For systems involving central forces, the orbit can be any of the conic sections given the mass (Sun) curves the Space around it. And which conic it will be is determined by the total energy of objects revolving around the centre of force.
All the planets can follow 4 types of potential orbits
- Spiral orbits
- Circular orbits
- Hyperbolic orbits
- Elliptical orbits
If the total energy is negative ( as in the case of planets), the eccentricity of the orbit will be either zero or one. If eccentricity is equal to zero, it will be a circle and if its less than one, its an ellipse. And for our planetary system, the calculated eccentricity is found to be less than one. Now another question comes why not circular orbits. This is because nature is not as perfect as we tend it to be 🙂
Orbits of planets in our solar system
Case of planets
If you threw a planet around the sun really hard its path would be bent by the sun’s gravity, but it would still eventually fly off at a tangent. Throwing it really hard would make it almost go straight, since it moves by the sun so quickly. As you reduce the speed, the sun gets to bend it more and more, and so the tangent is flies off on gets angled more and more towards moving backwards. So general hyperbolas are possible orbits. If you move it at the right speed, then it’ll be just slow enough that other tangent points ‘exactly backwards’, and here the motion will be a parabola. Less than this and the planet will be captured. It doesn’t have enough energy at this point to escape at all.
A key realization here is that the path should change continuouslywith the initial speed. Imagine the whole path traced out by a planet with a high velocity. An almost-straight hyperbola, say. Now as you continuously lower the velocity, the hyperbola bends more and more (continuously) until it bends “all the way around” and becomes a parabola. After this point, you’ll have captured orbits. But they have to be steady changes from the parabola. All captured orbits magically being circles (of what size anyway, since they have to start looking like parabolas at some point?) wouldn’t make any sense. Instead you get ellipses that get shorter and shorter as you get slower. Keep doing this, and those ellipses will come to a circle at some critical speed.
Case of Earth
In reality, when close to the Sun, the Earth has a little “too much speed” for it to stay that deep in the Sun’s gravity well. In other words, the local spacetime curvature induced by the Sun is not strong enough to keep the Earth as close to it as it is, given that it also moves sideways; the Earth will start to “climb out” of the gravity well.
Building on your intuitions from everyday life, you know that if you move fast at the bottom of a hill, you’ll be able to go up the hill, at the expense of your speed. You’ll go higher and higher, but also slower and slower. The same holds in the context of the Earth. The further out of the gravity well it climbs, the slower it will move. At a certain point it will have climbed so far out that it actually moves too slow to stay as far out of the well as it is; it will start falling back in.
If you consider also the Earth’s sideways motion and assume the Earth’s motion is exactly perpendicular to the line of sight between the Earth and the Sun at the point where it moves slowest, it is not hard to imagine that the point where the Earth has its lowest speed is on the exact opposite side of the Sun as where it will have its highest speed. From that, it is not hard to imagine that the net result of all this will be an elliptic orbit, rather than a perfectly circular one.
Scitech Labs 