The correct answer is: C. both (a) and (b)
The length of the tropical year is the time it takes for the Earth to orbit the Sun once, relative to the vernal equinox. It is currently about 365.2422 days long.
The Earth’s rotational speed is slowing down very gradually due to the tidal friction caused by the Moon’s gravity. This is causing the length of the day to increase by about 1.7 milliseconds per century.
The Earth’s orbit around the Sun is also not perfectly circular. It is slightly elliptical, with an eccentricity of about 0.0167. This means that the Earth’s distance from the Sun varies by about 3% throughout the year.
The combination of these two effects is causing the length of the tropical year to decrease very slowly. The current rate of decrease is about 0.002 seconds per century.
Here is a more detailed explanation of each option:
- Option A: small, progressive changes in the earth’s rotational speed.
The Earth’s rotational speed is slowing down very gradually due to the tidal friction caused by the Moon’s gravity. This is causing the length of the day to increase by about 1.7 milliseconds per century. The tidal friction is caused by the difference in the gravitational pull of the Moon on the near and far sides of the Earth. This difference in gravitational pull causes the Earth to bulge out slightly on the side facing the Moon. The bulge creates a tidal force that slows down the Earth’s rotation.
- Option B: small, progressive change in earth’s orbit around the sun.
The Earth’s orbit around the Sun is also not perfectly circular. It is slightly elliptical, with an eccentricity of about 0.0167. This means that the Earth’s distance from the Sun varies by about 3% throughout the year. The Earth’s distance from the Sun is at its closest point (perihelion) in January and at its farthest point (aphelion) in July.
The Earth’s orbit is also affected by the gravitational pull of the other planets in the solar system. These gravitational interactions cause the Earth’s orbit to change very slowly over time. The Earth’s orbit is currently getting more elliptical, which means that the Earth’s distance from the Sun is increasing slightly.
- Option C: both (a) and (b).
The combination of the Earth’s slowing rotation and its slightly elliptical orbit is causing the length of the tropical year to decrease very slowly. The current rate of decrease is about 0.002 seconds per century.
- Option D: None of the above.
This option is incorrect because it does not include both of the factors that are causing the length of the tropical year to decrease.