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edit 2: There seems to have been some announcement/extension by NASA (20-Oct-2017), possibly this will shed more light on the issues in this question.

edit 1: Several months have passed since this question was asked, presumably a decision how to best allocate both the xenon and hydrazine propellants has been made. Still, the issues of very different roles each propellant has in an orbit around Ceres is interesting and not straightforward due to the inhomogeneities of Ceres' gravity field at different altitudes.


The Spaceflight Now article Dawn mission managers await NASA decision on spacecraft’s future says:

Dawn’s primary mission ended in June 2016, and NASA officials approved a one-year extension that expires June 30. The fate of Dawn after June 30 remains uncertain, but senior managers at NASA Headquarters are expected to soon decide whether the spacecraft should be turned off, continue exploring Ceres, or depart the dwarf planet and perhaps fly by an asteroid.

[...]

Experts from JPL and Orbital ATK devised a hybrid method of controlling Dawn’s attitude with the two remaining reaction wheels and hydrazine thrusters, the spacecraft now must fully rely on its rocket jets, wrote Marc Rayman, Dawn’s chief engineer at JPL, in a mission update posted on a NASA website.

I can't quite follow it, but according to the article, sequential failure of some some if not of Dawn's initially four reaction wheels have required the use of hydrazine thrusters for attitude control.

I'm wondering if the hydrazine that is used for attitude control is spent mostly in switching between Earth-pointing and Ceres-pointing states, where the latter requires a faster-rotating attitude state? Why would a lower orbit use more hydrazine for attitude control? Or would it be actually for station keeping in an uneven gravity field?

Then there is the issue of high versus low orbit.

“The consequence is that Dawn uses more hydrazine in orbit around Vesta and Ceres than when it is journeying between worlds, orbiting the sun and maneuvering with its ion engine. And it uses more hydrazine in lower orbits than in higher ones,” Rayman wrote.

“One day at our low-altitude mapping orbit, which was at 385 kilometers, would be equivalent to about 18 days (of hydrazine fuel) at higher altitude, which is what we’re in now,” Raymond said.

“Lifetime at a lower altitude would likely be limited to weeks at this point,” she said.

Could someone clarify the issues of hydrazine budget:

  • how many reaction wheels are left?
  • why is Dawn's attitude control so much more expensive in low orbit around Ceres?
  • would Dawn's station keeping in low orbit around Ceres actually be a comparable drain to its attitude control?
  • does Dawn's ion thruster have too little thrust for station keeping in low Ceres orbit?

and how this would affect a decision to "stay high", "go low", or just go somewhere else and make better use of the Xenon?

I'm looking for an answer specific to this situation - Dawn, in its current state, around Ceres. General statements about what attitude control and station keeping are for alone aren't enough. I'm asking about the specific aspects in this case that NASA will consider as part of their decision on what Dawn will do next. Thanks!

note: Forward-looking question from 2013 Does the Dawn spacecraft have the potential for an extended mission? has a few good answers worth reading.

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    $\begingroup$ The Clash - "Should I Stay or Should I Go" (Live at Shea Stadium): youtu.be/oGIFublvDes $\endgroup$ – uhoh Jun 18 '17 at 11:14
  • $\begingroup$ If there are Mascons in Ceres, keeping a stable low orbit may require additional fuel. The mapping process will require fuel for attitude control to get good and precisely overlapping images. $\endgroup$ – Uwe Jun 18 '17 at 12:21
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    $\begingroup$ I don't have enough knowledge about the Dawn mission, but I would recommend answers to address the uncertainty of the Ceres gravity field (and gravity is proportional to 1/r^2), the difference between stations keeping and attitude keeping (the former with an ion prop needs low thrust for several days, the latter short burst for momentum dumping to spin the wheels down), and hence (items 1&2) the likely impossibility of using the ion prop for attitude control when in orbit around a small body, but more possible when further way. (Great question by the way!) $\endgroup$ – ChrisR Jun 19 '17 at 19:44
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    $\begingroup$ @ChrisR Thanks! I can see you are appreciating the complexities of the current situation. The only thing I'd add is that I think it's the higher order multipole components of the gravity field that are the problem, not any uncertainty in the spherically symmetric (monopole) $GM/r^2$ part, and these would increase even more rapidly with decreasing distance. By now there should be more than plenty of precision in $GM_{Ceres}$. $\endgroup$ – uhoh Jun 20 '17 at 4:02
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There is one wheel still operable (at least it was operable the last time they operated it), but Dawn no longer uses it. The third wheel failure was in April of this year (2017 for those reading this answer thousands of years from now).

Yes, gravity tugging on the very long lever arms called solar panels is a significant driver on hydrazine usage, made much worse the lower the orbit is. (Tidal forces go as $1/r^3$ or higher powers of $r$, so the forces are a strong function of altitude.)

That hydrazine expenditure is mainly about attitude, not maintaining the orbit parameters. They do still use the ion engines to adjust the orbit. But that operation also consumes hydrazine to point the ion engines in the desired direction, and for roll control during the maneuver.

This blog post by Marc explains more about the reaction wheel situation. If you want to know more about the end-game hydrazine budget, you could try to email Marc with your questions. I'd wager that he'll answer since he loves to talk about this stuff. You can find his email on people.nasa.gov.

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  • $\begingroup$ The blog is really thorough and filled with goodies of insight, all "275,000 words posted." It will take a little time to read and digest it all. Thanks for your help! $\endgroup$ – uhoh Oct 29 '17 at 4:24
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I think that your guess addressing the decreasing with the orbital radius $(1/r)^n$, $n=3...\infty$ of the non spherical terms for the gravity potential are probably the clue to the problem. This effect increases when you are more close to the major body.

It would be of interest to analyze the eigenvalues of the rotational dynamics system. When considering vehicle shape one can find plots like this one enter image description here

This plot was generated using a spherical gravity model, but considering the assimetries in the orbiter. $k_1, k_3 = f(I_1, I_2, I_3)$, and eigenvalues are proportional to $\sqrt{\mu/a^3}$, so if we are in the unstable case the unstabilities grows faster when going closer to the central body. A similar analysis could be performed including a non spherical gravity field body.

More a comment than an answer. Nice question by the way.

EDIT: link to explanation video

https://es.coursera.org/learn/spacecraft-dynamics-kinetics/lecture/DAQum/3-gravity-gradient-linear-stability-about-equilibria

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  • $\begingroup$ Thanks for your answer! I had thought that the use of hydrazine was needed to switch between Earth-facing and nadir-facing orientations, or maintaining nadir-facing for a non-circular orbit, but I never stopped to think about torques directly on the spacecraft from the gravity field, so this is really helpful! Can you add a credit for this figure? Crediting original sources is always good in SE. Also if you can add a link to some place where I can read more about what $k_1, k_3 = f(I_1, I_2, I_3)$ means and maybe how to do some of the math? $\endgroup$ – uhoh Oct 27 '17 at 10:31
  • $\begingroup$ Well, to maintain nadir-facing in circular orbit you need to take into account your satellite inertia assimetries. As I have studied this is the first order term when attempting attitude station keeping. A stability analysis is useful since if the system if unstable you would need to waste more control action (e.g. RCS or reaction wheels) to keep pointing. However, I also agree with you that switches between Earth-facing and nadir-facing contribute as well to lower the control budget. $\endgroup$ – Julio Oct 27 '17 at 13:40
  • $\begingroup$ I have found a nice video explaining the subject here, with a slightly different notation (the figure I posted is from my old space vehicle dynamics courses which slides are in spanish) es.coursera.org/learn/spacecraft-dynamics-kinetics/lecture/… $\endgroup$ – Julio Oct 27 '17 at 13:42
  • $\begingroup$ OK this is really interesting! I will watch the video and do some reading now... $\endgroup$ – uhoh Oct 27 '17 at 14:50
  • $\begingroup$ I added a second bounty, wanted to thank you for being the first person to post an answer explaining what was going on. Lucky for you the SE interface requires each bounty to be larger than the previous one :-) $\endgroup$ – uhoh Oct 30 '17 at 4:48
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To answer the question about staying at Ceres or going somewhere else:

Dawn does not have enough Xenon propellant left to enter orbit around another asteroid. It can leave Ceres, but can only do a flyby after that.

The promising potential for observing Ceres in elliptical orbits from closer than ever before makes a second extended mission there extremely attractive. NASA and the panel of scientists and engineers convened to provide an independent, objective assessment concluded that further exploration of Ceres would be the most valuable assignment for the spacecraft. It is noteworthy that Dawn is the only spacecraft ever to orbit two extraterrestrial destinations and even now, having significantly exceeded its original objectives, has the capability to leave Ceres and pay a brief visit to a third (although it does not have enough xenon left to orbit a third), but the prospects for new discoveries at Ceres are too great to pass up.

For the second mission extension, NASA is looking at putting Dawn into an elliptical orbit that has a lower periapsis than previous orbits:

For several months, the flight team has been studying the feasibility of flying the spaceship closer to Ceres than had ever been seriously considered. Dawn spent more than eight months in 2015-2016 circling about 240 miles (385 kilometers) above the dwarf planet. It had spectacular views of mysterious landscapes and acquired a wealth of data far beyond what the team had anticipated. Then Dawn flew to a higher altitude during its first extended mission for new observations. Now engineers are making progress on ways to operate the spacecraft in an elliptical orbit that would allow it to swoop down to below 125 miles (200 kilometers) for a few minutes on each revolution. Their results so far are very encouraging.

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  • $\begingroup$ OK this is important information, and actually addresses the "Should I stay or should I go" directly! Can you add a link or citation where the block-quotes are coming from? I don't find this text in the links in my question. $\endgroup$ – uhoh Nov 5 '17 at 10:29
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    $\begingroup$ It's from one of this week's Planetary Society blog posts. planetary.org/blogs $\endgroup$ – Hobbes Nov 5 '17 at 11:03

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