Final Answer:
The given statement "A planet's orbital speed varies as it travels along its elliptical orbit because as the planet gets closer to the Sun the force of gravity pushes the planet away from the Sun more strongly" is false because the variation in a planet's orbital speed is primarily attributed to the conservation of angular momentum, not the force of gravity.
Step-by-step explanation:
The first statement is false because the planet's orbital speed varies due to conservation of angular momentum, not because of the force of gravity. As a planet moves along its elliptical orbit, it experiences changes in gravitational potential energy, which results in variations in its kinetic energy and orbital speed. This is described by Kepler's second law, not by changes in gravitational force.
Kepler's third law can indeed be derived using Newton's law of gravity. Newton's law of gravity provides the necessary force acting between two masses, and when applied to a planet orbiting the Sun, it results in Kepler's third law, which establishes a relationship between the orbital period and the average distance from the Sun.
The statement about escape velocity is false. If an object achieves escape velocity, it will not return to its starting point. Escape velocity is the minimum speed needed for an object to "break free" from a celestial body's gravitational attraction.
Planets orbit the Sun in elliptical orbits due to gravitational forces, not friction. If friction were the dominant force, circular orbits would be expected. The absence of friction allows objects to maintain their motion indefinitely, consistent with Newton's first law of motion.
Kepler's laws are explained by Newton's laws of motion and gravity. Newtonian mechanics provides a more comprehensive understanding of the celestial motions described by Kepler's laws.
Finally, if not for gravity, the moon would indeed fly off into interplanetary space. Gravity is the force that keeps celestial bodies, including the moon, in orbit around larger masses. Without gravity, there would be no centripetal force to counteract the moon's inertia and keep it in orbit.