MPSC 2023 Prelims Paper-I · Question 41 of 100

Correct — option (1). A planet moves fastest when it is closest to the Sun and slowest when it is farthest away, and this is not an observation that has to be memorised on its own: it is a direct reading of Kepler's second law, the law of areas. That law says that the line joining a planet to the Sun sweeps out equal areas in equal intervals of time. Picture the thin triangle traced out by that line in one day. Near the Sun the line is short, so for the triangle to have the same area as one traced far from the Sun the planet must travel a long way along its orbit in that day — it must move quickly. Far from the Sun the line is long, so a much shorter arc of travel already fills the same area, and the planet crawls. Equal areas in equal times therefore forces the orbital speed to rise as the distance falls and to fall as the distance rises. The deeper reason is the conservation of angular momentum. Gravity always pulls the planet straight towards the Sun, so it exerts no twisting force about the Sun and the planet's angular momentum about the Sun cannot change. Angular momentum is the product of mass, distance and the component of velocity across the line to the Sun, so if the distance shrinks the speed must grow to keep the product fixed. Energy tells the same story: as the planet falls inwards, gravitational potential energy is converted into kinetic energy, and as it climbs outwards the exchange runs the other way. The point of nearest approach is called perihelion and the point of greatest distance aphelion; the Earth passes perihelion in early January and aphelion in early July, which is also why the northern winter half of the year is slightly the shorter one. Option (1) states exactly this relationship, so it is the answer.

• (2)The speed of Planet is faster when they are farther from the sun and slower when they are nearer to the sun. — This is the exact reversal of Kepler's second law and it is the trap the question is built around, because it appeals to an everyday intuition that a body far from a pull should be free to move quickly while a body close to it should be dragged and slowed. Orbital motion works the other way. The Sun's gravity does not act as a brake along the path; it acts as a centre-directed pull that speeds the planet up on the way in and slows it down on the way out. If this option were true the line from the Sun to the planet would sweep large areas when the planet is far away and small ones when it is near, which is precisely what the law of areas forbids, and angular momentum about the Sun would not be conserved.
• (3)The speed of Planet is same when they are nearer to the sun or farther away from the sun. — A constant orbital speed is what you would get if planetary orbits were perfect circles travelled at a uniform rate, which is the pre-Keplerian picture that Kepler's own work overturned. His first law establishes that the orbit is an ellipse with the Sun at one focus, so the planet's distance from the Sun genuinely changes over the course of one revolution, and once the distance changes the second law makes a change of speed unavoidable. Choosing this option usually means the candidate is carrying the school diagram of a circular orbit in mind. The orbits of most planets are only mildly elliptical, so the diagram is a fair sketch of the shape — but it is exactly the small departure from a circle that this question is testing.
• (4)The speed of Planet is faster when they are nearer to the sun or farther away from the sun. — This option never actually states a relationship. As printed it joins the two extremes with 'or' — faster when nearer to the sun OR farther from it — so it commits to neither, and a claim that a planet is fastest at one end or the other of its orbit, without saying which, carries no information a candidate could act on. Kepler's second law does commit: the radius vector sweeps equal areas in equal times, so the speed is greatest at perihelion and least at aphelion, which is what option (1) says. Read as covering BOTH extremes it is worse still, because 'faster' means nothing unless something else is slower — and note that the मराठी column prints this option with 'व' (and) rather than 'or', which makes that stronger reading the only one available to a Marathi candidate. It is the kind of choice that survives only if a candidate reads the first half of the sentence, sees the familiar words 'faster when they are nearer to the sun', and stops there — which is why it sits in the set at all. Reading each option to its full stop, and asking whether the sentence describes a state of affairs that could physically obtain, disposes of it without any knowledge of Kepler.

Kepler's three laws describe planetary motion without explaining its cause, and they are best held as three separate statements about three different things. The first law is about the shape of the orbit: every planet moves in an ellipse with the Sun at one of the two foci, which means there is a nearest point, perihelion, and a farthest point, aphelion. The second law is about the rate of motion along that shape: the radius vector from the Sun to the planet sweeps equal areas in equal times, which is another way of saying the planet is fast near the Sun and slow far from it. The third law is about the comparison between different planets: the square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit, so an outer planet takes disproportionately longer to complete a circuit. Newton later showed all three follow from an inverse-square law of gravitation; in particular the second law follows from nothing more than the fact that gravity is a central force, one directed straight at the Sun, which exerts no torque and so leaves the planet's angular momentum about the Sun unchanged. That is why the second law holds for any central force at all, not just for gravity.

MPSC's general science section reaches for Kepler regularly because the laws can be tested as pure recall, as a diagram, or — as here — as a plain-language statement that a candidate must judge true or false. The habit the question rewards is reading all four options to the end before choosing, because this set contains a reversal of the correct statement, a statement that quietly assumes a circular orbit, and one that is internally inconsistent. All four begin with the same nine words, so a candidate who scans only the openings has no way to separate them. The second habit worth building is to attach a physical reason to each law rather than a form of words: equal areas in equal times because angular momentum about the Sun is conserved, an elliptical orbit because the inverse-square law admits conic sections, a period-distance relation because the strength of the pull falls with distance. A law held with its reason survives a paraphrase; a law held as a sentence does not, and the Commission paraphrases freely — note that this paper's Marathi column puts the same alternatives in terms of maximum and minimum distance from the Sun rather than nearer and farther.

• Kepler's second law, the law of areas, states that the line joining a planet to the Sun sweeps out equal areas in equal intervals of time, which requires the planet to move fastest near the Sun and slowest far from it.
• The law of areas is a consequence of the conservation of angular momentum: gravity is a central force directed at the Sun, so it exerts no torque about the Sun and the planet's angular momentum about it stays constant.
• Kepler's first law states that each planet moves along an ellipse with the Sun at one focus, so the Sun-planet distance varies through the orbit between a nearest point called perihelion and a farthest point called aphelion.
• Kepler's third law states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit, so planets farther from the Sun take disproportionately longer to complete one revolution.
• The Earth reaches perihelion in early January and aphelion in early July; the seasons are caused by the tilt of the Earth's axis and not by this change in distance.

• Reversing the law of areas and believing a planet speeds up as it moves away from the Sun, which is what option (2) offers
• Assuming a circular orbit travelled at uniform speed, the picture Kepler's first law replaced and the assumption behind option (3)
• Reading only the opening words of options that all begin identically, which is how option (4) collects its marks
• Explaining the seasons by the Earth's varying distance from the Sun rather than by the tilt of its axis

Kepler appears in MPSC papers in three recognisable shapes. The first is straight attribution — which law says what, or which scientist stated the law of areas. The second is a statement-judgement item like this one, where the correct law and its exact reversal are both printed and the candidate has to know which way round it goes. The third is applied, asking where in its orbit a planet or a comet moves fastest, or why a comet is visible for a short time near the Sun and spends decades in the outer part of its path. Because the same content also underpins questions on satellites and on the seasons, it repays being learnt as physics rather than as three sentences, and the relationship worth fixing first is the simple one this question tests: closer means faster.

No directly related past PYQ was found.

• practice — not a real PYQ

  A planet moving in an elliptical orbit around the Sun has its greatest orbital speed at which of the following points ?

  • (a)Aphelion, the point farthest from the Sun
  • (b)Perihelion, the point nearest to the Sun
  • (c)The two ends of the minor axis, where the speed is equal
  • (d)The speed is the same at every point of the orbit

  Answer(b) Perihelion, the point nearest to the Sun — Kepler's law of areas requires the radius vector to sweep equal areas in equal times, so when the line to the Sun is short the planet must cover a long arc in the same interval. The same conclusion follows from the conservation of angular momentum about the Sun, which forces the speed to rise as the distance falls.

• practice — not a real PYQ

  Kepler's second law of planetary motion is a direct consequence of the conservation of which of the following quantities ?

  • (a)Linear momentum of the planet
  • (b)Angular momentum of the planet about the Sun
  • (c)Kinetic energy of the planet
  • (d)Mass of the Sun

  Answer(b) Angular momentum of the planet about the Sun — gravity is a central force, always directed along the line joining the planet to the Sun, so it exerts no torque about the Sun and the planet's angular momentum about it cannot change. The kinetic energy is not conserved, since it rises on the inward leg and falls on the outward leg as it trades with gravitational potential energy.