The following independent statements are made about hypothetical planets revolving around the Sun.
S1. A planet in an elliptical orbit spends equal times while covering the two halves of its orbit that lie on either side of the major axis.
S2. A planet at aphelion has the same linear speed as another planet whose circular orbit has the same radius as that aphelion distance.
S3. Two different planets having the same semi-major axis must have the same time period of revolution.
S4. If the semi-major axis of a planet were doubled, its time period would also double.
S5. The Sun is located at the centre of every planetary orbit.
Examine each statement in the light of Kepler’s laws.
(i) For each statement S1–S5, state whether it is consistent with Kepler’s laws or violates them.
(ii) For every statement that violates Kepler’s laws, identify the specific law that is contradicted and rewrite the statement in a corrected form, giving concise reasoning for the correction.