One plan becomes two plans

Editor's note: Those who have been following our blog will know that the MEX Flight Control Team at ESOC have been actively preparing for the flyby of comet C/2013 A1/Siding Spring on 19 October. Initial estimates gave the possibility that Mars Express might have to contend with a large particle flux – and that several (2? 3?) very high-speed (~56 km/sec!) particles might bash into the spacecraft. Happily, additional observations by ground and space telescopes (including the ESA/NASA Hubble Space Telescope) have allowed initial estimates to be refined and the risk is now understood to be much lower – and perhaps even as low as zero. In today's blog post, the team explain how this (happy!) real-life, real-time development is affecting their preparations for fly-by.

Comet C/2013 A1 Siding Spring seen on 6 September 2014 from Argentina. Image credit: César Nicolás Fornari https://www.facebook.com/cesar.fornari

Comet C/2013 A1 Siding Spring seen on 6 September 2014 from Argentina. Image credit: César Nicolás Fornari https://www.facebook.com/cesar.fornari

Late last year, estimates given in scientific papers estimated that over the duration of the encounter, the number of large cometary particles per square metre would be around 1. As MEX’s area in the most protected attitude is about 3m2, we could then expect about 3 potentially significant impacts. Not good!

By the middle of this summer, published estimates (based on new images and additional modelling) were indicating a flux of around 10-6 particles per m2, which, for Mars Express, very roughly equates to a 1-in-300,000 chance of being hit. It's starting to look like our comet C/2013 A1/Siding Spring will manifest itself as a more friendly passer-by than initially thought and that it won't be hurling clouds of large particles at unthinkable speeds towards Mars and its man-made satellites.

Closest approach: If Mars were Earth. Credit: NASA/JPL

Closest approach: If Mars were Earth. Credit: NASA/JPL

So why the big change?

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Mars and Moon seen together

Today's post was contributed by Michael Khan, who blogs on all things spacey over at Scilogs.de. He's contributed updates to several ESA blogs in the past.

This summer is bringing some interesting Mars observation opportunities.

Nothing as mundane as a mere 'encounter' between our Moon and Mars was included in those suggestions, but such encounters do occur, and they do constitute great photo ops for astrophotographers. Case in point: 7 June, when only a few degrees separated the Red Planet and Earth's companion. (Keep in mind that we are talking about apparent encounters here: the Moon and Mars appear to be in the same location of the sky, but of course, at all times, Mars will be at least 53 millions and sometimes 400 million kilometres distant). 

This particular encounter was not all that close – about two and a half degrees, or five times the apparent size the Moon. But it definitely looked close, and it was a pretty sight too. The tiny reddish orb contrasted very nicely with the Moon's grey bulk. 

For every type of observation, there is an ideal telescope. If a large field of view is required, the focal distance must be short. Such a telescope can be surprisingly compact, as this 2-inch, 330-mm refractor demonstrates.

For every type of observation, there is an ideal telescope. If a large field of view is required, the focal distance must be short. Such a telescope can be surprisingly compact, as this 2-inch, 330-mm refractor demonstrates.

You need a telescope with a short focal length and therefore a wide field of view to see both objects. Anything less than 400 mm works. Some astronomers regard such telescopes as mere toys, of use perhaps as a finder scope. But there are times where they are handy. This was one such instance. You can attach your camera to the telescope via an adapter, thus using the telescope like a telephoto lens. Alternatively, if you have a good telephoto lens, you might just as well use that. 

The trick is to find an exposure time that will do both bodies justice, once you have your gear in focus and pointing in the right direction. You can take off the camera and enjoy the scene with an eyepiece. No problem there – the human eye can process enormous differences in contrast. But digital cameras can't. Try a short exposure time and the Moon will come out all right but Mars will be so faint that you can barely see it; certainly you won't be able to see its colour. Then try a long exposure time (no too long or your image will be blurred) and Mars will come out nice and red but the Moon will appear a white blob, drowning out its surroundings.

In the end, you may find that getting a satisfactory picture (one that resembles what you just saw through the eyepiece), requires some cheating. Take two images – the first with a short exposure time, so the Moon looks right and the second with a longer exposure time, for Mars. Then you load both into an image processing tool on your computer (nowadays, very powerful software is available as freeware, choose the one you prefer), cut the area around Mars out of image 2 and paste it at the appropriate location in image 1. Make sure the background colours are right so one can't see where the pasting took place. 

That's all there is to it. It's not really cheating as long as you took both images yourself and as long as you don't hide the fact that this is a composite image. The people who make those pictures for the glossy magazines cheat a lot more than that. Anyway. What you should easily get is something like what I got, or better:

Moon and Mars seen over Darmstadt on 7 June 2014 at 22:18 CEST (composite). Telescope: 50/330 ED-Doublet TSED503 || Camera: Canon EOS 600D, ISO 800 || Moon aperture: 1/640 s || Mars aperture: 1/125s - Credit: Michael Khan

Moon and Mars seen over Darmstadt on 7 June 2014 at 22:18 CEST (composite). Telescope: 50/330 ED-Doublet TSED503 || Camera: Canon EOS 600D, ISO 800 || Moon exposure: 1/640 s || Mars exposure: 1/125s - Credit: Michael Khan

The telescope I used is a small refractor (it uses lenses, not mirrors) with a focal length of 330 mm and an aperture of 50 mm. The camera was a standard retail Canon 600D. The camera is attached directly to the telescope with a special adapter called a 'T2-ring' and then the telescope is mounted onto a sturdy tripod. With an ISO setting of 800, the Moon image was exposed at 1/640 s, the Mars image at 1/125 s. That's very much like standard photography. No extremely long exposure times required. 

Anyone who can take a picture with a DSLR can do this. So, what are you waiting for? Go out at night. Take pictures. Just do it!

Listening to Syzygy from a garden in France

This morning – Bertrand Pinel, a keen amateur radio-astronomer who's shared his work with us before – was awake to listen to Phobos making is Syzygy occultation of Mars Express.

Bertrand Pinel's 3.5m backyard antenna. Image credit: B. Pinel

Bertrand Pinel's 3.5m backyard antenna. Image credit: B. Pinel

At 01:11 UT (03:11 CEST), Mars Express was occulted by tiny Phobos, a roughly potato-shaped body measuring 27 km across its longest axis and 18 km across its shortest.

Bertrand (the same gentleman who gave us the Phobos sound recording) captured the drop in signal (as Phobos blocked the direct line of sight between MEX and Earth) using his own radio dish antenna in his garden in France. Some screen shots are included below from his signal processing equipment – you can see the gap and the times of occultation.

MEX-Phobos occultation Credit: Bertrand Pinel

MEX-Phobos occultation Credit: Bertrand Pinel

Thanks, Bertrand, for sharing!

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Mars Express, Phobos and the occult … ation

Today's post contributed by Michael Khan, a mission analyst at ESOC and an avid amateur astronomer – Ed.

Imagine you're playing Scrabble. The tiles on your rack don't look as if there is much you could do with them. No vowels. Three 'Y's, a 'Z', and a 'G'. Oh no! You might as well pass and exchange all tiles for new ones, Right?

You think you're good at online Scrabble? Well, I just put "syzygy" on the board - see if you can beat that! Credit: E. Yourdon CC BY-NC-SA

You think you're good at online Scrabble? Well, I just put "syzygy" on the board - see if you can beat that! Credit: E. Yourdon CC BY-NC-SA

Wrong! (Don't quit yet!)

Just look for a letter 'S' somewhere on the game board and you can append five of your tiles to spell the word SYZYGY (preferably such that it covers a triple word score). Thus you get rid of the 'Z' and the 'Y's and you earn heaps of points. There will be complaints around the table, but you can relax and let them complain: You really cleaned their clocks with this one. You win!

In astronomy, a syzygy defines a situation where at least three bodies are aligned. Eclipses, such as the 15 April lunar eclipse, are a perfect example of a syzygy in action.

Via Flickr E. Yourdon

In spacecraft operations, syzygies abound, and our Mars Express is no exception. Often, they are regarded as an unavoidable nuisance. When the spacecraft passes through the shadow of Mars and has to run on batteries, that is a syzygy of Mars Express, Mars and the Sun. When MEX is occulted by Mars and communications are interrupted, that is a syzygy of MEX, Mars and the Earth.

Other syzygies, however, offer real science opportunities. Stellar occultations by bodies in the Solar System have led to very important scientific discoveries.

To name but a few:

Fabulous view of Mars 15 May 2014

Today's post contributed by Michael Khan at ESOC. UPDATED 8.04 – corrected date for Mars & Spica to 17.07, and fixed several minor typos  – Ed.

Once again, it's opposition time. While the Earth requires one year1 to complete a full revolution, a Mars year, due to the planet's wider orbit, lasts 687 days. As Earth and Mars are plying their separate orbits with different speeds, the distance between each varies considerably with time. But once in a period of just over two years, they are aligned in what astronomers call an opposition. On that date, seen from Earth, Mars is located almost exactly in the direction opposite from the Sun, so stargazers can see the Red Planet high in the sky at midnight, and closer and brighter than at any other time.

Earth-Mars distance

The distance from Earth to Mars during the years 2000 to 2019

Because the Mars orbit is eccentric (i.e., it is elongated rather than circular), not all oppositions are equal. Many of you will remember the one in the autumn of 2003, when Mars approached Earth to as close as 56 million kilometres. It appeared like a surprisingly bright red star. In 2014, opposition will take place on 8 April, but again because of the eccentricity of the orbits, closest approach will in fact be a few days later, on 14 April. The distance from the Blue to the Red Planet will then be 92 million kilometres – two-thirds more distant than in 2003, so Mars will appear only a third as bright as it did 11 years ago.

Admittedly, observing Mars in the night sky is a lot less spectacular than it was, and it will again be, as soon as the year 2018. But still, you should have a look. It's impossible to miss, all the more so because right now it is close to the star Spica in Virgo; Spica is special, because it is in fact not one, but two stars – and big ones at that – that are orbiting a common centre of mass at very close quarters. Spica is interesting, it's massive, it's bright... and it's blue! So you currently have the brilliant blue Spica and the brilliant red Mars both in approximately the same direction in the sky.

Surely you don't need any more coaxing than that to get you to do some stargazing  – or do you? All right then... let's see which celestial bodies Mars will encounter in the course of the year. (Of course, we are talking about apparent encounters only, where the bodies involved appear to be separated by only a small angle. In terms of actual spatial distance, the distances will still be 'astronomical', with the exception of comet C/2013 A1 Siding Spring, which will buzz Mars on 19 October 2014. But as avid readers of our blog, you already know that).

Here is a list of star parties to which Mars has been invited this year. You are welcome to join – no need to feel like a gate crasher. All these events will be easily visible to the human eye. Using a pair of binoculars or a telescope is optional, but not mandatory.

On 14 April, the full Moon encounters Mars and Spica

On 14 April, the full Moon encounters Mars and Spica

This is an easy one for starters. And what's more, it happens on the day, 14 April, when Mars is closest to the Earth. Directly in the south around midnight (all times in the star charts below are given in GMT) the full Moon will intrude between Mars and Spica.

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Comet Siding Spring flyby cancelled?

In the closing weeks of March, astronomers worldwide were surprised to see a sudden increase in brightness for comet C/2013 A1 (Siding Spring). At the same time, try as they might, it was not possible to detect even the remnant of a nucleus in the rapidly expanding cloud of dust that had replace the previously still very small tail.

Is this a comet breaking apart? Credit: NASA, ESA, H. Weaver (APL/JHU), M. Mutchler and Z. Levay (STScI)

Is this a comet breaking apart? Credit: NASA, ESA, H. Weaver (APL/JHU), M. Mutchler and Z. Levay (STScI)

At the same time, the control team in Baikonistan reported that contact was lost with the Uranus-bound international spacecraft Behemoth, the first truly global attempt to explore our Solar System.

Aptly named, this spacecraft was launched three years ago, and – with a mass over 100 tons – is easily the largest (not to mention most expensive) space probe ever built. One moment it was still transmitting, the next moment it wasn't.

All efforts to re-establish contact with Behemoth have, alas, turned out to be fruitless. However, astronomers and engineers mapping the paths in space of the vessel and comet Siding Spring believe the trajectories may have intersected at a fateful point still far beyond Mars orbit. We may never know – but the laws of probabilities lead us to conclude that Siding Spring's sudden brightening and the equally sudden silence of Behemoth are not unrelated.

However, every cloud has a silver lining, as the saying goes. Astronomers have informed the Mars Express control team that due to the apparent disintegration of comet C/2013 A1 (Siding Spring), its potentially dramatic encounter with Mars on 19 October 2014 is therefore called off and all preparations for the event can cease, as no preventive measures will now be required. In fact, the MEX team have all headed off to the pub for a jolly celebration...

Click on 'Continue reading' to access the full story.

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Cosmic bully spotted by ESA and NASA

There are some great new Hubble images of our 'friend', Comet Siding Spring, due to pass by Mars at less than 136 000 km on 19 October – less than half the distance between Earth and our moon.

Comet Siding Spring imaged by ESA/NASA Hubble. Credit: NASA, ESA, and J.-Y. Li (Planetary Science Institute)

Comet Siding Spring imaged by ESA/NASA Hubble. Credit: NASA, ESA, and J.-Y. Li (Planetary Science Institute)

The passage of the comet may affect spacecraft in orbit around Mars, including ESA's Mars Express.

The image on the left above, captured 11 March by the NASA/ESA Hubble Space Telescope, shows comet C/2013 A1, also called Siding Spring, at a distance of 568 million km from Earth. Hubble can't see Siding Spring's icy nucleus because of its diminutive size. The nucleus is surrounded by a glowing dust cloud, or COMA, that measures roughly 19 000 km across.

The right image shows the comet after image processing techniques were applied to remove the hazy glow of the coma revealing what appear to be two jets of dust coming off the location of the nucleus in opposite directions. This observation should allow astronomers to measure the direction of the nucleus’s pole, and axis of rotation.

Hubble also observed Siding Spring on 21 January as Earth was crossing its orbital plane, which is the path the comet takes as it orbits the Sun. This positioning of the two bodies allowed astronomers to determine the speed of the dust coming off the nucleus.

"This is critical information that we need to determine whether, and to what degree, dust grains in the coma of the comet will impact Mars and spacecraft in the vicinity of Mars," said Jian-Yang Li of the Planetary Science Institute in Tucson, Arizona.

Compass and Scale Image for Comet C/2013 A1 Siding Spring (3 Epochs)

Compass and Scale Image for Comet C/2013 A1 Siding Spring (3 Epochs)
Source: Hubblesite.org

The image above shows a series of HST pictures of comet C/2013 A1 Siding Spring as observed on 29 October 2013, 21 January 2014 and 11 March 2014. The distances from Earth were, respectively, 605 million km, 552 million km, and 568 million km. The solid icy nucleus is too small to be resolved by Hubble, but it lies at the center of a dusty coma that is roughly 19 000 km across in these images.

When the glow of the coma is subtracted through image processing, which incorporates a smooth model of the coma's light distribution, Hubble resolves what appear to be two jets of dust coming off the nucleus in opposite directions. The jets have persisted through the three Hubble visits, with their directions in the sky nearly unchanged. These visible-light images were taken with Hubble's Wide Field Camera 3.

Discovered in January 2013 by Robert H. McNaught at Siding Spring Observatory, Australia, the comet is falling toward the Sun along a roughly 1-million-year orbit and is now within the radius of Jupiter's orbit. The comet will make its closest approach to our Sun on 25 October at a distance of 209 million km – well outside of Earth's orbit. The comet is not expected to become bright enough to be seen by the naked eye.

The Hubble Space Telescope is a project of international cooperation between NASA and the European Space Agency. NASA's Goddard Space Flight Center in Greenbelt, Md., manages the telescope. The Space Telescope Science Institute (STScI) in Baltimore conducts Hubble science operations. STScI is operated for NASA by the Association of Universities for Research in Astronomy, Inc., in Washington.

How to hide behind a planet

Remember those raging snowball battles you had as a child in the school yard, during recess? The best strategy, if you were in the thick of it, is to hide behind something (or someone) massive – such as a tree – or another guy on your team. The fatter the guy, the more protection he offered.

Snowball fight on the National Mall, Washington, DC. Credit: CC by-nc-sa/2.0/Joe Newman http://www.cosmicsmudge.com

Snowball fight on the National Mall, Washington, DC. Credit: CC by-nc-sa/2.0/Joe Newman http://www.cosmicsmudge.com

Ah, those were the days... alas, long past. Or are they?

In fact, the situation we are preparing for now, or at least the situation our spacecraft is going to face on 19 October, isn't all that different from the snowball fights of yore, at least in principle. Well, it is true that any cometary dust particles that might have MEX's name on them are likely to be microscopic. On the other hand, they will be travelling at 56 km/s and at that speeds, even microscopic dust can pack a hefty punch.

There are no trees in the immediate vicinity of Mars Express, but there is a rather 'fat guy' to hide behind – one with a diameter of almost 6800 kilometres. That's planet Mars, of course. The orbit of Mars Express around the planet is polar, it is eccentric (during every orbital revolution, which lasts 7 hours, the spacecraft passes as close as 350 km at the lowest point of the orbit (periares, in astronomers' parlance) and as far as 10 500 km at the highest point (apoares) above the Martian surface.

The fundamental laws of celestial mechanics cannot be infringed – not even a tiny little bit and not even in an emergency or when no one is looking – dictate that MEX moves much faster at periares than it does at apoares. Other more complicated laws of physics dictate that a spacecraft orbit is not immutable: its orientation in space and also its shape are subject to variations due to external forces, known as perturbations. Some of these variations in the orbital parameters are periodic, some are not, and you can't do much about them.

You might fight them – for a time – by using the rocket engines aboard the spacecraft and the propellant in its tanks, but that will be effective only if you have lots of propellant – precisely the one thing that Mars Express does not have. Our arrival at Mars and positioning onto the spacecraft's science orbit used up 90% of the fuel that was on board. After all, the spacecraft was designed for a two-year mission and it has been at Mars for more than 10. This gain in mission duration is thanks largely to the skill and ingenuity of the Flight Dynamics team in making the spacecraft perform the observations that the science team required with the least possible fuel expenditure.

By 19 October, the evolution of the orbit will be such that when viewed from the direction from which the comet will be arriving (we know this direction quite accurately and can therefore simulate the encounter with a computer), it will look like in the image below. This shows where the spacecraft would be on its orbit if we did nothing.

Mars Express zipping behind Mars

Mars Express zipping behind Mars

The closest encounter takes place at 18:30. This is when we expect the concentration of mostly microscopic particles of comet dust to be greatest. About an hour and a half later, Mars will pass through the orbital plane of the comet. That's where we foresee the highest risk of being hit by larger particles. Once again, there is a trade-off as the larger particles carry more energy but there are fewer of them. Let’s assume that the danger is greatest at closest approach (although as mentioned in a previous post, more observations are still needed to improve our models of what to expect in the encounter).

The approaching comet would see MEX pass behind Mars just after 16:30, and it would reappear about half an hour later. It so happens that the time when the spacecraft is behind Mars (and therefore protected from the dust that accompanies the comet) coincides with periares. If you recall, that is when it is also moving fastest on its orbit. The fact that the spacecraft is behind Mars for only half an hour, while the passage through the dust tail is likely to last a few hours, means that this alone is not a (full) answer to our problem of how to endure passing through a comet coma. It does, however, provide a short respite from exposure to potentially damaging particles.

There is one thing we can change, however. Note that if we do nothing, then at 18:30, at the closest encounter, MEX would be in the open, far from any protection. We can at least change the time of periares such that it occurs at 18:30, not 16:41. Though we can change neither the shape nor the orientation of the orbit, we can change this one parameter. And it will cost only very little propellant.

In essence, what we need to do is to delay the spacecraft passage behind Mars by 109 minutes. That sounds like a major task, and it is, if you try to do it just shortly before the comet is there. But we won't wait until then.

We plan to do a manoeuvre using the MEX engine already several months in advance. We can cut this delay to, for example, 109 slices of 60 seconds each. If we increase the orbital period by this 60 seconds, then 109 orbits later we have accumulated exactly 109 minutes of delay and MEX will be behind Mars when the snowballs hail down – or rather, when the onslaught of cometary dust is expected to peak.

We could also split the delay into 218 slices of 30 seconds, or 327 slices of 20 seconds, and so on. The important part is that the earlier the change is made, the more revolutions are available and so the smaller the change needed and hence the smaller the fuel consumption.

How do we delay the arrival of a spacecraft at a given position?

You won't believe this – it's done by increasing the orbital velocity. Nobody ever said that celestial mechanics was intuitive, right? You know that MEX’s orbit is an ellipse. Draw a line between the closest and the farthest point from Mars and you have the major axis; divide that by two and you have the semi-major axis. Every orbit represents a large amount of energy (that's why it takes a big rocket to launch something into orbit).

The orbital period (the time it takes to complete one revolution) depends on the orbital energy around a given planet (here Mars), and on nothing else. The orbital energy in turn depends on the size of the semi-major axis, and on nothing else. The larger the semi-major axis, the higher the orbital energy, the longer the orbital period.

Now, if you speed up a spacecraft, you add orbital energy, and therefore, inevitably, you increase its orbital period. This is a simple physical fact, and we are going to make use of it to maximize the chances MEX has of weathering the encounter with Comet Siding Spring.

We can't break the laws of physics but we can, and will, use physics to our advantage.

Ya gotta have a little ‘tude

This week's report on how the Mars Express flight control team is planning to deal with Comet Siding Spring is all about attitude – Ed.

We have now finalised our choice for spacecraft attitude through the comet encounter. As we’re sure many of you have also worked out, our chosen attitude is with the High Gain Antenna (HGA) facing the comet.

Mars Express in orbit around Mars. Credit: ESA/AOES Medialab

Mars Express - spacecraft directions

This was identified early on as a likely attitude as there are no internal components mounted directly on the front wall, plus the HGA should act as an improvised Whipple shield.

 

 

I'm in control, my worries are few
'Cause I've got love like I never knew
Ooo, ooo, ooo, ooo, ooo
I got a new attitude

– Patti Labelle, 'New Attitude'

It is not perfect, however, as there are still several components in the 'firing line' of cometary dust particles. All antennas will be facing the incoming dust particles, but one or two holes in the parabolic reflector dish of the HGA shouldn’t prevent it from functioning. The ASPERA instrument is also exposed, as is the forward Sun Acquisition Sensor (SAS) and two of the thruster pairs.

This diagram shows the major components in the spacecraft body. Credit: ESA

This diagram shows the major components in the spacecraft body. Credit: ESA

As the angle between the comet and the Sun will be around 89°, we also had to decide which of the faces (i.e sides of the spacecraft) should point towards the Sun.

As the solar panels are mounted on the left and right sides, if they were pointed at the Sun only the array on the side facing the Sun would be illuminated – and only on its end, so Mars Express would not be able to rely on solar power. The batteries are not able to support this configuration sufficiently long (up to 10 hours).

Pointing the top surface – where the instruments are located  – toward the Sun is generally not a good idea, but pointing the base – where the thrusters are – toward the Sun does not cause any problem (see our diagramme of MEX sides here  – Ed.).

Actually, this would provide some extra heat to the spacecraft fuel tanks and lines so we can save some power by not needing to use the on-board heaters as often. This angle also works out well for our solar arrays. They can still be facing the Sun (for full power) and yet lie edge-on to the expected particle 'flux' (stream of incoming particles), therby presenting the smallest target.

Mars Express with the solar arrays edge on - as they are only 20mm thick they had to be drawn larger to even be visible in this picture

Mars Express with the solar arrays edge on - as they are only 20mm thick they had to be drawn larger to even be visible in this picture

Mars Express with the solar arrays face on - the change in area is dramatic"

Mars Express with the solar arrays face on - the change in area is dramatic

 

So now that we have chosen our attitude, we now have to ensure that we stay so oriented!

Our current modelling shows that it is unlikely that an impact from the types of particles we expect could disturb the spacecraft's attitude. Even if it did, the on-board systems should be able to compensate. What we are more concerned about is if an impact were to cause a component to fail or behave strangely. This could then cause the on-board systems to think that the spacecraft is at risk and trigger a 'safe mode'.

Safe mode can be considered a spacecraft’s survival instinct; it's a mode that MEX enters automatically if it detects a condition or event that indicates loss of control or damage to the spacecraft. Usually the trigger is a system failure or detection of operating conditions considered dangerously out of the normal ranges. All non-essential systems are shut down and those that are vital will switch to their backup way of functioning; this is to try and isolate any suspected problem and prevent it from causing damage.

When a safe mode is triggered, the spacecraft automatically uses its SAS to point the front of the spacecraft and the solar arrays towards the Sun (ensuring that MEX has power). Next, the active Star Tracker (STR) makes a scan to determine in which attitude the spacecraft has ended up. With this knowledge the spacecraft consults an internally stored table containing the position in the sky of the Earth at that moment to determine in which direction the HGA needs to be pointed to re-establish communications. The spacecraft body is then rotated to point the HGA in that direction while simultaneously keeping the arrays facing the Sun.

The craft then starts sending a signal to Earth and waiting for a reply.

There are two transmitter types on MEX: X-Band and S-Band (we’ll explore why in a later post), but in safe mode, the spacecraft uses the lower bandwidth (and less complex) S-Band system at its lowest transmission rate, which results in a painfully slow communication rate of 9 bits per second (in comparison: in X-Band the maximum rate is 228 thousand bits per second!)

Furthermore, in entering safe mode, a small amount of fuel is consumed and the communications are a bit annoying (until we can restore the faster X-Band) but safe mode is by definition 'safe.'

So, two questions (you may have to go back a few posts for clues):

  • What do you think the problem would be if this were to happen on 19 October?
  • What are the weak points on the front of Mars Express?

(Click below on 'Page 2' for answers – Ed.)

We're also working on another plan to avoid nasty bits of comet, but we’ll save that for next time...

Andy, Michel, Kees, Simon, James and Luke

How to determine the orbit of a comet?

In movies about the impending end of the world due to a comet impact, one thing is certain: Detecting the comet and computing its orbit are dead easy. The scene starts with a computer screen showing a telescope image of a star field, where we can make out a faint, fuzzy little object that doesn't quite look as if it belonged there.

Control room at ESA's Optical Ground Station Credit: ESA

Control room at ESA's Optical Ground Station Credit: ESA

A scientist will throw a brief, disinterested glance at the screen and turn away. Then he stops. His eyes go wide and he snaps around to stare at the screen. He'll call in his colleagues. Computer programs are started, and people frantically hack away at keyboards. In no time at all, they will have identified the fuzzy blob as a comet that is hurtling in from the frozen recesses of space.

Bruce Willis at the 2010 Comic Con in San Diego. Credit: Gage Skidmore

Better call this guy!

What's more, in no time at all, they will have determined the comet's trajectory and they can categorically state that it will hit Earth. A few more frantic calculations and they also know the date and time of impact – Quick, call Bruce Willis!

Neat. But does it really work like that?

In actual fact, one single picture of a comet is just that: a single picture of a comet. All this picture tells you is that there is a comet which, at a certain date and time – a certain epoch (astronomers like to use common words with meanings that are just different enough from what you think the word means to create confusion, so they say 'epoch') – appeared to be near stars A, B, and C in constellation X. No more.

From one picture, you can't tell where it's heading; you don't know how close it will get to the Sun, nor if or when a close encounter with any other planet is due. To find out these things, you need more observations – many more of images that were taken at different dates, ideally spanning a long time frame. The longer the better.

Comet C/2013 A1 Siding Spring

There it is!

And even then, computing the orbit is not really a straightforward matter. In fact, it's a drudgery and you have to go about it in a roundabout way. The pictures don't tell you the comet's path. All they do is to tell you where the comet appeared to be seen at the stated epochs from wherever the observatory was located. But that is not what you want to know.

So you have to make an educated guess at the parameters that describe the comet's trajectory, also known – unsurprisingly – as its 'orbital parameters'. This initial guess (as even the mathematicians rather candidly refer to it) in all likelihood will be quite far off. That's OK, it's just a guess. But at least, you have something to work with.
Euklid-von-Alexandria 1

A famous mathematician

Once you have the initial guess, you have a set of orbital parameters that apply to a given reference epoch that you are free to choose. The known laws of celestial mechanics allow you, if you have a full set of orbital parameters at one epoch, to compute where the object will be at other epochs in the past or in the future. So you can compute where it would have been at the epochs when the comet images were taken. Because the Earth's orbit is well known, you can then compute in which constellation and next to which stars the comet would have appeared at these epochs, assuming that your initial guess holds.

For the initial guess, you will probably find out that the locations in the sky that you compute for the image epochs are quite different from what the images show. Hardly surprising, given that that was just the initial guess. But then you can make small changes to each of the orbital parameters for the initial guess to see which change makes the computed locations at the image epochs move closer to the actually observed locations. At all times, you can use the very accurately known positions of the background stars to get your bearings.

This procedure is known as 'orbit determination'.  It is very time-consuming and involves a lot of complicated and repetitive mathematical calculations, which is why nowadays we let a computer handle most of it. The entire process is known as 'parametric optimisation' and each step is referred to as an 'iteration'. As the optimisation process goes on and many iterations have been performed, you will see that for the epochs at which the images were taken, the computed locations, based on the current estimate of the orbital parameters, will move quite close to what you can see in the actual images.

This diagram is indicative of how the orbit determination accuracy for comet C/2013 A1 (Siding Spring) evolved over time.

This diagram is indicative of how the orbit determination accuracy for comet C/2013 A1 (Siding Spring) evolved over time. It shows a derived quantity: the expected encounter distance from Mars. Source of data: NASA/JPL

At some point, there will be no further improvement. The process will have 'converged' in mathematicians' parlance. But wait: this does not mean that you're done. It just means that you can do no better with the available information, in this case, the available set of photographic images. There is always some uncertainty in measuring just where an object is with respect to the background stars. Comets appear fuzzy and blurred. Who's to say what their exact position in the celestial vault is on that image you're gazing at? Might it not be a few hundredths of a degree further up? But, on a cosmic scale, such minute differences matter – a lot!

Furthermore, if the time span between the earliest and the latest available image is short (just a few weeks or even a few days) the information they contain may be ambiguous. Comets on a wide variety of orbits might still appear to be in that location over a short period of time. But you will see that in the results of the orbit determination, because the mathematical process involved will not only give you a best estimate of the orbital parameters, it will also tell you how accurate (or inaccurate) that best estimate is.

The problem is that if you know the orbit only approximately at that reference epoch you selected at the start of the process, and you want to propagate ( i.e. compute the time change in the orbit, subject to the laws of celestial mechanics and any effects that may change the orbit) this orbit to another epoch, you will find that any uncertainty in the initial parameters will balloon, the further you propagate.

In the diagram above, it took almost 200 days to find out that comet Siding Spring would not hit Mars. At that time, the uncertainty in the predicted encounter distance still ran into hundreds of thousands of kilometres. Though the most probable encounter distance was established fairly early, the uncertainty was still significant after more than a year of observation. It took 44 days of observation to achieve even a semblance of an orbit determination – one that was still all over the place, with a predicted mean Mars distance at flyby 900,000 km, with a high guess of 3.6 million!

Sincere thanks to Michael Khan for today's post – Ed.