Final answer:
The moon takes longer to orbit the sun because it is simultaneously orbiting the Earth, with gravitational forces maintaining the orbits of both bodies. Earth's gravitational pull is also responsible for the ocean tides due to the varying strength of pull on the water. Earth and the Moon share a common center of mass which orbits the Sun, with the Moon's orbit slightly elliptical.
Step-by-step explanation:
The correct statement that best describes the orbital relationship between the Earth, the moon, and the sun is: c) The moon takes longer to orbit the sun because it is also orbiting the Earth. The Earth and the Moon rotate around their common center of mass, which in turn orbits the Sun in an elliptical path. The gravitational interaction between the Earth and Moon is such that they exert equal and opposite forces on each other according to Newton's third law of motion, and this interaction causes the Moon to orbit the Earth. As for Earth's orbit around the Sun, the gravitational force from the Sun is central to keeping Earth in its nearly circular orbit, with only a 2% variation in distance from the Sun.
Furthermore, the gravitational force between the Earth and the Moon is also responsible for the ocean tides on Earth. The side of Earth closest to the Moon experiences a stronger pull, resulting in a high tide, while the opposite side also experiences a high tide due to Earth being pulled slightly away from the water on that side. These tidal forces are an observable effect of the Moon's gravity influencing the Earth.
The centripetal acceleration of the Moon in its orbit around Earth is caused by Earth's gravity and the path of the Moon's orbit is slightly elliptical. Earth and the Moon's common center of mass is located about 1700 km below the Earth's surface, indicating that the Moon's orbit has a significant effect on Earth as well. Thus, the orbital dance between these celestial bodies is a delicate balance of gravitational forces and motion.