MIRA 29
February 1993





Lyras second Double Double

by Vaughan Cooper

Date          11th August 1991

Time          22.00 U.T.

Conditions   Naked eye stars visible to the 4th mag.

Instrument  4" F4 Reflector 16x and 64x


The drawings on the cover show the position of Lyras second double double Σ2470 and Σ2474, a pair of 6th magnitude stars, some 3° NE of γ Lyra.

The first drawing illustrates the position of the pair relative to the constellation, as viewed with the naked eye, while the drawing to the left of the page illustrates the star field from γ to the doubles. The drawing on the right illustrates the doubles and general stars within the 0.5 deg field of view of my 4” Reflector.
Specifications taken from Webbs Celestial Objects for Common Telescopes:

My own comments in brackets,


Σ2470

R.A. 19h. 5min.

Dec 34° 38’ N

Primary 6.7 mag. white: Companion 8.2 mag. blue, separation 12.9", P.A. 271 .6°

Σ2474

R.A. 19h. 6min.

Dec 34° 28' N

Primary 6.7 mag. yellowish ashy: Companion 8.0 mag. ruddy, separation 17.3”, P.A. 258.7°


(A relative easy to find pair of stars, but only with increased magnification will the fainter companions stars reveal themselves, hence another candidate of a double double within Lyra to rival the much better known and brighter pair of ε 1.2. Lyra.  Of the two primaries l feel Σ2474 seems the brighter of the two, which is at odds to the specification, plus the position of the companions P.A. of the two pairs in my observation don't seem to agree with the specifications either.  l feel with regards to the P.A. this is really due to observational error as this is the first time l’ve attempted anything of this sort before, but take a look and see what you find.)


This is a good time to remind members that double star observations are one of the few programs that amateurs can carry out with not too much trouble from light pollution.  You don't have to discover a dark sky sight to find double stars if you have a star atlas and you practice a bit of star hopping.  Most of the extended objects in the sky, nebula or galaxies will quickly disappear in the all to familiar orange glow of local street lamps and will need high magnification and a clear atmosphere coupled with knowledge of the exact position for them to show much detail and structure from this area.





Two Lunar Craters


CRATER . . . . . . . MERSENIUS
LOCATION . . . . . 21° S 49° W
DATE. . . . . . . . . 1992 / 2 / 15
TIME . . . . . . . . . 19.15 UT to 20.30 UT
MOON . . . . . . . . 12 days old
LUNATION . . . . . 855
COLONG. . . . . . . 58
SEL. LIBRATION  -3.2 long. 1.4 lat.
OBSERVER . . . . . IL Clarke,  Warwickshire
CONDITIONS . . .  Not good, clear sky, windy, lot of shimmer, seeing Ant.I to III
INSTRUMENT . . . 102mm Refractor, 10mm & 7.4mm Plossl +1.8 Barlow = x100, x135 & x180

This was drawn because of a request from Harold Hill for an observation on this crater near the Mare Humorum.  Unfortunately the seeing conditions were not of the best and I feel that a lot of interesting detail is missing from the drawing.   In the few moments of good seeing, to quickly over to draw, glimpses of far more detail was visible.  The crater is about 72km (45 miles) in diameter with walls rising to over 2400m in places.  Both north and south ends of the crater had breaches in its walls, with the southern walls seemingly only a gentle slope before opening onto an area of small craters.  The other end, the north, looked a very rough area with a lot of disturbed broken rock.  Whether caused by the walls of the crater collapsing or by catering it was impossible to tell, but the craters in this area where noticeable larger that the southern ones. The floor of MERSENIUS is noticeable convex with a few small craters and what looked like a rill running north-south.  The east wall had a couple of high lights in one spot, which in a photograph on page 128 in Cherrington's "Exploring the Moon Through Binoculars" is a small crater set into the wall.  The northwest wall was terraced in several stages, with both ends running into craters.  The lower section looked to have a much lower slope than the higher cliffs.  This crater has many rills across its floor which I could not see, so when the seeing is better and the sun a little lower it will be worth paying another look.




CRATER . . . . . . . PLINIUS
LOCATION . . . . . 15° N 24° W
DATE. . . . . . . . . 1991 / 3 / 21
TIME . . . . . . . . . 20.00 UT to 20.30 UT
MOON . . . . . . . . 5 days old
LUNATION . . . . . 844
COLONG. . . . . . . 342
SEL. LIBRATION   -0.7 long. -4.5 lat.
OBSERVER . . . . . IL Clarke, Warwickshire
CONDITIONS . . .  Good, seeing Ant. IV
INSTRUMENT . . . 102mm Refractor, 10mm Plossl +1.8 Barlow = x180


The crater PLINIUS or PLINY as it is called in Cherrington's book "Exploring the Moon Through Binoculars", lies between MARE SERENITATIS and the northern edge of the MARE TRANQUILLITATIS.  It is about 45km (28 miles) in diameter.  It has a large central feature which looks like a twin crater or a miss-shaped mountain. The crater stands all alone between the two Mare and is very striking in the right lighting.  It's walls are terraced with a wider section sticking out like a tongue to the south.  The eastern side looked 'rounder' than the western side which was more uneven and rough.  At the north-west is the border of the MARE SERENITATIS, this area had a few small craters and hills.   The north facing side of the crater wall looked very rough and broken, as if that part of the wall had collapsed.  To the north ran a rill or cleft in an east-west direction.  This was darker on its southern edge and was joined by another rill running in a north-south direction, at an angle of about 100∞, on the north east side of PLINIUS.  I have tried a different drawing technique on this drawing using lines to follow the shape of the ground, but I don't think it's as good as the dotty way!





'Gravity Assist'
or How to Get Something for Nothing

by Ivor Clarke

We all know that there is no such thing as a free lunch, someone, sometime, somehow must pay the price.  Nothing is for free. So how can you launch an interplanetary probe into deep space when you haven't got enough thrust to reach a speed to get there in a reasonable time frame?  After all, if it takes say, 15 to 20 years to get somewhere, what are the chances of a complex piece of equipment arriving in full working order?
Back in the early sixties when the idea of constructing deep-space probes to the outer planets was first being debated, any suggestion of making a reliable spacecraft to last ten or more years was not considered possible with the then current technology.  The very thought of a mission to Saturn or beyond was enough to get the spacecraft engineers trembling.  The early moon shots had just crashed into the surface or went by into a lunar orbit.
Likewise the first missions to the planets, Mars and Venus where just fly pasts. All depended on a few hours as the probe neared its target.  None of these early craft could be controlled to the fine degree necessary to attempt the interplanetary billiards of today. The first was Mariner 10 launched in November 1973, which flew on to Mercury by way of Venus. The first multi-planet mission to use the gravity of one planet to get to
another.
All single journey planetary probes use what's called a Hohmann Transfer Orbit to arrive at the target.  This was named after the German engineer Walter Hohmann, who in 1925 hit on the idea of using an elliptical orbit to travel from one planet to another. This method is the most economical of energy but takes longer.  The direct shortest path across to another planet would use a massive amount of fuel and is not possible even with todays rocket engines.
Engineers call the measure of the amount of energy needed the Δv (the Greek letter Δ delta + v for velocity).  Thus Sputnik 1 had a Δv of 4.8 miles per second (7.8 km per second) for a low Earth orbit.  The Shuttle needs a Δv of 5.7 m/s (9.2 km/s) to reach the height for the space station Freedom.
An elliptical orbit with its trajectory just touching the orbits of both planets at perihelion and aphelion uses the smallest amount of fuel, but will take much longer to arrive as it has to travel about half way round the sun to meet the target.  As the spacecraft swings round the orbit it loses speed as it travels further out from the sun until it reaches aphelion and its destination.  If the target planet was not at the arrival point, the spacecraft would then swing back in an ellipse to its starting point on the other side of the sun.  When it arrived back at its starting point the Earth would not be there as the elliptical orbit of the space craft would be longer or shorter then the Earth's year depending on whether the spacecraft was inside or outside of the Earth's orbit.

When to go
This brings us to the concept of the Launch Window; this is the time when the two planets will be at the correct position in their orbits to use the Hohmann Transfer Orbit.
As all the planets have a different length of year and speed of orbital velocity, it is obvious that only at certain times can a spacecraft be launched into space to guarantee it will intersect the destination orbit at the exact point in time when the target is there as well.  With Mars this is about every 25 months depending on whether Mars is near perihelion or aphelion.  With Venus this is about every 520 days and Jupiter about every 13 months.
The Earth's velocity around the sun is 29.8 km/s, varying by only +/- 0.5 km/s due to eccentricity of the orbit. What this means is that all spacecraft can either add too or reduce this velocity to get to different orbits.  The Ulysses mission launched in October 1990, achieved a departure velocity of 11.4 km/s, the highest ever achieved by a space probe.  This gave it a combined speed of 41.2 km/s relative to the sun, because it was fired along the direction of the Earth's orbit.  This is a high enough speed to send it past the orbit of Uranus, and out to 22 AU if it wasn't heading for Jupiter.  On the other hand, if it had been fired in the opposite direction, back along the path of the earth's orbit, it would have been travelling at 18.4 km/s. relative to the sun.   This is lower then the speed needed to stay in orbit around the sun at Earth's distance and so it would have dropped in towards the sun, going to 0.23 AU, about half the distance of Mercury from the sun.  Both of these orbits would then return the craft to its starting position, the outer one many years later.

Only once every 175 years
But how can you get to Neptune if the fastest thing ever flown can only just make it out to just past the orbit of Uranus?
The answer is by Gravity Assist.
Voyager 2 had a Δv of 36 km/s when it left Earth, far short of the Δv of 50 km/s it would have needed to get to Neptune from Earth without gravity assistance.  But if you launch a satellite into space round a planet or moon with enough velocity, then it will stay in the orbit it was placed in if it is not subject to any other forces such as atmospheric drag or the gravitational pull of another large body.  This means that at any position in an elliptical orbit, the speed of the satellite will be the same on the in journey as on the out at identical distances from the moon or planet.  If the satellite is orbiting in an even ellipse it cant be otherwise.  This is the position that the spacecraft Hipparcos is now in after its motor failed to fire to put it in a geostationary orbit.  Its orbit is 36,000 km at apogee but only 500 km at perigee, with a period of about 10 hours.  So how can you increase speed?
Back in 1965 a graduate of Caltech working at the Jet Propulsion Laboratory in Pasadena, named Gary Flandro, came up with the answer while working under Elliot Cutting.  Cutting suggested that he examine the possibility of using the gravity of one planet to sling a spacecraft on to another.  So the concept of 'sling-shot' or gravity assist was born.
Astronomers had known for a long time that if a comet strayed to close to Jupiter or Saturn it would be deflected into another orbit or even thrown out of the solar system at a high speed by the transfer of kinetic energy from the planet to the comet.  But back in the mid sixties most of the engineers at JPL had doubt about the possibility of using gravity to boost the speed of a spacecraft.  It was thought that the gain on the approach would balance the loss on the outward flight so that the net gain would be zero, as in a normal elliptical orbit.  Flandro recalled in 1989, "My gravity-boost idea wasn't new, astronomers had known for a long time that a comet speeds up when it passes close to a planet.  I was the first to apply the same idea to a spaceship."
Luckily the idea was just in time to catch all the large outer planets in just the right position and the Grand Tour was on.  The next time they will be in the correct position will be in 2150!
Voyager II has given us the only close-up views we will have of Uranus and Neptune this century.

Speed for nothing?
So how does gravity help us to fly to the outer planets?  To use gravity assist to speed up a spacecraft, it must approach the intended planet from inside and behind the planets direction of travel in its orbit and aim to go behind the planet as seen from the sun.  As the spacecraft approaches it will start to fall into the gravity well of the planet.  Because the planet is moving along its orbit in roughly the same direction, the craft will be dragged along as it nears the planet picking up speed.  The spacecraft will be travelling faster than the planets escape velocity at this distance and so will add to its speed without any danger of being captured.
As both the planet and the spacecraft are travelling at different speeds and angles in respect to the sun, the gravity of the planet can be used to either slow down or speed up the craft.  For instance if the craft goes behind the planet in respect to the sun it will speed up by an amount depending on how close it goes to the planet.  If the craft goes in front of the planet it will be slowed and could even go into orbit.
The angle at which it approaches the path of the planet's orbit in respect of the sun and its 'miss-vector' or distance it will miss the planet by will govern the swing-by, with a small 'miss' driving the probe deeper into the planets gravity well; resulting in a larger deflection angle adding greater speed.  This will bend the spacecraft's path into a hyperbolic curve, so its path is now changed to a shallower angle to the sun (if it has gone behind the planet).  It is because the speed of the craft is greater then any orbital speed of any satellite and it is approaching at a steeper angle to the planet's orbital path then it leaves in respect to the sun that adds to its speed.  This is why it increases in speed, because it is not pulling away from the sun as fast as before the encounter.
At the Saturn encounter Voyager 2 reached its highest speed on its long journey to the stars.
But as the spacecraft gains kinetic energy, so the planet loses some of its orbital momentum by the same amount of energy.  The tiny space craft can gain much from the giant planets in speed and energy.  But the books must be balanced and the planet will be slowed down in its rate of spin and also loses some orbital momentum.  In the case of Jupiter, this was about a billionth of a second longer to its year, nothing to loose much sleep over!
This change in the angle of travel of the spacecraft, in relation to the sun, can results in enormous amounts of energy being transferred to the craft, resulting in greatly increased speed.
The trick of cause, is to know the mass of the planet, its diameter, height of its atmosphere, also are there any of its own satellites or rings in the way, then hit the spot aimed for at the right speed and distance to bend the spacecraft's direction to exactly the correct requirement needed.
Of cause a space craft must not fly too close to planets like Jupiter because of its strong magnetic fields and radiation belts unless its been especially hardened and protected.
On the Voyager small adjustments can be achieved by the spacecrafts Attitude and Articulation Control Subsystem (AACS) control jets.  There are 12 tiny thrusters to control the attitude and another 4 are used to correct the trajectory of the craft to that computed on Earth both before and after an encounter with a planet.
This is now done to an amazing accuracy with probes arriving on target only seconds out after years in space, light hours from earth.  Gravity Assist has given us the means to explore the whole of the solar system at much lower cost and much sooner than anyone would have dreamed of a few decades ago.
Both of the the two latest probes, the Ulysses Out-of-Ecliptic mission over the sun's poles and the Gallileo mission to Jupiter and its moons make use of the technique of gravity assist.  Indeed neither of the missions would have flown by using just the power of todays rockets.
Ulysses is now heading for the unknown regions after a close flyby over the north pole of Jupiter on February 8th 1992.  In September 1994 it will pass over the Sun's southern pole and hopefully on to the north polar regions in 1995.  On December 8 1992 the Galileo space craft shot past Earth at over 8.6 m/s, only 189 miles above Antarctica.  This was its second encounter with Earth after a space of two years and its last boost to send on its way to Jupiter which will be reached on December 7th 1995.
I am sure we have not seen the last of 'interplanetary billiards'.







Flagstaff Arizona and the outer solar system


By Mike Frost

"Well I’m standing on a corner in Winslow Arizona,

Such a fine sight to see...

It’s a girl - my lord! - in a flatbed Ford,

Slowing down to take a look at me..."


The Eagles - "Take it Easy"


I’m sure if Don Henley had been an astronomer he would have had just as much fun by heading west out of Winslow on Route 66, across the Painted Desert to Flagstaff.  En route he could drop in on the Barringer meteor crater, but as I’ve already told you about that remarkable site we’ll stay in the fast lane and cruise into Flagstaff.

The MoneyWise Guide to North America defines Flagstaff as "The most boring place on Earth to be stuck in waiting for a lift".  But what do they know?  Flagstaff has arid deserts and winter skiing, extinct volcanoes and meteor craters, Indian ruins perched precariously on cliffs, and the Grand Canyon barely an hour’s drive away.  For the astronomer, however, Flagstaff’s greatest glory is that it is one of the few places on Earth where a new planet has been discovered. (Name the others!).

In Flagstaff’s case, the planet was Pluto, discovered by Clyde Tombaugh in 1930. Tombaugh was a researcher at the Percival Lowell Institute, which to this day is a working astronomical observatory, situated on Mars hill, overlooking Flagstaff city (there is a separate deep sky observatory in the desert to the south of town).  The choice of Mars for the name of the site highlights the other great obsession of the Institute’s founder.

Percival Lowell, "the man with the tessellated eyeballs" is one of the great historical characters of astronomy.  An amateur observer of wealthy means, he determined to build an independent observatory which would benefit from the high altitude and clear skies of Arizona.  Due to a mistranslation of the Italian Schiaparelli’s observation of "canali" (channels), he became convinced that the surface of Mars was criss-crossed by canals, built by martian civilisations to irrigate their arid planet (just like Phoenix, the state capital, actually).  Lowell despatched an assistant, one Andrew Douglas, to investigate possible sites.  The result was a virtual dead heat between Flagstaff and what later became Kitt Peak observatory, to the south of Phoenix. Flagstaff won because of it’s proximity to the Santa Fe railroad, and other research institutes (including the U.S. naval observatory and Arizona State University) have followed Lowell’s.

Lowell proceeded to observe canals on Mars, a fiendishly tricky planet to observe, despite criticisms of his work from those who failed to agree with his theories.  Doubters were not tolerated at the Lowell observatory, however, and in particular Andrew Douglas was dismissed for daring to doubt his employer’s opinions.  Douglas, a versatile chap and something of a hero around Flagstaff, went on to develop the new theory of "dendro-chronology" or dating of wooden artifacts by their tree-rings.  There are a lot of ancient indian sites around Flagstaff, and they all seem to have been dated by Douglas’s dendro-chronology.

Back to Lowell. He became enthused by the success of Newton’s gravitational theories in predicting the existence of new planets: namely Neptune, discovered by Leverrier and Adams in 1846 (in Berlin, I think), and Vulcan, supposedly within the orbit of Mercury, which was eventually explained away by Einstein's theory of general relativity.  Lowell did his own laborious calculations and predicted a massive "Planet X", perturbing the orbit of Neptune from the outer reaches of the solar system.  He spent much of the latter part of his career searching for the elusive planet X, but on his death in 1916 the project began to slip into obscurity.

It was thirteen years later before an enthusiastic youngster named Clyde Tombaugh arrived in Flagstaff and began a diligent and laborious search for Planet X.  The magnitude of his task should not be under-estimated: during his eighteen month search he discovered several comets and dozens of asteroids.  His method of checking photographic plates was to use a "blink comparator", which flipped rapidly between two photographs of the same portion of the sky taken on different nights.  The area in the sky to be searched at a given time in the year was such that asteroids would show as large a change in position as possible, to make them easier to identify.

Eventually, Tombaugh spotted a tiny image moving slowly through the star fields - far too slowly for an asteroid.  He had discovered Planet X! Pluto, god of the Underworld, was an appropriate name in more ways than one: the first two letters commemorated Percival Lowell, whose vision - flawed in many other ways - had inspired the search.

Pluto was a lot smaller than Lowell had expected, and consequently much fainter.  It’s orbit was also highly eccentric and inclined to the ecliptic - indeed, Pluto is currently closer to the Sun than Neptune.  Pluto’s unusual orbit has prompted speculation that the planet is actually an escaped satellite of Neptune, particularly since Nereid, the outermost large Neptunian satellite, has an equally unusual retrograde orbit.  However Voyager in 1989 found no definitive evidence of a Neptunian catastrophe.

In some respects Tombaugh was lucky to discover Pluto.  The planet’s mass is far too low to cause the perturbations to Neptune’s orbit which Lowell had worked from -» indeed, with a longer and more accurate set of measurements Neptune’s orbit now seems well accounted for by the current roster of planets.  Additionally, other observers had narrowly missed Pluto in other photographic searches (ten years earlier, Humason at Mt Wilson had photographed the planet but the image lay on a flaw in the plate). However, it would be unfair not to recognise Tombaugh’s tenacious and painstaking observations, and at the Flagstaff observatory the staff are clearly proud of their predecessor’s famous discovery.

The dome in which Tombaugh made his discovery is still in use, so the public aren’t allowed inside, but you can view the exterior of the dome.  From the visitor’s centre in the old observatory library the you make your way through the trees along the "solar system walk".  Along the path, at intervals corresponding to their mean distance from the sun lie plaques announcing each planet: Merctuy, Venus, Earth and Mars are almost on top of each other, then a big gap to Jupiter, Saturn and Uranus.  Almost at the end of the path is Neptune, and then one final plaque, for Pluto, overlooking the dome.

One post-script to the story of Pluto.  In 1978, James Christie observed Pluto very accurately to see if it was due to occult any stars.  To his complete surprise the planet’s image was elongated - Pluto had a moon!  Charon, the moon, is a substantial proportion of the mass of Pluto, making Pluto/Charon the best candidate for a double planet in the Solar System.

Where do you suppose Charon was discovered?  At the U.S. Naval Observatory in Flagstaff, of course - so the city still claims Pluto as it’s own!







FORMULAE AND TIPS

by JM Townrow




1. Angular resolution (arc sees.)   =        4.5    where A = Aperture

                                                           ———

                                                               A               in inches


                                                   or   =  115   with 'A' in millimetres

                                                           ———

                                                              A


The above should be regarded as the maximum possible.



2. Resolution in the focal plane (in microns)


                                     =  focal ratio   (i.e. f no.)

                                         —————

                                               2

                                                           (actually more like .55f no.)


The above should be regarded as the maximum possible.



3. Maximum angular resolution of the human eye = 1 arc minute


For practical purposes allow a margin and take this as 2 arc. minutes - about 1/7 mm. viewed from 25cm. (10").


To achieve maximum resolution visually a telescope needs only sufficient magnification to make its finest resolution subtend 2 arc minutes,  i.e.    120A        (A in inches)

                                                                     ———

                                                                       4.5


This approximates to the aperture in millimetres.


Greater magnification serves only to reveal diffraction phenomena.



4. Limiting magnitude (visual). Apertures in inches.


Aperture      Mag               Aperture         Mag

      2          12.1                    8              15.1

      3          13.0                   10             15.6

      4          13.6                   12             16.0

      5          14.1                   15             16.5

      6          14.5


The above should be taken as maxima.



5. Telescope magnification  =   focal length objective

                                               ———————————

                                               focal length eyepiece



6. Scale of 1 degree  =  focal length of objective

                                     ————————————

                                                  57.3


A degree is one part in 57.3, i.e. 1" viewed from 57.3" subtends 1 degree.


From this simple rule one can work out how much sky is subtended by various parts of one's hand.



7. Combining resolutions;


             r1 + r2 + r3 + . . . .  = r     (in distance units - typically microns)


        or   1  + 1  +  1 +  . . . .  =  1  (in lines per mm. - e.g.)

              Rl     R2    R3                                                   R


It follows from the above that where maximum film resolution is equal to maximum image resolution the maximum resolution of the combination is only half as good as either.



8. Film factor.  This is intended to express the usefulness of a particular film for high resolution astronomical photography.

The higher the figure the better.


         Factor = film speed

                      —————

                           r a 


Where r = resolution e.g. in microns.  For ordinary films this is typically between 5 and 20 microns but for Kodak Technical Pan is claimed to be 2.5 microns.


The factor assumes that blur is directly proportional to exposure time.  This tends not to be the case with very short or long exposures.  Don't forget about reciprocity failure, which reduces

the effective film speed and differs from film type to film type.



9. High resolution photography with an UNDRIVEN TELESCOPE.   If image blur is to equal maximum possible resolution then the maximum permissible exposure (in seconds) is given by :—


        4.5   (for A in ")     or     115     (for A in mm.)

        ——                              ——

        15A                              15A



10. Photography with an UNDRIVEN CAMERA.  The criterion here is that the blurred image of a point object should have a diameter not exceeding 25 microns (or .001").   Exposure in seconds.


      maximum exposure  =        350

                                           ——————

                                            focal length     (in mm.)



11. Simple formula for lens imaging;


         1     +    1    =    1

         —          —         —

         u           v           f


Where        u   =   object distance from lens

                  v   =   image distance from lens

                  f   =   focal length of lens



12. Make extensive use of similar triangles for simple optical calculations.  Projection distances, magnifications etc, can be computed easily.



13. How to place your meridian to a fraction of a degree.


    1.  Suspend a line between two points, (i.e. as a clothes line)

    2   Suspend from this line a plumb line.

    3   Work out when your local noon is from the BAA Handbook using

         your exact longitude (1 degree = 4 mins. time) and the Solar Equation

    4   Mark the shadow of the plumb line at local noon.



14. How to set up an equatorial mounting fairly accurately.


    1  Construct an angle equal to your latitude in some stiff sheet material.

        Offer this up to your polar axis (to be precise "axle") and using a spirit

        level set the axis.

    2  Use an engineer's "V block" plus a spirit level to make the declination

        axis horizontal.

    3  Use the shadow of the telescope tube (or projected solar image) together

        with knowledge of the local noon to rotate the whole telescope to the correct

        position.


Remember a degree is 1 part in 57.3 and represents 4 mins. of time.



15. Construct rectangles on tracing paper to lay over the maps in Norton's Star Atlas indicating the fields of view of your various camera/lens combinations.



16. Newtonian diagonals.  The formula (straight out of the text book but saves a lot of trouble) for computing the minor axis of an elliptical diagonal for a Newtonian reflector is:—


        w  =  d (D - a)  +  a

                 ————

                       f


where    w  =  minor axis of diagonal

             D  =  diameter of main mirror

              f  =  focal length of main mirror

             a  =  width of focal plane (i.e. field to be fully illuminated)

             d  =  distance from focal plane to diagonal



17. Try to be familiar with both imperial and metric units, particularly those of distance.  Metric units are fine for passing examinations but in the real world you need to know both.

Learn to convert in your head - very easy.


        1m = 39.4"    (approximate to 40")


        1" = 25.4mm. or 2.54cm.   (approximate to 25 & 2.5)


       .001" (a 'thou')  =  25.4 microns (approximate to 25)


       1mm = 39.4 thou (approximate to 40)


The approximations suit mental arithmetic admirably»


If any members have any other Hints and Tips, this is the place to pass them on.  Not only will they help other members if printed in MIRA, but they will be a useful source of reference in the future.  All kinds of ideas for observing, use of telescopes, things to make, best books to read on cloudy nights...... you know the sort of thing.  Just send them to the Editor and I'll do the rest.







Solar Observations

By Vaughan Cooper