Final answer:
The question revolves around the speed of a comet at different points in its orbit based on Kepler's second law. Angular momentum conservation indicates that the comet's speed will be inversely proportional to its distance from the sun. Therefore, the comet travels faster when closer to the sun and slower when farther away.
Step-by-step explanation:
The student's question concerns the change in speed of a comet as it gets closer to the sun. According to Kepler's second law, the area swept out by the comet in a given amount of time is constant, so when the comet is closer to the sun, it must travel faster to sweep out the same area as when it is further away. The law implies that the comet's speed increases as it approaches perihelion (nearest point to the sun) and decreases as it moves toward aphelion (furthest point from the sun).
To answer the student's question specifically, we need to use the conservation of angular momentum, which states that the angular momentum of the comet is conserved as it moves along its orbit, assuming no external torques. Angular momentum, L, is given by L = mvr, where m is the mass of the comet, v is its speed, and r is the distance from the sun. Since the mass of the comet does not change, and angular momentum is conserved, then mvr must be a constant (mv1r1 = mv2r2). The ratio of the comet's speed at one position to its speed at another position is inversely proportional to the distance from the sun at those points.
Using the given data for speed and distance at one point in the comet's orbit, and the question's requested point in the orbit, we can set up a proportion to find the unknown speed. If 2.5×10⁴ m/s is the speed at 2.9×10¹¹ m, and we want to find the speed at 4.3×10¹⁰ m, we can use the relation (2.5×10⁴ m/s) × (2.9×10¹¹ m) = v2 × (4.3×10¹⁰ m). Solving for v2 gives us the comet's speed at the closer distance to the sun.