Measuring the Distance to Mars

Posted by John Clark on 10th January , 2010

I am looking for collaborators on other continents to make this measurement.

The diagram below illustrates the principle.  Observers on different continents will see Mars against a slightly different background.

Parallax principle

Of course, the diagram is vastly exaggerated.  The distance from Earth to Mars at the forthcoming closest approach is going to be about 100 million km, or about 13,000 times the size of the Earth.  The nearest stars are about 40,000 times the distance to Mars; and most stars are an awful lot more distant still.

I have made the following rough calculation of the size of the effect, between say my home in King’s Lynn and Cape Town.

It is about 10,000 km from the UK to South Africa over the Earth’s surface (My house to Cape Town is actually 9632 km), so the chord length (straight line distance through the Earth) is about 9,000 km.  Mars will be at about 100,000,000 km away at its closest approach, so we are looking for a parallax of 9,000 parts in 100,000,000 or about 18.6 arc seconds. A measurement good to 1 arc second would therefore have an error of 1 in 18.6 or 5.4%.  Obviously a measurement good to 0.5 arc sec would have half that error.  With good amateur equipment that should be feasible.

I am more than happy to help with the maths needed to post-process the photos.

I have been asked what angle of view is needed.  I used a free program called Cartes du Ciel (http://www.stargazing.net/astropc) to work out the apparent positions of Mars from my home and Johannesburg, on January 16 2009 at 22:00 UT and at later times that night.  The difference is in apparent positions is about 15.3 arcseconds.  If the field of view is about 0.5 degrees across, that’s quite noticeable.  There are about 10 stars of 12th magnitude or higher in the field of vision against which to work out the position of Mars.  I think the best procedure is to use the tried-and-tested technique of exposing one set of photos correctly for the planet and one set correctly for the stars.

A serious issue is that Mars moves quite fast against the starry background.  It moves about 18 arcseconds per hour on the night of 16/17 January 2009.  By opposition it will move even faster.  I think the best way to deal with this given the unpredictability of cloud cover is to image once an hour or so in all locations to the best of our ability and interpolate the positions of Mars to deal with non-simultaneity.

If you’re interested, please leave a reply by clicking on “Comments” or “No Comments” below.  Be sure to leave your e-mail address.  I will get back to you within 24 hours.

Pictures from the Night of Sunday 31 Jan/Monday 1 Feb 2009

Please note that copyright in each picture rests with its author.  Images loaded by kind permission of the authors.

Kos Coronaios,  Louis Trichardt, South Africa

Kos’ times are all SAST.  Subtract 2 hours for Universal Time.

Picture 034 single 10 sec frame 800 ISO 22-25-04_1_1

Picture 034 single 10 sec frame 800 ISO 22-25-04_1_1

Picture 053 single frame 6 sec ISO 1600 at 00-38-52_1

Picture 053 single frame 6 sec ISO 1600 at 00-38-52_1

Picture 002 one single 10 second frame 1600 ISO 01-13-06_1

Picture 002 one single 10 second frame 1600 ISO 01-13-06_1

Picture 002 one 10 second frame at 3600 ISO 01-47-37 _1

Picture 002 one 10 second frame at 3600 ISO 01-47-37 _1

Picture by George Carey, Bromsgrove,  Midlands, UK

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Mars_22:00:53_UT_neg_lines_b

John Clark, King’s Lynn, UK

IMG_2805 2010-01-31 21-07 UT

IMG_2805 2010-01-31 21-07 UT

IMG_2811 2010-01-31 21-46 UT

IMG_2811 2010-01-31 21-46 UT

IMG_2813 2010-01-31 22-18 UT

IMG_2813 2010-01-31 22-18 UT

IMG_2815 2010-01-31 22-25 UT

IMG_2815 2010-01-31 22-25 UT

IMG_2817_Mars_2010-02-01_00:22_UT

IMG_2817_Mars_2010-02-01_00:22_UT

Rain from a clear sky!

Posted by John Clark on 17th December , 2009

Last night for a few seconds, when out with the telescope & camera, I got rained on for a few seconds.

From time to time clouds were passing by, but the sky was not only clear, but very black, when this rain fell.  Normally there’s an orange glow in towns, which is caused by the reflection of streetlight from water droplets suspended in the air; but not last night.

Amazing.  Anyone else experienced this?

I’m the spouse or partner of an astronomer. What are the benefits of the Observatory Workstation?

Posted by John Clark on 11th November , 2009

The observatory Workstation is intended to reduce the cost of astronomy and to reduce the time spent on repeatedly setting up equipment.

An obvious source of tension is the cost of the other half’s hobby.  Our aim is to cost approximately half as much as the very cheapest, entry-level models of the competition.  The best selling competitor products cost at least three times as much as ours.  An observatory building requires much more of a foundation than our product.  We got a quote for putting our product on a concrete base.  It would have cost almost as much again as the observatory workstation.  To put a building on a concrete base would cost quite a bit more.  We strongly believe that other observatories are much more expensive than they need to be.

Why might your other half want an observatory?  There are broadly three reasons.

  1. To reduce the time spent setting up for an observing session.  Astronomers all know the frustration of seeing a clear night and beginning the laborious set-up procedure only to watch the clouds roll in before the first look down the telescope.  Also, time spent setting up is time not spent with the family, reading bedtime stories to the kids, maintaining the house and making all the other little contributions to family life.
  2. To keep the telescope and cameras cool.  If they are kept in a heated house, it is an hour before they have cooled down enough to be used outside. Digital cameras and telescopes don’t work as well when they are warm.
  3. To store the observing equipment securely, and free up space in the house and garage.

Finally, many observatories are made of moulded plastic.  This can look out of place in a domestic garden.  We have designed our product to look nice, and to blend into a well-cared-for garden.  It also does not obviously look as if it is full of valuable equipment.  A conventional observatory with a dome does rather hint to potential thieves that it might contain rich pickings.

The Discovery of the Solar System

Posted by John Clark on 8th November , 2009

Nowadays we take the existence of the solar system as a given.  It wasn’t always like that.  In fact we have only really known of its existence for about 400 years.  Before then the general assumption was that the universe was centred on the Earth.

The question is: what changed?

First, we have to understand some facts about how the ancients viewed the universe.

The first known civilisations were not only surprisingly good at astronomy but they also passed their records to later civilisations.

Thus the ancient Greeks were aware of the earlier astronomy of Babylon and India, where there had been civilisations for thousands of years before ‘classical’ Greek civilisation.

In particular, they all know that while most of the thousands of stars they could see in those light-pollution-free days had fairly fixed positions, a handful moved around the sky.  The Greeks worked out that there were five of these wandering stars, Mercury Venus, Mars Jupiter and Saturn.  This was not a trivial achievement: the Babylonians had separate morning and evening planets.  Legend has it that Pythagoras was the first to realise that they are one and the same planet, which we call Venus.

All five of these planets are bright objects, which are very easy to find in the night sky.

The two photos below, taken by the author, show Mars against the stars 25 nights apart.

Mars moving

These five planets (and those discovered much later) move in characteristic ways.  Mercury & Venus are never visible at midnight.  They are evening and morning stars.  Mars, Jupiter and Saturn can in principle be visible at any time of night.  All three of them travel along a characteristic looping path.  They perform one loop a year.   (Mars only performs one every two years.  We now know that this is because in the ‘missing’ years it is on the other side of the Sun from us.)

This movie, due to Wikipedia contributor Eugene Alvin Villar, shows the path taken by Mars during 2003.

Apparent_retrograde_motion_of_Mars_in_2003

At least one Greek writer, Aristarchus of Samos, worked out that this behaviour could be explained by having the planets orbit the Sun.  We only know about his work because Archimedes referred to it.  His manuscript did not survive; and his ideas did not become mainstream.

The explanation of planetary motion that did become mainstream was that they all go around the Earth, orbiting in circles-within-circles, called epicycles.    So there was no ’solar’ system at all.  The Sun was merely one more object which was thought to orbit the Earth.

File:Ptolemaic elements.svg

Source: http://upload.wikimedia.org/wikipedia/commons/2/29/Ptolemaic_elements.svg

It is often thought that these ideas were overthrown in a great burst of discovery around the year 1600.  In fact this is an exaggeration, although somewhat true.  Ptolemy’s data were gradually refined throughout the Middle Ages.

Copernicus had access to better data than Ptolemy.  Contrary to popular belief, he did not have the Sun at the centre of the universe.  He had everything orbit an empty point in space.  And his model did not eliminate epicycles.  Quite the opposite: he had more epicycles than Ptolemy.  His motive was a belief that Ptolemy ‘fiddled’ his model by not insisting on uniform circular motion; he rectified this problem.

Johannes Kepler, the Imperial Mathematician at Prague, benefited from the immense amount of data collected by his predecessor Tycho Brahe, who had collected precise data over 10 Mars orbits, or about 20 years.  ‘Precise’ meant that his positions were accurate to about three arcminutes or 1/20 of a degree.

Kepler did not at first know how Mars moved; and it took several years of trial and error for him to work out that it orbits the Sun along an ellipse with the Sun at one focus.  People knew a lot less about ellipses then than now, and knew virtually nothing about gravity, so Kepler was a real pioneer trying to find his way through unknown intellectual territory.  What is so remarkable about him is the sheer originality of what he did.

He had the wit to realise that if Mars and Earth orbit the Sun, he knew from Tycho’s data how long a Mars orbit takes (687 days), and knew that if Earth is at E1, then the next time Mars reaches the same place in its orbit, Earth will be at E2 because 687 days is a little under two years.  By comparing the triangles S-E1-M and S-E2-M in the diagram, Kepler could work out the distance to Mars from geometry.

Mars rangefinding

Once he had done this, he knew that the epicycles, the circles-within-circles, just weren’t there.

Kepler was aware of Copernicus’ work, and of that of his contemporary Galileo. Galileo was not good at appreciating the work and ability of other people, which could make him come across as arrogant; and which made him some powerful ecclesiastical enemies.  He hadn’t time of day for Kepler.  Despite this fault he was an extremely able man.  Fortunately the one time when he did pick up and run with someone else’s idea was when he heard about the newly invented telescope.  He wasn’t the only one to try this new invention on the heavens, but he was perhaps the boldest, certainly the most thorough, and was able to communicate what he discovered very effectively.  In a very short space of time, he discovered that Jupiter has satellites, and that Venus shows phases.  The former discovery showed conclusively that not all orbiting bodies orbit the Sun.  The phases of Venus can only be understood if it orbits the Sun, not the Earth.  If Venus and the Sun orbit the earth, the phases of Venus must appear to us to be either always crescent if Venus is the nearer; or always gibbous if the Sun is the nearer to us.  In fact, as the picture below shows, the phase is gibbous when Venus is behind the Sun relative to us and crescent when it is nearer to us than the Sun.

The phase of Venus changes from gibbous to crescent

The phase of Venus changes from gibbous to crescent. Photos: John Clark

Galileo also showed that the Earth’s gravity causes all objects to fall at the same speed, regardless of the mass of the object.

Isaac Newton, born the year Galileo died, picked this idea up and incorporated it into his theory of gravity.  In modern language, Newton’s law of gravity states that all bodies, whether on Earth or not, attract one another with a force

newton's law of gravity

where G is a constant, M is the mass of one body, m is the mass of the other, and r is the distance between them.

There is an important twiddly bit to this law.  Newton was not the only person to work out the law, but he was the only one to prove the important corollary that spherical bodies attract as if they were point masses at their centres.  Since the Sun and planets are roughly spherical, this means that the law can be applied to them.  Proving this was a very great achievement.  Newton could only do it because he had invented a whole new branch of mathematics: calculus.

Once this was established, it was a rather shorter step for Newton to show that his law implies that orbiting planets travel in ellipses with the Sun at one focus, as Kepler had discovered.  Actually, he showed that they can also travel in parabolas or hyperbolas, in which case they never return: they only ever visit the Sun once.

Much if not most of Newton’s book on the Solar System is concerned with the orbits of comets.  He was obviously very keen to show that they too orbit the Sun.

By the time Newton died in 1727, Earth, Jupiter and Saturn were known to have satellites; and planets and comets were known to orbit the Sun.

As telescopes improved, another planet was discovered.  Its discoverer, William Herschel, at first thought it was a comet.  No-one suspected that there were more than the five known planets.  This is so strongly true that Galileo had noticed this planet, Uranus, as a moving object, but did not recognise it for what it was.

Another planet was discovered in 1801:  Ceres.  We now know it as the largest asteroid, but the astronomers of the time had a more pressing problem than finding out what Ceres is:  it was about to disappear behind the Sun for Earthbound observers.  The discoverer, Giuseppe Piazzi, had exactly 24 observations of its position.  People were very keen to find it again once it had passed behind the Sun.  Unlike the main planets, it is a very faint object that is not at all easy to find.  Remember that Kepler needed data going back 20 years to work out the orbit of Mars.  Enter another mathematician as great as Newton: Karl Friedrich Gauss.  He worked out a way to estimate the orbit of Ceres from just three observations.  This method revolutionised the science of orbits.  Working out an orbit was now a ‘quick hit’, rather than a lifetime’s work as for Kepler and Newton.

A handful of asteroids were discovered over the next few years.  Work stopped when the Napoleonic Wars disrupted life in Europe.  They were all too small to resolve as anything more than points of light.  This is still nearly true: the Hubble Space Telescope can just about resolve Ceres as a disc.  Hence people began to call them asteroids, not planets.  Discovery of asteroids resumed in the mid 19th Century and has been going on ever since.  Nowadays asteroid discovery is mostly the preserve of dedicated amateurs.  Most but not all of them lie between Mars and Jupiter.

Meanwhile the planet Neptune had been found in 1846 by analysing the orbit of Uranus.  Its orbit was being perturbed by a very massive, as yet unseen, body.  This fact together with a belief that the Sun-to-planet distances fitted a simple pattern, told people where to look.  The distances were thought to obey the Titus-Bode law.  Neptune’s distance from the Sun is a poor fit to the Titus-Bode law, which is not nowadays taken seriously except by a few diehards.

People tried the same trick to locate the next planet out from Neptune.  Its position was guessed by working out perturbations in Neptune’s orbit.  With great fanfare, in 1930, the planet was announced and named Pluto.  Unfortunately, the perturbations in Neptune’s orbit were not real, but the result of a mathematical error.  Even more unfortunately for Pluto, when a satellite was discovered in 1978, Newton’s law of gravity could be used to work out its mass.  This mass was found to be tiny compared to the other planets.

What we know of the planets themselves has mostly come from spacecraft sent to observe them.  I think it is fair to say that we now live in a golden age of discovery about planets unmatched since the days of Kepler, Galileo and Newton.

Since the year 2000, the next phase of Solar System exploration has been driven by the advent of high quality digital photography and computer image analysis.  The sky can now be systematically and automatically searched for solar-orbiting objects beyond Neptune.  There are lots of them, mostly tiny, but a few are comparable in size to Pluto.

Since Pluto is really too small to be a major planet, a new category of object called a dwarf planet was devised.  The dust has not yet settled on this definition: it upset a lot of people, and the voting mechanism used by the International Astronomical Union to re-categorise Pluto has attracted fierce criticism.

Most of the trans-Neptunian objects have orbital radii (strictly speaking orbital semi-major axes) in the range 40-80 AU, where one AU is the Earth-Sun distance.  Neptune is about 30 AU from the Sun.  These objects are known as the Kuiper belt.  They appear to be lumps of impure ice.

One of the dwarf planets, Sedna, is ten times further from the Sun than the others, at nearly 500 AU.  It may not be a Kuiper belt object.  The existence of a cloud, the Oort cloud, between stars has been hypotheisied, by Jan H. Oort and by Ernst Opik, the grandfather of British politician Lembit Opik.  It has yet to be observed.  Perhaps Sedna is the first Oort cloud object to be discovered.  Stay tuned.

Mars_2009-11-02_03-21-12_UT

Posted by John Clark on 5th November , 2009

Mars_2009-11-02_03-21-12Mars was about 109 million miles away when this picture was taken.  Seeing conditions were poor: the air was very turbulent and the wind was blowing my telescope about.  Nevertheless, you can just make out the North Polar ice cap.

How to Keep Dew off Your Camera Lens During Astrophotography

Posted by John Clark on 5th November , 2009
A long Lens Hood

A long Lens Hood

You need a good long lens hood to keep dew at bay during astrophotography, but so far as I can see, you can’t buy one.

What you can buy is one like this.

A Typical Rubber Lens Hood

It is much too short to be an effective dew hood. To locate one, Google ‘rubber lens hood’.  It costs less than £10 ($15), and is made of flexible rubber.  It screws onto your camera lens.  The lens usually has the diameter of the screw thread written on it.   You will need this information to buy the hood.

So, if you can find the right diameter tube, you can slide it onto the rubber; and you have solved the problem of how to screw your dew hood onto your camera lens.  You can use a tube slightly narrower than the maximum diameter of the rubber lens hood, in which case you put it outside the rubber, or one slightly bigger than the rubber hood, in which case you can stretch the hood over the end of your tube.

2009-05-04_05-03-32_04052009059
Depending how big your lens is you could use a yoghurt pot, a cream pot or a cola bottle.
A white one like the above needs to be blackened otherwise stray light will fog your image.

IMG_2140
Remove the label from the cola bottle and cut out the cylindrical part of the bottle. (The top is great as a funnel for pouring screen washer fluid, oil etc into your car, by the way.)

You can’t blacken this tube with paint – it is too flexible.  The paint will flake off.

I used electrical insulation tape.

IMG_2142

First stick the tape in the axial direction inside the tube.

Spiralling the tape on the inside is unwise for two reasons.  First it is a pain to do; and secondly it stretches as you unroll it, and when it shrinks back later, the spiral unpeels.

IMG_2147

It is also full of static electricity.  The easiest way to prevent it sticking where you don’t want it is to feed one hand through the tube, and pull a length of tape through.

Make the tape slightly too long and fold the excess back, sticking it to the outside.

Do this first because you can see what you are doing and can see and correct any bits you miss.  Just peel the tape off and stick it back down if you make a mistake.

When you have covered the inside, tape the outside.  It is now OK to wrap the tape in a spiral.

IMG_2150

You don’t absolutely have to tape the outside, but it will make a stiffer product, and double up the lightproofing, helping to keep out streetlight and moonlight.

IMG_2152

IMG_2153

Now squeeze the rubber lens hood to fit it inside the tube, and you’re done.  The compressive stress in the rubber will hold the tube on.

It is light as a feather and will keep dew off even if you point almost vertically.

For truly vertical photography you may still need to use a hairdryer from time to time to remove dew.  I always have one ready by my telescope.  Use it gingerly – you don’t want to crack any glass!

If there’s a full-ish moon around, I hold one of those gardener’s kneeling mats to shade the aperture, because stray moonlight is so bright it will reflect off black surfaces.