Which of the following methods is used for measurement of distance between Earth and planets ?

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Correct — option (1), the parallax method. Parallax is the apparent shift in the position of a nearby object against a distant background when the object is viewed from two different places. It is an everyday effect and can be demonstrated without any apparatus: hold a pencil at arm's length, look at it with the left eye alone and then with the right alone, and the pencil appears to jump against the wall behind it. The jump is not in the pencil but in the observer, and its size depends on how far away the pencil is — bring it closer and the shift grows, hold it further off and the shift shrinks. That inverse relationship is what turns the effect into a measuring instrument. Suppose the same object is observed from two points separated by a known distance b, called the basis or baseline, and suppose the directions to the object from those two points differ by a small angle θ, called the parallax angle. If b is small compared with the distance to the object, the two lines of sight and the baseline form a very thin triangle in which the baseline is an arc of a circle of radius D centred on the object, so b equals D times θ with θ measured in radians, and the distance follows as D equals b divided by θ. Everything on the right-hand side is measurable: the baseline is a length on the Earth that can be surveyed, and the parallax angle is obtained by measuring the direction of the planet against the background of the far more distant stars from each of the two stations at the same moment. Nothing has to travel to the planet and nothing has to come back from it, which is precisely why the method works across distances that no physical instrument can span. The same principle scales upward. For a star, a baseline of a few thousand kilometres on the Earth's surface gives a parallax angle too small to measure, so the observations are made six months apart from opposite points of the Earth's orbit around the Sun, which gives a baseline of twice the Earth-Sun distance; this is stellar parallax, and it is the origin of the parsec, the distance at which a baseline of one astronomical unit subtends an angle of one second of arc. The method also measures sizes as well as distances, since once D is known the angular diameter of the planet multiplied by D gives its actual diameter. Option (1) is therefore the answer.

Why the other options are wrong — (b) Direct distance measurement means laying a known length against the distance to be measured — a tape, a chain, a measuring wheel — and counting how many times it fits. It is the basis of ordinary surveying and it is exactly what cannot be done here. There is no physical path along which a measuring instrument could be carried from the Earth to a planet, the separation changes continuously as both bodies move along their orbits, and even the nearest planet is at a distance millions of times greater than the largest instrument that could be built. The option is worth taking seriously for a moment rather than dismissing, because it identifies the exact difficulty that makes astronomical distance measurement a subject at all: every method used in astronomy is indirect, inferring a distance from an angle, from a travel time or from a comparison of apparent and known brightness, precisely because the direct method is unavailable.  (c) This is not a recognised technique for determining astronomical distances, and no established method of measuring the separation between the Earth and a planet goes by this name. Measuring along a slope with a tape or chain belongs to terrestrial surveying, where distances are short enough to be spanned physically and where the practical problem is reducing a measurement made along sloping ground to its horizontal equivalent. That problem does not arise, and could not arise, in astronomy. The option is included as a plausible-sounding technical phrase, and it tests a specific discipline: a candidate should reject a term because it does not belong to the subject the question is about, not accept it because it sounds technical. When an unfamiliar name appears among three familiar ones, the first question to ask is which branch of science the name belongs to.  (d) The echo method determines a distance by sending out a sound, waiting for it to be reflected from the target and return, and multiplying the speed of sound by the time taken before halving the result, since the sound covers the distance twice. It is how the depth of the sea is sounded and how the distance of a reflecting surface such as a cliff can be found. It cannot work between the Earth and a planet for a reason that has nothing to do with the arithmetic: sound is a mechanical wave and requires a material medium to travel through, and the space between the Earth and the planets is very nearly a vacuum, so no sound leaves the Earth's atmosphere and no echo returns. The distinction to hold is between mechanical waves, which need a medium, and electromagnetic waves, which do not, and it is the reason reflection methods are available to astronomy only in their electromagnetic form.

Concept: Distances in physics span an enormous range, and no single technique covers it. Very small lengths are found by indirect inference, ordinary lengths by direct comparison with a standard, and astronomical distances by geometry or by timing a signal. The parallax method is the geometrical technique and it is the foundation of the astronomical distance scale. Its content is a single relation: if an object is viewed from two points separated by a baseline b, and the two directions to it differ by a parallax angle θ, then the distance is b divided by θ, with the angle in radians. The two measurements that feed the formula are of quite different kinds — b is a length surveyed on the Earth or, for stars, taken from the size of the Earth's orbit, while θ is an angle read off against the background of very distant objects — and the accuracy of the result is limited almost entirely by how finely the angle can be measured. That limitation sets the reach of the method: parallax angles shrink as distance grows, so the technique works for the Moon and the planets from a terrestrial baseline, for the nearer stars from the baseline of the Earth's orbit, and not at all for objects beyond a certain range, for which brightness-based methods take over. Two related ideas are usually taught alongside it. First, once the distance to a body is known, its angular diameter as seen from the Earth multiplied by that distance gives its true diameter, so parallax yields sizes as well as distances. Second, modern practice within the solar system no longer relies on parallax for the highest precision: radar ranging to the planets and laser ranging to the Moon time the return of a reflected electromagnetic signal, which is a reflection method of the kind the echo option gestures at, but using waves that cross a vacuum, which sound cannot do. The unit that came out of stellar parallax, the parsec, remains in use as the standard astronomical measure of distance and is defined as the distance at which one astronomical unit subtends one second of arc.

State PCS 2022 Q36 — Science & Technology PYQ with Answer

State PCS 2022 Q36 — Science & Technology PYQ with Answer