Why is it that the earth does not fly out of orbit or is drawn towards the sun?

Answer

Dear Wout,

The earth orbiting the sun (just like the moon orbiting the earth) is an example of a system in equilibrium. The point is that the earth, which according to Newton’s first law always wants to go straight in the absence of external forces, is deflected just enough by the gravitational pull of the sun to describe a closed orbit around it. Suppose you throw a ball horizontally from the surface of the earth. If you don’t throw too hard, the ball will fall a bit further on the earth’s surface, the harder you throw the further. If you throw the ball with a certain sufficiently high speed, it will fly so far that it falls behind the (round) earth, and starts to orbit around it. If you throw even harder, the ball will simply fly away from the earth: this is the so-called escape velocity. The link on the right may be intended for children, but it contains a very instructive program to illustrate all this. The chance that an object that once passes past another object is attracted just enough to continue to orbit around it is indeed very small. Sun and Earth, however, originated from the same rotating, shrinking gas cloud, which explains the equilibrium.

As for the decreasing mass of the sun, as long as the sun is in its normal adult life, there is no problem. It is indeed true that the sun produces its energy by converting mass according to E=mc², but this mass loss is negligible compared to the total mass of the sun, even for 10 billion years. Let us demonstrate this. If you know that the sun radiates about 4*10^26 (a four with 26 zeros) Joules of energy per second, you can calculate with the above formula that the sun becomes about four billion kilograms per second. This seems huge, but if you know that the sun currently has a mass of 2*10^30 (a 2 with 30 zeros) kg, you can calculate that during the adult lifetime of the sun less than 0.07% of its mass is lost. The Earth’s orbit does not change noticeably. However, this will not last. A star (like the sun) is nothing more than a nuclear power station, which gets its energy from the nuclear fusion of hydrogen. This process can only take place at the very high temperatures near the center of the star. One day the fuel will run out, and the star will be over. Our sun will run out of fuel in about five billion years. The result is that the core contracts, and the outside (due to the law of action and reaction) expands. Such an object is called a red giant. Finally, the outer layers are completely blown away, leaving a dead, cooling object in the center: a white dwarf. During and after the red giant phase, a star emits an enormous amount of material and thus becomes noticeably lighter. As a result, the orbits of all planets will move further from the sun. For the (or long scorched) earth, this means salvation: if it remained in its current orbit, it would be swallowed by the growing sun.