Science

How does the Earth orbit the sun without losing energy?

Physics is hard to understand because it violates everyday observation, intuition, and common sense.

Take “Newton’s First Law” as an example. It states that an object in motion tends to stay in motion unless influenced by an outside force. This violates everyday experience.

Things in motion tend to stop! Push a small object (coin, pen, cup) across a table; it doesn’t tend to stay in motion. It stops. Throw a ball and it stops. Everything stops. It takes a lot of study to truly understand Newton’s First Law, because it disagrees with what we observe every day.

Of course, it doesn’t really disagree, because friction is supplying the force. But friction is hard to calculate. That’s what makes physics hard.

In fact, physics was discovered by looking at things where friction is small or negligible, such as the orbits of planets, and heavy falling spherical-like objects. Newton realized that the Moon was falling, falling around the Earth due to the same force that makes an apple fall.

When we do physics demonstrations in class, we buy expensive apparatus for which friction is virtually absent, such as masses suspended on air bearings. We need to do this because the simple equations of physics work only in such circumstances.

Physicists are generally uncomfortable with friction. You have a mechanical problem that involves friction? You should probably speak to an engineer, not a physicist.

Engineers work with friction all the time. Physicists avoid it. Look at any physics text for the chapters on friction. Typically you’ll see a short mention in the book for freshman, and then very little after that.

Physics works best when there is no friction. The two most important examples: space, and the atom. In between, it is hard to do physics because friction can only be modeled approximately.

Now with all that introduction, the answer to your question: out in space the vacuum is so high that friction is negligible. That’s why the Earth orbits without losing energy. There is nothing for it to give its energy to.


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 mm and velocity vv is given by K=12mv2K=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/rE=12mv2−GMm/r, where GG is Newton’s gravitational constant, MM is the mass of the Sun and rr is the distance between the Earth and the Sun. (The potential energy part is actually negative, hence the minus sign.) This quantity, EE, is constant: energy is conserved.

You can see from this expression that when rr is smaller (the Earth is closer to the Sun), the second term in the expression becomes bigger (rr 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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