MPSC 2022 Prelims Paper-I · Question 36 of 100

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.

• (2)Direct distance measurement — 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.
• (3)Slope tapping method — 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.
• (4)Echo method — 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.

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.

The science section of an MPSC paper is set at roughly school level and draws heavily on the standard physics syllabus, of which measurement and units is an early and frequently examined chapter. Parallax is one of the two or three topics from that chapter that appear regularly, along with significant figures, dimensional analysis and orders of magnitude, because it can be tested in a single sentence and has a clean right answer. Questions on it come in three forms: name the method, apply the formula to given numbers, or identify what the method can and cannot do. The defence against all three is to hold the relation D equals b divided by θ together with a physical picture of the thin triangle it comes from, since a formula memorised without the picture is easily inverted under pressure. This particular item also rewards a habit that pays throughout a science section: when an option carries an unfamiliar technical-sounding name, ask which branch of science it belongs to before asking whether it is correct. Two of the wrong options here are real techniques used in the wrong domain — direct measurement in surveying, echo ranging in sound — and one is a name that belongs to no astronomical method at all. Sorting them by domain answers the question even for a candidate whose recall of the parallax formula has failed.

• Parallax is the apparent change in the position of a nearby object against a distant background when it is observed from two different points; the size of the shift decreases as the object's distance increases.
• If a baseline of length b separates the two observation points and the parallax angle between the two lines of sight is θ in radians, the distance to the object is D equals b divided by θ.
• For planets the baseline is a measured separation between two points on the Earth's surface, and the parallax angle is found by measuring the planet's direction against the background of far more distant stars from both stations at the same time.
• For stars the terrestrial baseline is too short, so observations are taken six months apart from opposite points of the Earth's orbit, giving a baseline of twice the Earth-Sun distance; this is the basis of the parsec, the distance at which one astronomical unit subtends one second of arc.
• Once the distance is known, the angular diameter of the body multiplied by that distance gives its actual diameter, so the same method yields sizes as well as distances; sound-based echo methods cannot be used in space because sound requires a material medium.

• Inverting the parallax relation and writing the distance as the baseline multiplied by the angle, which a candidate who has memorised the formula without its geometry does under pressure
• Forgetting that the parallax angle must be expressed in radians before the relation is applied, when astronomical angles are usually quoted in seconds of arc
• Accepting an unfamiliar technical-sounding option without first asking which branch of science the term belongs to, since two of the wrong options here are genuine techniques from surveying and from acoustics
• Supposing that a sound-based echo method could be used across space, when sound is a mechanical wave and cannot travel through the near-vacuum between the Earth and the planets

Basic physics reaches MPSC papers as single-sentence recall questions and as short numerical problems, and the chapter on units and measurement supplies both kinds. The recall form, used here, names a quantity and asks for the technique, or names a technique and asks what it measures. The numerical form gives a baseline and a parallax angle and asks for the distance, and it is worth practising with the angle given in seconds of arc so that the conversion to radians becomes automatic. Astronomy questions in this section stay close to the school textbook and rarely require anything beyond the parallax relation, the definitions of the astronomical unit, the light year and the parsec, and an understanding of why sound cannot travel through space. Because the science section is answered quickly by well-prepared candidates and slowly by everyone else, these questions are disproportionately valuable: they are among the few in the paper that can be settled with certainty rather than judgement.

No directly related past PYQ was found.

• practice — not a real PYQ

  A planet is observed from two points on the Earth's surface separated by a baseline b, and the two lines of sight differ by a parallax angle θ measured in radians. The distance D of the planet is given by which relation ?

  • (a)D equals b multiplied by θ
  • (b)D equals b divided by θ
  • (c)D equals θ divided by b
  • (d)D equals b multiplied by the square of θ

  Answer(b) D equals b divided by θ. The baseline is treated as a short arc of a circle of radius D centred on the planet, so that b equals D times θ with the angle in radians, and rearranging gives the distance. The physical sense of the relation is a useful check against inverting it: a smaller parallax angle means a more distant object, so the angle must sit in the denominator. Note that an angle quoted in seconds of arc must be converted to radians before the relation is used.

• practice — not a real PYQ

  Why can the echo method, which measures distance by timing a reflected sound, not be used to find the distance between the Earth and a planet ?

  • (a)Because the speed of sound is not accurately known
  • (b)Because sound is a mechanical wave and cannot travel through the near-vacuum of space
  • (c)Because the reflected sound would return too quickly to be timed
  • (d)Because planets do not have solid surfaces to reflect sound from

  Answer(b) Because sound is a mechanical wave and cannot travel through the near-vacuum of space. A mechanical wave propagates by disturbing the particles of a medium, so where there is effectively no medium there is no wave, and no signal leaves the Earth's atmosphere. Reflection-based ranging is nonetheless used in astronomy, but in its electromagnetic form: radar ranging to the planets and laser ranging to the Moon time the return of a signal that can cross a vacuum.