Astronomy of time (tropical year): The length of the tropical year (interval between successive spring equinoxes) is decreasing very slowly. This slow decrease primarily results from which long-term changes in Earth's motions? Choose the most accurate cause.

Given data

• Tropical year is measured from equinox to equinox; subtle secular variations are observed.

Concept/Approach
Very small, long-term changes arise from orbital perturbations (e.g., precession, gravitational interactions) and from rotational changes (e.g., tidal friction slowly altering Earth's rotation rate). Together these contribute to tiny secular shifts in the tropical year.

Common pitfalls
Attributing the effect to only one component; in reality, both orbital and rotational dynamics are involved.

Final Answer
Both (a) and (b)