It has been so long since the last time, but now I have realised that the Magnetism chapter presentation wasn’t uploaded!

Well, here you have Diana’s presentation. Mine is gonna come soon!!

PS: Please, if for any reason you see that there is something left to put on the blog, don’t hesitate to tell next time you see me arround!!

Thank you very much

MA

Navigation for Grip Limited

I found this on my travels and is a prime example of NOT to use navigation to enhance an experience in my opinion anyway. For starters it takes forever to load, as it does each segment individually. Second of all, if you’re too lazy to close each window after you’ve read inside it, you find yourself having to spend even more time closing them all so that you can read another tab. In all fairness if you find the main navigation irritating, they have included a bar at the top to which opens up with all the links. Have a look for yourself.

Check out!

Kind Regards

MA

Department of Physics

User’s Guide to the Night Sky

The Ecliptic: the Sun’s Annual Path on the Celestial Sphere

As the Earth orbits around the Sun over the course of the year, we observe the Sun to track out a circle around the celestial sphere. This track of the Sun on the celestial sphere is called the ecliptic. Relative to the “fixed” stars we observe the Sun to move eastwards on the celestial sphere completing one full circuit of 360° over the year (~365.25 days), i.e. an eastward motion of ~1° per day. The zodiac is the set of constellations on the ecliptic, (i.e. those that the Sun travels through in the course of the year). The traditional twelve zodiac constellations are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius and Pisces.

The animation above shows the Sun moving along the ecliptic (green line) over the course of one year. This diagram is in ecliptic coordinates, i.e. relatively to ecliptic (longitude measures the angle around the ecliptic and latitude measures the angle away from the ecliptic). By definition the Sun tracks along the zero ecliptic latitude line.

The Earth’s spin axis is tilted by 23.5° with respect to the Earth’s orbital plane (the ecliptic plane). The direction of Earth’s spin axis is fixed in space.

The tilt of the Earth’s spin axis with respect to the ecliptic plane results in the Sun tracking out an seemingly sinusoidal path on the celestial sphere when viewed in the projection with the celestial equator horizontal.

The animation above shows the Sun moving along the ecliptic (green line). This diagram is in equatorial coordinates, i.e. Right Ascension and Declination. The (red line) is the celestial equator. In the course of the year, the Sun spends six months above the celestial equator (~21st March to ~20th September) and six months below (~20th September to the ~21st March). It is this 23.5° tilt of the Earth’s spin axis with respect to the ecliptic plane which causes the seasons.

Each year we see the Sun cross the celestial equator moving northwards on about 21st March. This is the vernal (March) equinox and at this time the Sun, by definition, is at RA = 0^h, Dec = 0.0°. At the equinoxes at every location on the Earth the Sun spends 12 hours above the horizon and 12 hours below the horizon. The Sun rises precisely in the East and sets precisely in the West; the Sun is on the celestial equator. This animation shows the track of the Sun across the sky as seen from Durham at the time of the equinox.

For northern hemisphere observers the Sun stops moving up the celestial sphere reaching its highest point on about 21st June, i.e. at the summer (June) solstice. The word solstice means “Sun standing still”. At this time the Sun is at RA = 6^h, Dec = +23.5°. At this time northern hemisphere observers receive the maximum amount of sunlight because the Sun is highest in the sky at noon and is above the horizon for the longest period. This animation shows the track of the Sun across the sky as seen from Durham at the time of the summer solstice.

On about 20th September, the Sun crosses the celestial equator moving southwards. This is the autumnal (September) equinox. At this time the Sun is at RA = 12^h, Dec = 0.0°.

The Sun reaches its lowest point at the winter (December) solstice on about 21st December. At this time the Sun is at RA = 18^h, Dec = −23.5°. Northern hemisphere observers receive the minimum amount of sunlight at this time as the Sun is lowest in the sky at noon and is above the horizon for the shortest time. This animation shows the track of the Sun across the sky as seen from Durham at the time of the winter solstice.

This animation shows how the position of the midday Sun changes over the year as seen from Durham.

A good approximation to the Sun’s position is given by

RA [deg] = λ + 2.45 sin 2λ        sin Dec [deg] = 0.4 × sin λ   ( or Dec [deg] = 23.5 × sin λ ) ,

where λ is the Sun’s ecliptic longitude. &lambda can be estimated by assuming that the Earth’s orbit is circular ( λ = 0° on 21st March, λ = 30° on 21st April, λ = 60° on 21st May, λ = 90° on 21st June, etc). For example, estimate the Sun’s RA and Dec on 21th January? At this date the Sun’s λ = 300° (i.e. about two months before the vernal equinox). Using the above formulae we estimate that on the 21st January the Sun’s RA = 299.1° (19^h 56.4^m) and Dec = −20.3°.

Here you have a quick Wikipedia explanation of how the Equation of Time (relationship between apparent and mean times )varies throughout the year.

You might find it interesting

MA

Equation of time

From Wikipedia, the free encyclopedia

The equation of time — above the axis a sundial will appear fast relative to a clock showing local mean time, and below the axis a sundial will appear slow.

The equation of time is the difference between apparent solar time and mean solar time. At any given instant, this difference will be the same for every observer. The equation of time can be found in tables (for example, The Astronomical Almanac) or estimated with formulas given below.

Apparent (or true) solar time can be obtained for example by measurement of the current position (hour angle) of the Sun, or indicated (with limited accuracy) by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time average to zero (with zero net gain or loss over the year).^[1]

During a year the equation of time varies as shown on the graph; its change from one year to the next is slight. Apparent time, and the sundial, can be ahead (fast) by as much as 16 min 33 s (around 3 November), or behind (slow) by as much as 14 min 6 s (around 12 February). The equation of time has zeros near 15 April, 13 June, 1 September and 25 December.^[2][3]

The graph of the equation of time is closely approximated by the sum of two sine curves, one with a period of a year and one with a period of half a year. The curves reflect two astronomical effects, each causing a different non-uniformity in the apparent daily motion of the Sun relative to the stars:

• the obliquity of the ecliptic (the plane of the Earth’s annual orbital motion around the Sun), which is inclined by about 23.44 degrees relative to the plane of the Earth’s equator; and

• the eccentricity of the Earth’s orbit around the Sun, which is about 0.0167.

The equation of time is also the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth.

The equation of time was used historically to set clocks. Between the invention of accurate clocks in 1656 and the advent of commercial time distribution services around 1900, one of two common land-based ways to set clocks was by observing the passage of the sun across the local meridian at noon. The moment the sun passed overhead, the clock was set to noon, offset by the number of minutes given by the equation of time for that date. (The second method did not use the equation of time; instead, it used stellar observations to givesidereal time, in combination with the relation between sidereal time and solar time.)^[4] The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides.^[5][6]

Naturally, other planets will have an equation of time too. On Mars the difference between sundial time and clock time can be as much as 50 minutes, due to the considerably greater eccentricity of its orbit. The planet Uranus, which has an extremely large axial tilt, has an equation of time that can be several hours.

The Earth revolves around the Sun. As seen from Earth, the Sun appears to revolve once around the Earth through the background stars in one year. If the Earth orbited the Sun with a constant speed, in a circular orbit in a plane perpendicular to the Earth’s axis, then the Sun would culminate every day at exactly the same time, and be a perfect time keeper (except for the very small effect of the slowing rotation of the Earth). But the orbit of the Earth is an ellipse, and its speed varies between 30.287 and 29.291 km/s, according to Kepler’s laws of planetary motion, and its angular speed also varies, and thus the Sun appears to move faster (relative to the background stars) at perihelion (currently around January 3) and slower at aphelion a half year later. At these extreme points, this effect increases (respectively, decreases) the real solar day by 7.9 seconds from its mean. This daily difference accumulates over a period. As a result, the eccentricity of the Earth’s orbit contributes a sine wave variation with an amplitude of 7.66 minutes and a period of one year to the equation of time. The zero points are reached at perihelion (at the beginning of January) and aphelion (beginning of July) while the maximum values are in early April (negative) and early October (positive).

Graph showing the equation of time (red solid line) along with its two main components plotted separately, the part due to the obliquity of the ecliptic (mauve broken line) and the part due to the Sun’s varying apparent speed along the ecliptic due to the eccentricity & ellipticity of the Earth’s orbit (dark dash-dotted line)

Aquí os dejo algunas de las presentaciones del temario para piloto privado. Al menos las vistas en clase.

He de decir que las presentaciones son en español dado que las clases se imparten en este idioma.

Espero que os sirvan.

Ante cualquier duda, no dejéis de preguntar

Un saludo

MA

Hello everyone.

Here you have some of the presentations from the JAR-FCL syllabus for private pilot licence. At least the ones seen in class.

I have to tell you that all these presentations are written in spanish due to the fact of this being the official language for the Licence in Spain.

I hope they’d be of your interest.

Should you have further questions, don’t hesitate to contact me.

MA

Within it you will be able to see, in a more visual manner, the interrelation between the perihelion, aphelion, Earth’s axis tilting angle towards the ecliptic and some other stuff that might be of your interest and can help you out on the understanding of the Earth’s movement arround the Sun and it’s own rotatory movement.

http://web.me.com/uriarte/Earths_Climate/Appendix_5..html

Good luck

MA

Use it wisely!!;-)

Here you have the explanation given in class about the use of the ETAS in relation with the WCA.

hope you find it useful!!