The correct answer is option 1, Kepler’s second law. Kepler’s second law, also known as the Law of Equal Areas, states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. This law describes how the speed of a planet varies as it moves along its elliptical orbit around the sun.

Statement 1, "The earth does not move along its orbit at a constant rate," is true according to Kepler`s second law. It means that the speed of Earth changes as it moves around the sun. This is because Earth`s orbit follows an elliptical path, and as it gets closer to or farther from the sun, its speed changes.

Statement 2, "The earth moves fastest at perihelion and slowest at aphelion," is also true according to Kepler`s second law. Perihelion is the point in Earth`s orbit where it is closest to the sun, while aphelion is the point where it is farthest from the sun. At perihelion, Earth moves fastest due to the sun`s gravitational pull being stronger. At aphelion, Earth moves slowest because the gravitational pull is weaker.

Therefore, the correct option is 1, Kepler’s second law,