Which of the following statement is correct ?

Question

UnlockIAS · Accepted Answer

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.

Why the other options are wrong — (b) 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.  (c) 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.  (d) 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.

Concept: 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.

State PCS 2023 Q41 — Science & Technology PYQ with Answer

State PCS 2023 Q41 — Science & Technology PYQ with Answer