Final answer:
The comparison of moons A, B, C, and D via a double number line could refer to their distances or speeds in orbit around a planet. Experiments simulating the Earth-Moon-Sun system help understand the Moon's phases and orbit. The use of scale models can effectively demonstrate the relative sizes and distances in the Earth-Moon system.
Step-by-step explanation:
Understanding Moon Phases and Orbits
To represent the differences between moons A, B, and C and moon D, you can use a double number line to show various attributes such as their distance from the planet they orbit or their orbital speeds. For moons in elliptical orbits, revealing how speed varies at different points can be crucial. For instance, suppose at point A (perihelion) the moon's speed is uA and at point B (aphelion) the moon's speed is uB, you might find that angular momentum remains constant if no external forces act on it, as proposed by Kepler's laws.
The phases of the Moon, as seen from Earth, change over a month because half of the Moon is always illuminated by the Sun, and as the Moon orbits our planet, different portions of this illuminated side become visible to us. The concepts of angular momentum, phases, and the various positions of the Moon in its orbit can be explored with experiments such as holding a tennis ball to represent the moon and observing phases, or on a larger scale, using a globe and a smaller object to simulate the Earth-moon system's proportions and distances.
To better appreciate the Moon's orbit and size compared to Earth, one could also use a grain of sand and a speck of dust to represent the relative sizes of Earth and the Moon, respectively. Such hands-on activities encourage deep understanding of celestial mechanics and the appearance of the Moon from Earth.