Measuring the sky Astronomical Distances An Approximation n

Measuring the sky

Astronomical Distances An Approximation n n n If we would consider that the Earth has the size of a pea, then the Sun would have the size of a big melon, the distance between them being of “only” 33 meters (meaning approximately the length of a Boeing 737 -300). Considering this analogy, the closest star (Proxima Centauri) would be located at a distance of about 9000 kilometers, a very long flight for that particular plane! For measuring distances beyond the Solar System, astronomers use the following measuring units: • light year : the distance traveled by light in vacuum in a year (946080000 km). • parsec: an abbreviated term from the “one-second parallax” and it represents the distance from which the semi axis of the Earth’s orbit sub stretches an angle of one second (a parsec has 3. 26 light years ); for comparison, the moon disc observed from Earth sub stretches approximately 30 minutes of an arch ( half of a degree ). The number of stars in the galaxy is approximately equal to the number of sand grains in a bucket, and the number of stars in the entire universe is equal to the total number of sand grains on the entire Earth. How much does 0. 01 arcsec mean? If you look at a one-centimeter finger from a distance of 200 kilometers, you will see it under an angle of 0, 01 arcsec.

The analysis of the distances in the outer space n n 1. The triangulation method The estimation of the distances of the cosmic objects is based on the simple trigonometric method of establishing the distance to an inaccessible, but visible. 2. Considering a tree C situated beyond a river. We have to find out the distance from obs A to tree C. For this purpose, obs measures from A to B the distance called base. Afterwards, with the help of a universal instrument (teodolite), we measure the angles BAC and ABC. We apply the sinus theorem in the ABC triangle. The observer, moving from A to B, apparently moves the view distance to C. This is called a paralytic move. By keeping the same base, we can see that the size of C depends on the distance: the bigger it is, the smaller the distance is. The angle C under which we can see the base is called parallax point C. The distance is determined when we know the parallax.

n AC/sin B=AB/sin C n C=180 -(A+B) n AC=AB sin B/sin (A+B).

Establishing the distances and sizes of the stars n n n In order to determine the distances to the stars, we use the paralytic movement phenomenon. The paralytic movement is the apparent movement of the object, determined by the observer’s movement. OBS: The paralytic movement is bigger when the object is closer and the base is larger. If we choose a base whose length is easy to measure and we determine the angles between the base and the directions towards the object seen from the base extremity, then we can calculate the distance to the object, without directly measuring it.

The Parallax Considering the Earth as P and a star S at a known distance r. We consider R as being the terrestrial radius. From the Earth we can measure the angle (beta) under which we can see the star’s diameter: R=r sin β

The annual parallax n The stellar distances being bigger than the planetary ones, the P radius can’t build a base. We establish the distance between the Sun and the Earth. It is called the annual parallax the angle under which we can see from the centre of the star the Earth’s orbital radius when it is perpendicular on the Earth-star direction sin П= SP/D.

The Height Parallax n n The angle under which the observer on the star would see the terrestrial radius corresponds to the place of observation. Considering the star S, observed from the location A, with the zenith distance z. We consider D as being the distance to the star and r as the terrestrial radius. We apply the sinus theorem in OAS. If we consider the star placed in a horizontal position, z=90, we obtain the horizontal parallax.

n n Sin p=p=r/D p’/r=sin(180 -z)/D p’=r sin z/D p’=p sin z.

The proof of the Earth’s movement around the Sun n n The parallax phenomenon: during a year, each star describes on the sky a closed curve, its shape depending on the direction to the star and the angular distances depending on the distance to that star. Copernicus assumed that the annual parallax of the stars must exist, but because the distance between the stars and P are so huge, their parallactical movements are basically insignificant. That’s why astronomers from the 17 th -18 th centuries couldn’t notice this parallactical movement.

n n n The two movements, the heliocentric one and the geocentric one couldn’t be distinguished if there wasn’t the stellar parallax phenomenon. If the Earth wouldn’t revolve around the sun, an observer from the Earth would see each star always in the same direction; the star would project on the cosmic sphere in the same place. Still, the Earth moves itself and, with it, the observer also moves. Because the observer moves, the stars have to show a paralytic movement. If the observer and the Earth would move on a straight line, the paralytic movement would act unconditionally on the same direction and from one month to the next and from one year to the next some star would move in the sky always in the same direction.

n Because the observer moves with the Earth around the Sun during a year on an orbit with the shape of a circle, and after a year it repeats the same journey, the stars must present a parallactical movement with the period of one year. Each year, this apparent movement of the stars must repeat itself. It has to be periodical. Besides that, the parallactical movement, as we know depends on distances. That’s why the stars that are closer to us must present bigger parallactical movements, and the ones that are farther away – smaller parallactical movements.

n n When the people started to observe accurately the movements on the sky, they observed that the stars considered fixed weren’t fixed at all. These objects seem to move one from the others as the Earth moves from the Sun. The fact that the Earth moves around the Sun from a part to another of the solar system is very useful. This means twice a year our point of view concerning the distanced objects changes radically. “Fixed” stars

The Parallax in the Solar System n n In the Solar System, the apparent movement of the planets due to the Earth’s movement around the Sun, is complicated by the planets own movements around the Sun. This combination leads to an apparent backwards movement of the planets. This is what we call a retrograde movement. The characteristics of each planet’s movement consists in the fact that the planet is moving faster or slower than the Earth, and once a year, it describes a knot on the starlit sky

Cepheids and variable stars n n n A variable star means a star that pulses, meaning their luminosity changes rhythmically after a few days. A more luminous variable star has a bigger period Thus, by measuring a star’s period, we can calculate the luminosity, and then compare it to the magnitude observed from the Earth, we can find out how far that star is located

Radio calculation – another method of determining distances n Radiolocation allows us to determine precisely the distance to the nearby cosmic bodies. It consists in sending a radio wave with a determined wave length, emited in the direction of the respective cosmic body. By hitting its surface, the radio wave is reflected and it is intercepted by the observatory. By measuring the time between the moment of emission and reception , and by knowing its velocity, we can determine precisely the distance.

The history of astronomy n Aristotle: he considered that each planet, including the Sun and the Moon were each fixed on a transparent cosmic sphere. On the farthest of those spheres were situated all the stars. All those stars were concentric and in the middle of them was the immobile Earth. As for him, cosmic spheres were rotating around the Earth with different velocities partially involving each other, and this is why the apparent movements of the stars were taking place. This system is called geocentric.

Ptolemaeus n He was maintaining the geocentric system, but to explain the apparent movements in the shape of knots of the planets on the cosmic sphere, he imagined a system of epicycles. The epicycle is a smaller circle on which a planet moves with a constant angular velocity. At the same time the centre of this circle moves evenly on a bigger circle, with the Earth in the middle. The plans of those two circles were different. By composing these movements, we have the apparent curve with successive knots.

The revolutionary discovery of Copernicus n n The geocentric system of Ptolemaeus became too complicated and it arose mismatches between calculations and observations. Nicolaus Copernic described for the first time the real configuration and the movements of the planets from our solar system. His conclusion was that the Earth is moving. Thus, he explained the rise and fall of the stars by the daytime rotation of the Earth, and the apparent movement of the Sun on the ecliptic by the annual movement of the Earth around the Sun. His theory is based on the fact that all planets revolve around the Sun. The planets do not have their own light. They, as the Earth, are illuminated by the Sun.

Thus, according to Copernicus theory, the Earth became one of the planets that occupy the third position as opposed to the distance to the Sun. Copernicus explained the apparent roads of the planets, in shape of knots, by the fact that the Earth is moving at the same time with each planet. Because the revolving of the planets around the Sun take place at different times, it happens that the Earth surpasses a planet that then seems to move towards west from the stars. If the Earth will move at the time of the revolving in opposite direction of this planet, the planet will apparently move towards east.

n Copernicus determined the planets’ periods and the relative distances between the planets and the Sun ( taking as a unit of measure the distance Sun – Earth ), but he could not determine precisely the true shape of the planets’ orbits.

Johann Kepler n n Johann Kepler: he explained the true movement of the Earth and the planets. He established three laws that concur with the planets’ movements observations on the cosmic sphere. Galileo Galilei: he built a small telescope with which he discovered the existence of mountains on the Moon, a fact that proved the resemblance of the cosmic objects. He also discovered 4 satellites of Jupiter. Then, he discovered Venus’ phases, a fact that proved that Venus receives light from the Sun and then reflects it. He observed the dark patches on the surface of the Sun.

He also discovered that the luminous band, called The Milky Way, is composed of numerous stars. This proved that the Universe is much more bigger than people thought, the fact that the Universe was rotating around the Earth in only 24 hours being almost impossible. n Galilei confirmed, throughout ingenious observations, Copernicus’ theory n

Giordano Bruno n He stated that the stars are a sort of suns, situated at a great distance from us, that the Universe is endless and that there is an infinite number of stars and planets. Also, he said that there has to be life somewhere else. He was sentenced to death by the inquisitors, because he refused to give up on his beliefs.

Determining longitude and latitude n n Determining longitude is based on comparing the local time of the place where we are situated with the local time of the originary meridian, because the difference of the geographical longitude of two points is equal to the difference of their local times, at a given moment. Determining the geographical latitude is achieved by measuring the height of the polar star above the horizon at the moment of the superior or inferior culmination, having in mind its distance from the sky’s pole.

The discovery of Neptune and Pluto n n In 1781, the English amateur astronomer William Herschel discovered, with the help of the telescope, the seventh planet from the Sun, Uranus. By studying the movement of this new planet, at the beginning of the 19 th century, perturbations which couldn’t be attributed entirely to the known planets were observed. It was assumed that they were due to another unknown planet. The French astronomer, Le Verrier decided to solve this problem: knowing the perturbations produced by a planet, he determined the weight, its orbit and position at a given time. In September 1846, at Verrier’s request, the astronomer Galle from Berlin finds the new planet at only 52 minutes from the position indicated by him. It was named Neptune. Even after discovering Neptune, there were still left unjustified perturbations from Uranus, which indicated the existence of a transneptuniene planet. In 1930 this planet was also discovered and it was called Pluto. Thus, we could determine the perturbed masses (the third part of the system) as being nearly the size of Jupiter, so planetary masses. Thus the existence of other planetary systems was evidenced, the statement that the Earth could have an exceptional position being infirmed once again.