To determine which planet is closer to the sun, we can use Kepler's third law of planetary motion, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis of its orbit (R), which represents the distance from the sun. Mathematically, this is expressed as:
[tex]\[ T^2 \propto R^3 \][/tex]
Given the durations (orbital periods) of the two planets:
- Planet Y has an orbital period of 224 days.
- Planet Z has an orbital period of 320 days.
Let's analyze these durations step-by-step:
1. Understanding the Proportionality: According to Kepler’s third law:
- A shorter orbital period (T) means that the planet has a smaller semi-major axis (R), implying it is closer to the sun.
- Conversely, a longer orbital period (T) means a larger semi-major axis (R), implying the planet is farther from the sun.
2. Comparison of Year Durations:
- Planet Y: 224 days
- Planet Z: 320 days
Planet Y has a shorter period compared to Planet Z.
3. Conclusion from the Orbital Periods:
- Since Planet Y has a shorter year duration (224 days) compared to Planet Z (320 days), Planet Y must be closer to the sun.
4. Gravitational Force Consideration:
- The sun exerts a greater gravitational force on planets that are closer to it.
- Therefore, the planet closer to the sun (Planet Y) will experience a stronger gravitational pull from the sun.
Considering all these points, the correct explanation is:
Planet Y, because the sun exerts a greater gravitational force on it than on planet Z.
