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Dawn distance to Ceres ≈ distance to moon

  1. Jan 7, 2015 #1

    marcus

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    The average distance to the moon is about 1.28 light seconds.
    Today the Dawn probe is about 1.5 light seconds from Ceres.
    http://dawn.jpl.nasa.gov/mission/live_shots.asp

    Ceres diameter is about 1000 km, which means roughly 1/3 the size of the moon (diam = 3500 km)

    The Dawn spacecraft is beginning to get into the range of proximity where Ceres will begin to appear roughly comparable in size to how the moon looks from Earth. Not yet---at the moment it would look only a QUARTER as big, one fourth the angular size of the moon seen from Earth. But getting there.
     
    Last edited: Jan 7, 2015
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  3. Jan 7, 2015 #2

    marcus

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    Marc Rayman, chief engineer of Dawn mission has posted a journal entry for December 29
    http://dawnblog.jpl.nasa.gov
    which summarizes some interesting background on Ceres and what is known or conjectured so far. What stands out for me is that given its size and mass it could consist of roughly 30% water---and have the most water of any object in the inner solar system except for Earth. Escape velocity from Ceres surface is only 500 m/s making it comparatively easy to get on and off of.

    For comparison, Mars escape velocity is 5030 m/s, about TEN TIMES the speed, which means 100 times as much kinetic energy is involved in landing and taking off.

    That means Ceres has potential longterm historical importance as a vast (comparatively accessible) water resource if our species expands out from Earth and water continues to play a biologically and industrially important role. Rayman's latest journal piece is a fairly long essay covering a number of interesting topics. Here I will just quote a brief excerpt
    ==excerpt from Marc Rayman's 29 December journal==
    Ceres apparently formed far enough from the sun under conditions cool enough for it to hang on to water molecules. Indeed, scientists have good reason to believe that water (mostly in the form of ice) may make up an astonishing 30 percent of its mass. Ceres may contain more water than Mars or any other body in the inner solar system except Earth. (Comets, of course, have high proportions of water too, but they are so minuscule compared to this behemoth that each one harbors a quite negligible amount of water when measured against Ceres’ huge inventory.) Although some of the moons of the outer planets also are ice and rock, and they display very interesting characteristics to the impressive and capable spacecraft that have flown past (in some cases repeatedly, as the craft orbited the host planet), no probe has had the capability to linger in orbit around any of them. Dawn’s in-depth exploration of Ceres will yield more detailed and complete views than we have obtained of any icy moon. Radioactive elements incorporated into Ceres when it was forming would supply it with some heat, and its great bulk would provide thermal insulation, so it would take a very long time for the heat to escape into space. The sun, faraway though it is, adds still more heat. As a result, there may be some water warm enough to be liquid. (The concentration of any chemical impurities in the water that affect its freezing point, as salt does, may make an important difference in how much is liquid.) This distant, alien world may have lakes or even oceans of liquid water deep underground. What a fantastic possibility! There will be no liquid on the frigid surface. Even ice on the surface, exposed to the cold vacuum of space, would sublimate before long. But ice could be just beneath the surface, perhaps well less than a yard (a meter) deep. Ceres then may have a thin, dusty crust over a mantle rich in ice that might be more than 60 miles (100 kilometers) thick. Its warmer core is likely composed mostly of rock.
    ==endquote==
    Permanent link: http://dawnblog.jpl.nasa.gov/2014/12/29/dawn-journal-december-29/#more-1702
     
    Last edited: Jan 7, 2015
  4. Jan 8, 2015 #3

    marcus

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    fulltraj-4.jpg
    Today, for the first time, the Dawn craft is within 0.003 AU from Ceres. that is, it is less than 1.5 light seconds from goal.
    The actual figure they gave as of 8 January just now, when you googled "where is Dawn now?" is 0.002999 AU
    http://dawn.jpl.nasa.gov/mission/live_shots.asp
     
    Last edited: Jan 8, 2015
  5. Jan 9, 2015 #4
    www.space.com/22891-ceres-dwarf-planet.html

    Small solid rocky bodies have average densities of ~3 tons per cubic meter. Ceres is only 2.

    Mars has subsurface ice. Even our Moon does. And Ceres is colder still.

    Knowing nothing else, I suspect that Ceres has lots of ice, vaguely like Mars
     
  6. Jan 9, 2015 #5
    http://scitechdaily.com/scientists-find-evidence-previously-unrecognized-water-reservoir-mars/

    Rock has a density of ~3, ice ~1, Ceres ~2

    So the volume of ice shell equals the volume of the rocky core. That is, the total volume of Ceres is twice that of the core

    R^3~= 2r^3

    r ~= 0.8 R ~= 400 km

    According to this quick calculation, Ceres has a global glacial crust, like that of Mars, but ~100km thick

    A few more weeks and months will tell
     
  7. Jan 9, 2015 #6

    OmCheeto

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    Thanks for keeping us up to date Marcus!
    I've been looking for new images of Ceres, but can't seem to find any.
    So I just went through all of your Vesta threads. Very interesting. Those bands. Very strange. Graben?
    But very much anticipating the Ceres orbit.

    ps. Sorry about my newfound speech impediment. :redface:
    I've been perusing Twitter for the last two hours.
    I didn't start using Twitter until the Philae landing.
     
  8. Jan 10, 2015 #7

    marcus

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    I'm glad you mentioned the remarkable wrinkles running around the equator of Vesta, and the hypothesis that they might be "graben", or subsidence troughs resulting from the shock of a collision at the south pole. That space.com article by Choi is interesting. I hadn't seen it. BTW I haven't learned to use Twitter yet. I may have to in future. For time being I am glad you are (no joke) and that you might help keep us posted on whatever comes up as Dawn approaches Ceres. I am not likely to take up with Twitter any time soon, life being complicated enough already.
    The speech impediments at this end are home grown (not sure how Twitter could make them worse.)
    I'll copy your space.com link: http://www.space.com/17827-vesta-troughs-asteroid-collision.html
     
  9. Jan 10, 2015 #8

    marcus

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    To keep us up to date on the approach to Ceres. The ratio of diameters to the moon is about 1000 km to 3500 km. So Ceres is about 28% as wide as Earth's moon.

    The moon has an angular size of about half a degree. So we can estimate how big Ceres looks in the sky, seen from the spacecraft. The spacecraft is roughly as far from Ceres as we are from the moon so Ceres should look about 1/4 the size of the moon, and have an angular size of about 1/8 of a degree.

    they have an illustration at the "live shots" website that is a kind of "diagram" of how Ceres would look from the spacecraft. It is a grayish brownish dot in the center of a frame that is supposed to represent a 30 degree field of view. The dot is small at present---as 1/8 of a degree is small in a 30 degree field. If the diagram is 8 inches wide on your computer then the dot is about 1/30 of an inch----like a 32nd of an inch on some rulers.

    Over the next several weeks that dot will get bigger (if the public outreach people at Dawn office keep it current, and I think they will). More realistically, it should look like a half moon, with one illuminated hemisphere towards the sun, and one in shadow. Dawn is gradually overtaking Ceres along roughly the same orbit track. So it sees the "half-Ceres" phase. But the grey dot in the illustration is too small and schematic to show phases (at least so far).
     
  10. Jan 10, 2015 #9

    marcus

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    Hey! I just looked at today's http://dawn.jpl.nasa.gov/mission/live_shots.asp
    and today's view of Ceres from Dawn
    and I saw a crescent or half-Ceres phase in the small diagrammatic dot. They put in that detail. You may not be able to see it in this attachment
    but if you go to:
    http://neo.jpl.nasa.gov/orbits/fullview2.jpg [Broken]
    it is visible as a bright white sector of the otherwise dull mouse-colored dot in the center of the diagram. The mission outreach team is conscientiously keeping us informed about how the world looks from the vantage of their probe, down at the level of 1/32 of an inch details. :w
    The distance they give for today is 420,670 km and if I paste
    "420,670 km in light seconds" into google I get 1.40 light seconds.
    Moon's distance from Earth is 1.28 light seconds. So since the real size of Ceres is 28% of Moon,
    the current angular size of Ceres is
    28*1.28/1.40 = 25.6% of the angular size of the moon. At the moment.
    Here are two simulated views for comparison the second one is current.
    c10J.jpg
    .
    http://neo.jpl.nasa.gov/orbits/fullview2.jpg [Broken]
     
    Last edited by a moderator: May 7, 2017
  11. Jan 10, 2015 #10

    OmCheeto

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    Those are all marked, "simulated view". :oldgrumpy:

    ps. Why is it that @Dennis Roscoe can capture Hubble quality intergalactic images, but Hubble can't take a good picture of Ceres?

    I can only come up with PF, unapproved, conspiratorial theories:
    1. Hubble saw the picket signs, and the government sequestered them.
    2. Moby was receiving signals from the Cerians. Hence, why we haven't heard his music, for a long, long, time........​



    I would imagine that creatures from a Ceres sized planet would be tiny. But I'm not an exobiologist, nor even a biologist, so please, don't listen to me.
     
  12. Jan 11, 2015 #11

    marcus

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    Distance down to 1.346 light seconds. Enjoyed the droll movie about aliens :) I can't picture what Ceresians would evolve to be. Maybe they are just trees anyway.

    In the simulated view of Ceres, from a position beside the spacecraft, the sunwards direction seems to be DOWN as the picture frame is presented. The bright-lit hemisphere of the planet is down, and maybe a little to the left.

    I guess that could make sense, with the solar panels spread out nearly horizontal (but the simulation may not be trying for detailed realism.)

    1.346 cs is near 1.28 cs the distance from us of the moon. As mentioned earlier, the real width of Ceres is about 28% of the moon's. So at the same distance it would look 28% as big in the sky.

    About how it looks now, I'd guess, since the distance is nearly the same. Wish we could fast forward, I'm eager to see the real thing :)
     
    Last edited: Jan 11, 2015
  13. Jan 11, 2015 #12

    marcus

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    In this picture the original approach trajectory plan is in red. After an brief thruster outage in September 2014, a longer approach was planned shown in green. You can see the red trajectory comes in already at a slower speed (day circles closer together) is captured sooner and spirals in to the target orbit in only a few days. The green trajectory comes in at faster speed (day circles farther apart) and OVERSHOOTS. It then kind of stalls and hangs there in a hairpin turn, with many day circles close together and then falls back towards Ceres and spirals in.
    They are conserving their hydrazine resource which must be used to orient the ship because two gyro wheels can't be used. The main thrust is always the solar electric xenon ion beam (shown as blue green tail in some of the illustrations). Hydrazine is used for orienting the crafts attitude.
    I'll try to find out more about what went into replotting the approach trajectory.

    appro.jpg

    In the diagram, the sun is far to the left. Ceres orbital motion is directly IN TO THE PICTURE. The spacecraft is running roughly parallel to Ceres in orbit, but slightly closer to the sun. So since the sunward direction is to the left, craft is shown as coming in towards Ceres from the left.
    It is also like Ceres, in orbit around the sun, so it is also moving into the picture frame.
    This illustration is from http://dawnblog.jpl.nasa.gov/2014/11/28/dawn-journal-november-28/
    where there are more diagrams and explanations.
     
    Last edited: Jan 15, 2015
  14. Jan 11, 2015 #13

    marcus

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    http://en.wikipedia.org/wiki/Dawn_(spacecraft)
    http://dawn.jpl.nasa.gov/mission/ion_prop.asp
    In case anyone is interested Dawn has 3 ion thrusters each of which develops 90 mN
    or about 1/10 newton of thrust. They are being used alternately, one at a time (according to the account I've read) and are mounted on gimbals so they can adjust attitude.
    The "specific impulse" listed is 3100 seconds. Meaning that using an amount propellant mass which would weigh one Newton in earth gravity can deliver an amount of momentum which is 3100 Newton seconds. This is better than chemical propellants by roughly a factor of 10.

    When Dawn was at Vesta the first (to me) interesting pictures came when it was within 150,000 km and that was still quite blurry. What I think of as sharp pictures came in at 50,000 km.
    Eventually Dawn got into a close orbit where it was within 250 km or so of the surface.
    I saw something recently that suggested Dawn might take a picture or so on 13 January, which is Tuesday. But I wouldn't count on it. They have to be free to change plans in order to conserve propellant and attitude-control.
    In any case the craft is still more than a light second from Ceres, more than 300,000 km. At that distance judging from the Vesta pictures, the image would not be especially informative (or so it seems to me).

    Something kind of interesting is that having some thrust turned on helps reduce vibration and waggling. It helps stabilize the craft and makes for better photographs. It is a handicap that two of their gyro wheels have gone out. They plan to use the ion thrusters to keep a gentle force on the craft while they are taking pictures.

    Actually I have a big respect for the Dawn team. They are resourceful and making do very well with what they've got. Their craft was launched in September 2007, if I remember right. It has been on the road over 7 years and is still running.
     
    Last edited: Jan 15, 2015
  15. Jan 15, 2015 #14

    marcus

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    It is interesting how planet physics people have estimated the mass, density, differentiation (crust, mantel, core) of Ceres. This is important because it leads to the hypothesis of a ~100 km thick mantel layer that is largely water ice.
    Mass was determined by observing NEAR ENCOUNTERS with much smaller objects in the asteroid belt.
    Here is a sample paper of that type:
    http://www.doiserbia.nb.rs/img/doi/1450-698X/2005/1450-698X0571037K.pdf
    The roundish oblate spheroid figure---the equatorial diameter is larger than the polar diameter---was measured rather precisely by Hubble Space Telescope
    http://arxiv.org/abs/0711.1152
    Equatorial radius 479.7 km and polar radius 444.4
    The rotation period (9 hours) was determined using HST by observing surface features.

    The same rate of rotation will produce MORE oblateness in an homogeneous body than if the body differentiated into layers, because the differentiated body has more of its mass in the central core and a smaller moment-of-inertia. The homogeneous body has mass distributed radially farther out, so will tend to become more flattened by rotation

    Ceres mass was estimated at around 4.76 x 10-10 solar masses.

    This led to an estimate of density of about 2.2 g/cc, roughly twice that of water. But silicate rock density is about 3.5 g/cc. So it is hypothesized that Ceres is a mixture of rock and water ice.
    However it is not FLATTENED enough by rotation to indicate that the mix is homogenous. It is hypothesized (because of its nearly spherical shape) to be differentiated into core mantel and crust.

    For extra detail I will quote from the November 2007 paper:
    ==quote http://arxiv.org/abs/0711.1152 ==
    Adopting a mass for Ceres of M = 9.43 ± 0.07 × 1020 kg (average of most recent measurements [Viateau & Rapaport, 1998; Michalak, 2000; Kovacevic & Kuzmanoski, 2007]), we find a mean density ρ = 2 206 ± 43 kg.m−3. This value is relatively high for a hydrated G-type asteroid like Ceres, but can be explained by a low porosity [see Britt et al., 2002], and is similar to the density of the icy outer Jovian satellites Ganymede and Callisto.
    ==endquote==
     
    Last edited: Jan 15, 2015
  16. Jan 15, 2015 #15

    marcus

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    There's some good information in earlier entries in the Dawn journal (kept by mission director Marc Rayman)
    http://dawn.jpl.nasa.gov/mission/journal.asp

    http://dawnblog.jpl.nasa.gov/2014/01/31/january-2014-dawn-journal/ (basics of getting into orbit, first observational orbit around Ceres will be polar at altitude of 13,500 km (above surface).
    http://dawnblog.jpl.nasa.gov/2014/02/28/dawn-journal-february-28-2014/ (more detail about this orbit, called RC3, what observations will be made at this altitude)
    http://dawnblog.jpl.nasa.gov/2014/04/30/dawn-journal-april-30-2/
    Then the plan is to spiral down to orbits closer to the surface. Here's a quote:
    ==quote==
    The first coils around Ceres will be long and slow. After completing its investigations in RC3, the probe will spiral down to “survey orbit,” about... 4,400 kilometers above the surface. During that month-long descent, it will make only about five revolutions. After three weeks surveying Ceres from that new vantage point, Dawn will follow a tighter spiral down to the ... high altitude mapping orbit (HAMO) at ...1,470 kilometers. In the six-week trip to HAMO, the craft will wind around almost 30 times. It will devote two months to performing extensive observations in HAMO. And finally as 2015 draws to a close, it will fly an even more tightly wound course to reach its low altitude mapping orbit (LAMO) at ... 375 kilometers, where it will collect data until the end of the mission. The ship will loop around 160 times during the two months to go from HAMO to LAMO. (We will preview the plans for survey orbit, HAMO and LAMO in May, July and August of this year, and if all goes well, we will describe the results in 2015 and 2016.)
    ==endquote==
    http://dawnblog.jpl.nasa.gov/2014/10/31/dawn-journal-october-31/ (story of tense days in Sept 2014 when a cosmic ray knocked out the #1 thruster and the main antenna drifted out of alignment. The team struggled to restore full communication, recover normal operation, and reconfigure trajectory so as not to miss Ceres)
     
    Last edited: Jan 15, 2015
  17. Jan 15, 2015 #16

    marcus

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    The Dawn "live shots" page gives the current distance to Ceres as 349.88 thousand km. If I type 349.88 megameter into google, I get:
    "349.88 megameters = 1.16707406 light seconds"

    My goodness, google calculator understands the word "megameter"!

    Anyway, Dawn is now 1.17 light seconds from her destination, considerably CLOSER than we are to the moon, which is 1.28 light seconds on average.
     
  18. Jan 15, 2015 #17

    OmCheeto

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    I also noticed that Dawn is slowing down. On the snapshot you took on the 10th, it was traveling at 0.16 km/sec. It is now traveling at 0.15 km/sec.

    I discovered yesterday that Dawn will start orbiting at 13,500 km, then over several months, it will descend to 3 more orbital heights: 4430, 1480, & 375 km.
    ref: http://dawnblog.jpl.nasa.gov/2014/08/31/dawn-journal-august-31/

    I doodled these distances relative to the size of dawn, but still had trouble visualizing what Ceres would look like, so I dug around the house, and found a baseball.
    At its lowest orbit, it's the equivalent to looking at a baseball 1 inch in front of your eye.
    That seemed a bit close, so I calculated the ISS orbital height in terms of baseball scale, and discovered that it orbits only 2.3 mm above the earth/baseball surface.
    At which point, I took off my glasses, and poked myself in the eye, with my baseball.

    The baseball turned out to be a good choice, as Dawn's equivalent distance to Ceres yesterday was about 100 feet, which is just 10 feet short of my property line as measured from the street. It's also closing in on Ceres at about 3 feet per day, and will catch up in about 27 days.

    ceres.2015.dawn.png
    planned orbital distances​

    According to Dawn's twitter account yesterday, a picture is going to be taken this week, and published on the 20th.
    https://twitter.com/NASA_Dawn
     
    Last edited: Jan 15, 2015
  19. Jan 16, 2015 #18
    Using numbers from Wikipedia, earth's break up rotation period would be about 13 minutes, whereas less dense Ceres would break up at a 22 minute spin period

    So the ratio of actual spin period to break up rate is almost 5x higher for earth, meaning Ceres is in some sense spinning 5x "relatively faster" or something else like that
     
  20. Jan 16, 2015 #19
    Earth has a flattering ratio of 1.00335

    Ceres' is 1.0717

    So the deviation from 1 is about 22x higher for the asteroid

    That happens to be the square of the relative rotation rate ratio

    I think that means that the flattening ratio is basically equal to the ratio of centrifugal force to gravitational force

    That might mean something significant
     
  21. Jan 16, 2015 #20

    marcus

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    Interesting comparisons! Please consider including some Wikipedia links about how the "breakup rotation rate is calculated and/or how the flattening ratio is calculated. It would save others (like myself) the bother of hunting. I can be remarkably lazy about hunting for stuff and being given a link can sometimes make a difference.

    TEFL, I would guess that the overall density makes quite a difference. Earth density is about 5 g/cc, if I remember right. And Ceres is about 2 g/cc. It would seem to me that the denser body would have an easier time holding together, because more compact.

    Also with differentiated bodies (crust, mantel, core) it would make a difference what the ratio of densities between mantel and core is. If the mantel is water ice and the core is silicate rock, then the ratio is 1: 3.5
    On the other hand if the mantel is rock (say 3.5) and the core is iron (say 8) then the ratio is 3.5 : 8
    those aren't realistic numbers---just picked for illustration. Other things (like overall density) being equal I would guess that more pronounced differentiation, a greater difference in density, makes it easier to hold together. And reduces flattening.

    I'm not familiar with these concepts, but I like very much that by observing overall density and flattening they've been able to deduce something about the differentiation.
    Thanks for helping me get a quantitative handle on this!
     
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