate it. Or it is not yet decided how to proceed. Maybe it got too far out of synch with real Dawn and needed to be restarted. Perhaps the simulation will resume when something is resolved. Or maybe it's off for good.

 

[OmCheeto]

Mystic simulator has been shut off---the last view was dated 6 December 7:22 UTC. That was Saturday 5 December at 11:22 PM pacific time.

So here it is 10 PM pacific Sunday the 6th, almost a full 24 hours that the simulation has been off. I have no idea why. Maybe at this point getting into the final orbit is too complicated for the person running Mystic to want to simulate it. Or it is not yet decided how to proceed. Maybe it got too far out of synch with real Dawn and needed to be restarted. Perhaps the simulation will resume when something is resolved. Or maybe it's off for good.

Still no update on MYSTIC.
DSN Madrid #63 is sending a signal to Dawn.
Time = Dec 7, 2015 18:27 UTC

No chatter on twitter, facebook, jpl, nor nasa, that I can find.

 

[marcus]

Thanks for alerting us! Now I see Madrid #63 is inactive and Goldstone #25 is receiving signal from Dawn. So I would guess the probe has turned off engine after the long (nearly two month) descent.

If that's right then and it's according to the plan Rayman described, the probe is at least approximately in the desired orbit (LAMO) and they are now considering whether they need it to perform a "TCM" (trajectory correction maneuver) to in effect fine-tune the orbit----for stuff like optimal observation, stability, low hydrazine cost, or other.

If anyone is joining us, if you look at the solar system map here:
http://dawn.jpl.nasa.gov/mission/live_shots.asp
You see that the Earth is now at about right angles from the Sun-Ceres line. The Sun-Earth line is about 90º to the right of the Sun-Ceres line. Rotation is counterclockwise so that means that
Ceres rises above the horizon around NOON local time.
and it would set about 12 hours later, towards midnight local time.

So it is just a few minutes past noon now, Goldstone time (12:20 PM pacific time) and it makes sense for Deep Space Network (dsn) to be switching to antenna in Goldstone, CA.

Now the communication suddenly became two-way. DSN shows Goldstone#25 both sending and receiving.

 

[OmCheeto]

Thanks for alerting us! Now I see Madrid #63 is inactive and Goldstone #25 is receiving signal from Dawn. So I would guess the probe has turned off engine after the long (nearly two month) descent.

If that's right then and it's according to the plan Rayman described, the probe is at least approximately in the desired orbit (LAMO) and they are now considering whether they need it to perform a "TCM" (trajectory correction maneuver) to in effect fine-tune the orbit----for stuff like optimal observation, stability, low hydrazine cost, or other.

We are once again psychically synchronized, as I also just noticed that.
And poo poo on Evo for saying this is not the "PsychicsForum".

Evo; "Hi QuantumTheology, this is a Physics Forum, not a Psychics Forum. Many people wander in here by mistake due to a spelling error. Perhaps you were looking for a psychics forum"? [ref: PHYSICSforums]​

 

[marcus]

==quoting new status update from Rayman==

December 7, 2015 -Dawn to Stop Ion-Thrusting Today in Low Altitude Orbit

Dawn is scheduled to conclude ion-thrusting for its spiral descent shortly before noon today. At that time, it will be orbiting about ... (385 kilometers) above Ceres, closer than the International Space Station is to Earth. After it turns to point its main antenna to Earth, navigators will begin to measure its orbital parameters very accurately. During the next two days, they will analyze the orbit carefully and decide on Dec. 9 whether to make an adjustment at the end of the week. (It is likely such a trajectory correction maneuver will be needed.) The November Dawn Journal explains this in more details.
==endquote==

 

[marcus]

Mystic simulator has been updated to 8 Dec but doesn't seem to be in regular operation.
http://neo.jpl.nasa.gov/orbits/fullview2.jpg
What it shows is:
8 Dec 21:11 UTC, altitude 356.63 km, 25º past N pole
heading south over Ceres dayside.
That would correspond to 8 Dec 13:11 hours pacific time, or 1:11 PM which was about 3 hours ago.

DSN shows two-way communication with Goldstone #25, but it looks like Dawn is just sending a 10 bit per second tracking signal. As Rayman indicated, they are going to be accurately determining the orbit she happens to be in, to see whether and how it needs to be corrected.

Postscript: just checked as of 9 Dec 8:20am pacific. Simview said 9Dec 16:15 UTC, 377.47 km, about 30 degrees past S pole.
That UTC is so close to 8:20 am pacific that it suggests the simulator is back in regular operation. So maybe Mystic is again squared away with real Dawn.

 

[marcus]

Yeah, signs are Simview is back up and running.
9Dec 16:15 UTC, 377.47 km, about 30 degrees past S pole
9Dec 16:36 UTC, 378.61 km, about 45 degrees past S pole*
9Dec 16:58 UTC, 377.86 km, about 70 degrees past S pole
9Dec 17:23 UTC, 374.23 km, about 85 degrees before N pole
9Dec 17:45 UTC, 368.77 km, about 65 degrees before N pole
...
9Dec 18:30 UTC, 358.08 km, about 10 degrees before N pole
9Dec 18:52 UTC, 356.13 km, about 15 degrees past N pole*
9Dec 19:14 UTC, 357.16 km, about 42 degrees past N pole
9Dec 19:38 UTC, 360.68 km, about 73 degrees past N pole
...
9Dec 21:32 UTC, 376.75 km, about 15 degrees past S pole
9Dec 21:53 UTC, 377.97 km, about 40 degrees past S pole*
9Dec 22:17 UTC, 377.57 km, about 60 degrees past S pole
9Dec 22:39 UTC, 374.99 km, about 80 degrees past S pole

Rayman on 7Dec: " ...they will analyze the orbit carefully and decide on Dec. 9 whether to make an adjustment at the end of the week. (It is likely such a trajectory correction maneuver will be needed.) The November Dawn Journal explains this in more details."

Barring numerical error the current max (apoapsis) could be at 45º past S pole. And since thruster is off, min (periapsis) might be expected to occur around 45º past N pole.
[Postscript: That isn't working out as i expected. The minimum altitude came a few degrees earlier.]

http://neo.jpl.nasa.gov/orbits/fullview2.jpg
https://eyes.nasa.gov/dsn/dsn.html
http://dawn.jpl.nasa.gov/mission/status.html
http://solarsystem.nasa.gov/images/galleries/Ceres_Layers_br1.jpg (this cutaway should now be updated)

 

[marcus]

Just as a reminder, what now happens has consequences for human history because Ceres is (by a wide margin) the nearest icy dwarf planet and offers an advantageous site for chemical and materials manufacture in low gravity. Whether or not this will be developed depends somewhat on Ceres layer structure and chemical composition
Thinking has changed about the layer structure (Lakdawalla report on recent AAS conference) because at least in some regions craters remain sharply defined and are slow to smooth out---suggesting they are supported on a slow-flow rock+ice mix that could be as much as 60% rock. The searchable online cutaway GRAPHICS go back to 2005 and 2006 when scientists had only Hubble space telescope images to go on. I couldn't find any updated cutaway diagram showing more recent guesses about layer structure.
There were also reports at that AAS conference of detection of ammonia-bearing clays in the hydrated minerals at Ceres' surface, by optical/IR spectroscopy, which would be important if confirmed. Nitrogen is a key chemical element for both manufacturing and biology--common in outer solar system bodies but unexpected on an asteroid belt body like Ceres.
Anyway if things work out as planned we now get to learn a great deal more about Ceres' chemical and layer composition. This kind of graphic will hopefully be revised:

The icy layer should be more indicative of a 60-40% rock+ice mix. Orbit tracking should be able to map subsurface irregularities in density. Gamma and neutron spectroscopy is to measure the abundances of various chemical elements in surface material, to a depth of about 1 meter.

The last (chemical abundances) is especially significant so I'll bring forward the graphic. Spectroscopy depends on activation by cosmic ray particles.

Impact by cosmic rays (high energy protons, mainly) causes a sparkle. The frequencies of the gamma-ray sparkle reveal the identities/abundances of the atoms giving off the sparkle. Moreover among the scattered neutrons the fraction of them which have been slowed by successive collisions with hydrogen nuclei reveals the amount of hydrogen (e.g. water ice) in the surface material.

 

[OmCheeto]

Ahhhhhh!

The new issue of Nature is out!​

http://www.nature.com/nature/journal/v528/n7581/full/nature16172.html

http://www.nature.com/nature/journal/v528/n7581/full/nature15754.html

Mysterious bright spots on Ceres are probably salt

Haven't read any of them yet. Should be interesting.

 

[marcus]

Thanks for alerting us! Here's a quote from the abstract of the first article you linked:
"...Here we report spectra of Ceres from 0.4 to 5 micrometres acquired at distances from ~82,000 to 4,300 kilometres from the surface. Our measurements indicate widespread ammoniated phyllosilicates across the surface, but no detectable water ice. Ammonia, accreted either as organic matter or as ice, may have reacted with phyllosilicates on Ceres during differentiation. This suggests that material from the outer Solar System was incorporated into Ceres, either during its formation at great heliocentric distance or by incorporation of material transported into the main asteroid belt."

Here's the Nature editor's summary:
"The VIR spectrometer onboard NASA's Dawn spacecraft has obtained infrared spectra of the dwarf planet Ceres at distances of 82,000 to 4,300 kilometres and at wavelengths of 0.4–5 μm, including the 2.6–2.9 μm spectral region not accessible to Earth-bound telescopes due to atmospheric absorption. The data indicate the widespread presence of ammoniated phyllosilicates across the asteroid's surface. No water ice could be detected, though small localized occurrences of water ice cannot be excluded. The discovery of ammonia implies that material from the outer Solar System was incorporated into Ceres, either during its formation at great heliocentric distance or by incorporation of material transported into the main asteroid belt."

I looked up "phyllosilicates." They comprise several groups of hydrated layered silicates one of the larger groups being "clay minerals":

• Clay mineral group
  • Halloysite - Al2Si2O5(OH)4
  • Kaolinite - Al2Si2O5(OH)4
  • Illite - (K,H3O)(Al,Mg,Fe)2(Si,Al)4O10[(OH)2,(H2O)]
  • Montmorillonite - (Na,Ca)0.33(Al,Mg)2Si4O10(OH)2·nH2O
  • Vermiculite - (MgFe,Al)3(Al,Si)4O10(OH)2·4H2O
  • Talc - Mg3Si4O10(OH)2
  • Sepiolite - Mg4Si6O15(OH)2·6H2O
  • Palygorskite (or attapulgit)- (Mg,Al)2Si4O10(OH)·4(H2O)
  • Pyrophyllite - Al2Si4O10(OH)2

 

[marcus]

The third article you pointed to is well-written for wide audience and covers a bunch of topics, not just the one mentioned in title.
http://www.nature.com/news/mysterious-bright-spots-on-ceres-are-probably-salt-1.18980
It could be the most useful. It is a News article by Alexandra Witze, it is non-technical, says things simply and clearly.

I got a good impression of Alexandra Witze as a journalist, so I checked
==quote==
Alexandra Witze, Retained Correspondent, Boulder, Colorado
Alex covers the Earth and planetary sciences, with a little dabbling in astronomy. She studied geology at the Massachusetts Institute of Technology and science communication at the University of California, Santa Cruz. Among other places she has worked as a journalist for Science News and the Dallas Morning News; she also ran Nature's US news operations from Washington DC between 2005 and 2010. Alex rejoined the journal in 2013.
a.witze@us.nature.com
==endquote==
10Dec 00:33 UTC , 356.61, 30degrees past N pole.
10Dec 01:18 UTC, 364.01, 90 degrees past N pole.

 

[OmCheeto]

A new status report is out.
They will be doing a small orbital correction maneuver, between the 11th and 13th.

December 9, 2015 -Dawn at Lowest Orbital Altitude at Ceres

 

[marcus]

Simview now shows Dawn performing TCM (trajectory correction maneuver). It is not simply retrothrusting as it was during the main descent.
Then the ion beam was in the direction of motion, to slow down. Now the beam is sideways the direction of motion.
As if the orbit was askew---not exactly over the poles---and a sideways push was needed to true it up and make the orbit more exactly polar.

Here, as I interpret it, we see the ion beam pointed at 9 o'clock while the probe is crossing the terminator at the S pole in about a 4 o'clock direction. The thrust is only partly aligned with the direction of motion.

 

[mfb]

Thrusting directly over the poles (as shown in the image) doesn't make an orbit more polar, it shifts the orientation of the orbit relative to the terminator. They ruin my earlier estimate of the maximal remaining probe lifetime!

 

[marcus]

Yes, I can see how it might change your estimate of how long the probe can remain in permanent sunshine before it begins to fall into Ceres' shadow for part of each orbit. That was a pretty robust estimate though, as I recall, and not apt to change too much. The dwindling supply of hydrazine is more critical---so much so that it would be tactful to avoid mentioning it.

Still, it is a great success that Dawn is finally down in LAMO, at target altitude! I feel jubilant about this--relieved and heartened. At last some gamma spectroscopy of the chemical elements in the surface! When my wife heard the news she proposed toasting Dawn with something fizzy. ==quote Rayman==

December 11, 2015 -Dawn Ion-Thrusting to Adjust Orbit

Dawn is now using its ion engine to adjust its orbit. This maneuver (explained in the November Dawn Journal.) will synchronize the spacecraft 's orbital motion with Ceres' rotation around its axis to fit with the plan for the extensive observations that will begin next week.

Yesterday while the flight team was preparing Dawn's flight plan, the spacecraft tested its backup camera. Controllers occasionally run the camera through a series of tests to verify that it remains in good condition should the primary camera have a problem. (The test of the camera was performed eight years to the day after its first operation in space.) Although the results have not been analyzed in detail yet, all indications are that the backup is in excellent condition.
==endquote==
12Dec 3:36 UTC, 385.44 km, passing over S pole (positive inline thrust)
Judging from Simview the main function of the TCM (correction maneuver) was to raise the average altitude from around 360-370 to 385
12Dec 4:23 UTC, 384.15 km, 55º past S pole
12Dec 5:09 UTC, 376.16 km, 80º bef N pole
12Dec 5:55 UTC, 366.25 km, 30º bef N pole
12Dec 6:19 UTC, 364.65 km, passing over N pole
You can see why they are applying positive inline thrust. They want to raise the altitude into the 380s instead of having it sagging down in the 370s. Higher altitude means longer orbit period. The orbit period wants to be finely adjusted to synch with Ceres rotation to get efficient coverage of the surface.

I suspect the main reason they raised the LAMO altitude from original 375 to 385 has to do with timing.

 

[marcus]

Judging by simulation, the TCM is complete. Simview shows the probe at [edit: or near] altitude 385 km with ion engine turned off.
12Dec 15:34 UTC, 385.48 km, 60º past S pole
12Dec 15:57 UTC, 381.97 km, 80º past S pole
12Dec 16:20 UTC, 377.11 km, 75º bef N pole
12Dec 16:44 UTC, 371.71 km, 50º bef N pole [edit: I added some more data points, still seems close enough]
12Dec 17:06 UTC, 367.77 km, 24º bef N pole
12Dec 17:30 UTC, 366.54 km, right over N pole*
12Dec 17:53 UTC, 368. 50 km, 30º past N pole
...
12Dec 18:39 UTC, 377.96 km, 85º past N pole
Now the long awaited gamma ray spectroscopy of Ceres surface material can begin.
http://dawn.jpl.nasa.gov/mission/status.html
http://neo.jpl.nasa.gov/orbits/fullview2.jpg
http://dawn.jpl.nasa.gov/mission/journal.asp
https://eyes.nasa.gov/dsn/dsn.html (Madrid antenna #55 is in standby)
http://dawn.jpl.nasa.gov/mission/live_shots.asp

 

[OmCheeto]

Judging by simulation, the TCM is complete. Simview shows the probe at 385 km with ion engine turned off.
12Dec 15:34 UTC, 385.48 km, 60º past S pole
12Dec 15:57 UTC, 381.97 km, 80º past S pole
Now the long awaited gamma ray spectroscopy of Ceres surface material can begin.

Yay!

...
https://eyes.nasa.gov/dsn/dsn.html (Madrid antenna #55 is in standby)
...

Canberra #35 was also in standby @ 15:34 & 15:57.

ps. Has anyone else tried to analyze the specific orbital energy? My graph comes out sinusoidal, so I'm not sure what's wrong.

x axis = time in hours ____ t₀ = Nov 27, 2015 17:46 UTC
y axis = energy

I haven't really sat down to figure out why the energy gets higher the closer the orbit is to Ceres, but I checked around, and saw that's just the way it is.

[edit #1: Doh! Canberra #35 is now unassigned]
[edit #2: Madrid #65 in two way com @ 17:44 UTC, 10.00 b/sec?]

 

[mfb]

How did you calculate the energy?
Maybe you need a different value for Ceres' radius?

Where are the pole crossings in that graph?

 

[marcus]

Om, it looks like Simview thinks periapsis of the new orbit is right at the N pole. (see post#756). That would be neat, no?

 

[OmCheeto]

Om, it looks like Simview thinks periapsis of the new orbit is right at the N pole. (see post#756). That would be neat, no?

Yes, it does appear that way, but I'm still stuck on homework problems from 2 weeks ago.
I'm trying to find the answers to mfb's questions, but I have so many goofy graphs going on at once, I have no idea what is going on.
If anyone has any questions, about how NOT to be a scientist, just ask.

 

[marcus]

Let's compare formulas we use.
specific potential energy at radius R: -GM/R
specific kinetic energy in circular orbit at radius R: (1/2)v² = (1/2)GM/R

It seems like the specific total would be KE+PE = -(1/2)GM/R
so the deeper down in the well you go, the faster the orbit so the KE increases, but the PE gets more negative, and it's twice as big, so the total gets more negative. The smaller R gets, the more negative the specific orbital energy.

You probably have gone beyond this, to non-circular orbits, and have a more complicated formula. Can you write conveniently write down the formula you are using?

 

[marcus]

Since we turned a page, I'll bring forward the post summarizing some reasons one might be especially interested in studying Ceres and in the current exploration by Dawn.
==quote post #748==
Just as a reminder, what now happens has consequences for human history because Ceres is (by a wide margin) the nearest icy dwarf planet and offers an advantageous site for chemical and materials manufacture in low gravity. Whether or not this will be developed depends somewhat on Ceres layer structure and chemical composition
Thinking has changed about the layer structure (Lakdawalla report on recent AAS conference) because at least in some regions craters remain sharply defined and are slow to smooth out---suggesting they are supported on a slow-flow rock+ice mix that could be as much as 60% rock. The searchable online cutaway GRAPHICS go back to 2005 and 2006 when scientists had only Hubble space telescope images to go on. I couldn't find any updated cutaway diagram showing more recent guesses about layer structure.
There were also reports at that AAS conference of detection of ammonia-bearing clays in the hydrated minerals at Ceres' surface, by optical/IR spectroscopy, which would be important if confirmed. Nitrogen is a key chemical element for both manufacturing and biology--common in outer solar system bodies but unexpected on an asteroid belt body like Ceres.
Anyway if things work out as planned we now get to learn a great deal more about Ceres' chemical and layer composition. This kind of graphic will hopefully be revised:
View attachment 93140

The icy layer should be more indicative of a 60-40% rock+ice mix. Orbit tracking should be able to map subsurface irregularities in density. Gamma and neutron spectroscopy is to measure the abundances of various chemical elements in surface material, to a depth of about 1 meter.

The last (chemical abundances) is especially significant so I'll bring forward the graphic. Spectroscopy depends on activation by cosmic ray particles.
View attachment 93141
Impact by cosmic rays (high energy protons, mainly) causes a sparkle. The frequencies of the gamma-ray sparkle reveal the identities/abundances of the atoms giving off the sparkle. Moreover among the scattered neutrons the fraction of them which have been slowed by successive collisions with hydrogen nuclei reveals the amount of hydrogen (e.g. water ice) in the surface material.
==endquote==

Judging by simulation, the TCM is complete. Simview shows the probe at [edit: or near] altitude 385 km with ion engine turned off.
12Dec 15:34 UTC, 385.48 km, 60º past S pole
12Dec 15:57 UTC, 381.97 km, 80º past S pole
12Dec 16:20 UTC, 377.11 km, 75º bef N pole
12Dec 16:44 UTC, 371.71 km, 50º bef N pole [edit: I added some more data points, still seems close enough]
12Dec 17:06 UTC, 367.77 km, 24º bef N pole
12Dec 17:30 UTC, 366.54 km, right over N pole*
12Dec 17:53 UTC, 368. 50 km, 30º past N pole
...
12Dec 18:39 UTC, 377.96 km, 85º past N pole

12Dec 19:25 UTC, 385.33 km, 45º bef S pole
12Dec 19:49 UTC, 387.07 km, 24º bef S pole
12Dec 20:11 UTC, 387.88 km, right over S pole**
12Dec 20:35 UTC, 387.88 km, 30º past S pole**
12Dec 20:58 UTC, 386.84 km, 50º past S pole

 

[OmCheeto]

How did you calculate the energy?

specific energy = v^2/2 - mu/(altitude + imm.rad.)

imm.rad. = immediate radius of Ceres, where r(theta)=(a*b)/sqrt((b*cos(theta))^2+(a*sin(theta))^2)
a = major axis = 481,500 meters
b = minor axis = 445,500 meters
theta = angle in radians from the equator heading ccw
mu = G * (mass of Dawn + mass of Ceres) = 6.67e-11 * (1240 + 9.38e18)​

Maybe you need a different value for Ceres' radius?

I need a different brain...

Where are the pole crossings in that graph?

 

[mfb]

specific energy = v^2/2 - mu/(altitude + imm.rad.)

imm.rad. = immediate radius of Ceres, where r(theta)=(a*b)/sqrt((b*cos(theta))^2+(a*sin(theta))^2)
a = major axis = 481,500 meters
b = minor axis = 445,500 meters
theta = angle in radians from the equator heading ccw
mu = G * (mass of Dawn + mass of Ceres) = 6.67e-11 * (1240 + 9.38e18)​

The given height values don't look like MYSTIC takes the oblateness of Ceres into account. Does the agreement get better if you use a single value for the radius? I would also try different values for the radius to see if others fit better.

 

[marcus]

The 2 minute youtube records the moment when Laurent Fabius says he hears no objection and so
"L'accord de Paris pour le climat est accepté"
Climate day (12 December) was also "Ceres Day"---when Dawn was finally in near orbit and could get down to real business.

 

[Janus]

Let's compare formulas we use.
specific potential energy at radius R: -GM/R
specific kinetic energy in circular orbit at radius R: (1/2)v² = (1/2)GM/R

It seems like the specific total would be KE+PE = -(1/2)GM/R
so the deeper down in the well you go, the faster the orbit so the KE increases, but the PE gets more negative, and it's twice as big, so the total gets more negative. The smaller R gets, the more negative the specific orbital energy.

You probably have gone beyond this, to non-circular orbits, and have a more complicated formula. Can you write conveniently write down the formula you are using?

For none circular orbits, the first equation still applies for any point of the orbit. The second equation becomes -(1/2)GM/a, where a is the semi-major axis of the orbit.

 

[OmCheeto]

The given height values don't look like MYSTIC takes the oblateness of Ceres into account. Does the agreement get better if you use a single value for the radius? I would also try different values for the radius to see if others fit better.

Along with all of the previously mentioned derogatory phrases my mother used to call me, she also called me a "doffa henna". Which I believe means; "Idiot chicken". But don't quote me on that translation.

In my previous graphs, I was off by 2 orders of magnitude for the mass of Ceres.
Inserting the correct mass of Ceres, and using: average radius + altitude = r
I come up with the following graph:

This makes a tad bit more sense to me.
I spent several hours trying to figure out the gravitational field around an oblate spheroid, but could not comprehend any of the maths.
The only thing I could extract, was that the force of gravity at the poles is greater than at the equator.
I'm guessing that this might explain the shape of this new graph.

This apparently was previously such an obscure, aka hypothetical, problem, that there is little discussion about it here at PF. At least that I could find.

But it was fun looking. DH mentioned an article in one thread about "gravitational anomalies of the moon", with disastrous consequences.
Hopefully, the Dawn crew is familiar with gravitational potholes.

[edit]

For none circular orbits, the first equation still applies for any point of the orbit. The second equation becomes -(1/2)GM/a, where a is the semi-major axis of the orbit.

I'm still scratching my head about this, as "a" is a constant.

 

[mfb]

Okay, the equator energy is too high, so we are closer to the center than the calculation assumes (as the speed value is directly from MYSTIC). If your latest plot was done with a constant radius for r, using the adaptive radius would make it even worse. There are two symmetric oscillations per orbit, so there is no periapsis/apoapsis problem left (at least not dominant).

The gravitational force is stronger at the poles if you are on the surface (there being at the poles makes you closer to the center) - in orbit for a given height, it is stronger over the equator. We would have to estimate the quadrupole component of the gravitational potential to include that effect.

 

[marcus]

Just to keep us up to date (don't let this interrupt the orbital energy discussion) according to Simview the correction maneuver is accomplished and Dawn is in LAMO, with engine off.
DSN graphic shows Madrid antenna #65 in two-way communication

It seems pretty clear (at least to me) that what Simview calls "altitude" is altitude above an idealized spherical Ceres, not above the actual surface of the body. I'm not sure what sphere radius Simview uses---maybe 473 km, which I've seen quoted as the average R_av of the true oblate dimensions. In that case, in case some notation might be helpful: Let's have H stand for the "altitude" term.

Dawn's radial distance from center = D = R_av + H = 473 km + "altitude".

In a few minutes Dawn will pass over Ceres S pole and that might roughly coincide with D_max or apoapsis. We'll see. I'll record what Simview says at that point, and check later how well it agrees.

It's fascinating how much smoother the surface is in the wide equatorial belt, and how much sharper the craters are in polar regions. As if the proportion of ice to rock is higher in equatorial subsurface material, so that it flows more easily---e.g. 40-60% rock to ice. And as if the proportion of ice is lower in polar subsurface--e.g. 60-40% rock to ice--providing a stiffer foundation for longer-lasting craters.

13Dec 18:10 UTC, 376.33 km, right at S pole*

I think that is the H_max of the corrected orbit (simulation) so will tentatively mark it with an asterisk. Well see if H declines at the next reading, and whether H_min comes at N pole (if that is not too much to ask of Mystic

Postscript: Yes! H_max = 376 km and it came right at the S pole. I'm thinking we should be on the lookout for H_min about 3 or 3:30 hours from H_max: around 1 PM pacific or 21 hours UTC. Hope I don't get too busy with something else and forget.

Postscript:
13Dec 20:53 UTC, 356.27 km, right at N pole*
A spread of almost exactly 20 km. H was decreasing up to that point, so if it's the min as I guess it will increase at the next reading.
Yes it increased
13Dec 21:16 UTC, 357.70 km, 20º from N pole

It seems that Simview has fallen into a pattern where the "altitude" H is going to be between 356 and 376km, with H_min at N pole and H_max at S pole.

To check consistency I took a reading around H_min again. It occurred as expected
14Dec 02:17, 356.25 km, 8º to N pole
the readings immediately before and after were larger (358.55 and 357.20)

So we can say with reasonable confidence that the semimajor axis a = 473+366 = 839 km.
as far as Simview is concerned, assuming 473 is right for the Ceres average radius
2 pi ((839 km)^3/(G*938e18 kg))^(1/2) = 5.36= 5: .36*60 = 5:22

20:53 + 5:22 = 26:15 = 24+2:15 hours, which is pretty close to 2:17!

 

[marcus]

Since I haven't checked in on Dawn much so far today, I'll take a look at the new orbit according to Simview. See if it's consistent with our perceptions of it yesterday. It looked then as if the "altitude" (probe distance from center, minus something like 473 km, the average body radius) was going to be between 356 and 376 km with (approximately at least) the min coming at Ceres' Npole and max at Spole.

I'll tag the max and min with asterisks.

Here are some fresh readings:
15Dec 01:49 UTC, 373.70 km, 70º to S pole
15Dec 02:12 UTC, 375.77 km, 45º to S pole
15Dec 02:35 UTC, 376.32 km, 24º to S pole*
15Dec 02:58 UTC, 375.88 km, right at S pole
15Dec 03:21 UTC, 374.84 km, 30º from S pole

Assuming the estimate of 5:22 hours for the orbit period (see previous post) is right the time to periapsis (min "altitude") is about 2:41, so we might expect it around 15Dec 05:16 UTC, just adding 2:35 and 2:41.
That's 9:16 pm pacific time, hope I don't forget : ^)

15Dec 05:17 UTC, 357.65 km, 30º to N pole
15Dec 05:40 UTC, 356.68 km, right at N pole*
15Dec 06:03 UTC, 358.90 km, 20º from N pole

 

[OmCheeto]

A new mission status update is out.

December 14, 2015 -Dawn Preparing for New Observations