If the orbit of a planet around the Sun is an ellipse, the Sun is located at which special point of that ellipse?

Introduction / Context:
Kepler laws of planetary motion describe how planets move around the Sun. According to the first law, planets move in elliptical orbits rather than perfect circles. In geometry, an ellipse has special points called foci, which play an important role in defining its shape. This question checks whether you know where the Sun is located in that elliptical path.

Given Data / Assumptions:

• The orbit of the planet is elliptical, not circular.
• An ellipse has two focal points called foci.
• The options mention centre, focus, incentre, and circumcentre.
• We apply standard geometry and Kepler first law.

Concept / Approach:
In geometry, an ellipse is defined as the set of points such that the sum of the distances to two fixed points (the foci) is constant. The centre of the ellipse lies halfway between the foci, but the foci are not at the centre. Kepler first law states that each planet moves in an elliptical orbit with the Sun at one focus. This means that the Sun is not at the centre of the orbit, but at one of the two foci of the ellipse. Incentre and circumcentre are terms used for triangles, not for ellipses, so they are not relevant to planetary orbits.

Step-by-Step Solution:

Verification / Alternative check:
Astronomy diagrams in textbooks show planetary orbits drawn as ellipses with the Sun off centre, located at one focus. This explains why a planet is at varying distances from the Sun during its orbit, leading to phenomena such as perihelion and aphelion. Observational data of planetary positions over time match the predictions of elliptical orbits with the Sun at a focus rather than at the centre.

Why Other Options Are Wrong:

• The exact geometric centre of the ellipse is wrong because Kepler law clearly states a focus, not the centre.
• The incentre is wrong because it is a concept from triangle geometry where angle bisectors meet.
• The circumcentre is wrong because it is the centre of a circumscribed circle around a polygon and has no role in defining an ellipse.

Common Pitfalls:
Many learners still imagine planetary orbits as perfect circles with the Sun at the centre because that idea is simpler. This mental picture leads them to choose the centre option. To avoid this, remember the phrase elliptical orbits with the Sun at one focus. This phrase captures both the shape and the correct position of the Sun.

Final Answer:
At one of the foci (focus points) of the ellipse