Explanation:

- Halley's comet is a well-known comet that orbits the sun.

- It is famous for its regular appearances in Earth's sky.

- Option 1: 85-86 years - This is not the correct periodicity.

- Option 2: 45-46 years - This is too short for Halley's comet's cycle.

- Option 3: 75-76 years - This is the correct periodicity of Halley's comet.

- Option 4: 30-31 years - This is also too short for Halley's comet.

The periodicity of Halley's comet is approximately every 75 to 76 years, which aligns with option 3. .