How does the Earth orbit the sun without losing energy? Your question reveals a fallacy that hindered the development of physics from the times of antiquity until the early modern ages, Newton and others. The idea that staying in a state of motion requires energy. It does not. Now this goes contrary to our terrestrial experience. Carts don't move by themselves, they need horses to pull them. Cars come to a halt if they run out of gas. Airplanes fall out of the sky. Boats stop dead in the middle of the sea if nothing pushes them. So clearly, motion requires a continuous input of energy, no? Or maybe it is not motion. Energy is required not to keep the cart moving but to overcome the resistance of the mud in which its wheels are stuck. Cars might move forever if it weren't for friction of the wheels and air resistance. Airplanes could just glide to other continents if the air didn't stand in the way. These factors are absent in space. There is no mud, no friction, no air. The Earth is moving through space with nothing slowing it down, and simply staying in that state of motion requires no additional input of energy. Even the ancients recognized that the celestial sphere is subject to different rules; they just didn't know why it was so that here on the Earth, motion required work, whereas in the skies, the Sun, the Moon, the planets were happily moving about forever without any apparent force acting on them. Since Newton's times, we know the reason: The rules are, in fact, the same, it's just that here on the Earth, there is always something in the way. To be a little more precise about orbital motion: The kinetic energy of an object such as the Earth, with mass m and velocity v is given by K=12mv2. This alone tells you already that so long as the velocity is unchanged, the kinetic energy is unchanged as well; no energy needs to be added to maintain constant velocity. But the Earth's velocity is actually not constant; sometimes the planet is a little closer to the Sun and moves a little faster, sometimes it's a little farther away and moves slower, as its orbit is slightly elliptical. The total energy is the sum of the kinetic and potential energies: E=12mv2−GMm/r, where G is Newton's gravitational constant, M is the mass of the Sun and r is the distance between the Earth and the Sun. (The potential energy part is actually negative, hence the minus sign.) This quantity, E, is constant: energy is conserved. You can see from this expression that when r is smaller (the Earth is closer to the Sun), the second term in the expression becomes bigger (r is in the denominator) so the first term must get bigger, too, which means higher velocity. It's from basic equations like these that Kepler's laws of planetary motion (which he deduced empirically, from meticulous observation) can be derived. Here on the Earth, these equations must be modified to account for dissipative forces such as air resistance or friction. These forces don't exist in space. That's why our intuition, developed from experience here in the terrestrial environment, misleads us. |
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