# Scale down the Solar system according to Earth

Let's say I have an OCD and I want everything to be perfect. I want all the planets and The sun of our solar system to be equal in size. Apart from that, I want the distance between the orbits to be exactly same for each planet, their speed around the sun and their own orbital speed to be same too.
What would happen? Would there be devastating consequences or not much? As far as I have guessed, EARTH will become colder because sunlight will be less hot and reach us slowly.

• The mass of the sun and planets stays the same? And what about the asteroid belt and the dwarf planets? Commented Feb 13, 2015 at 10:33
• What's your scaling factor? Are you going for equal mass worlds, or do I simply compress your Jupiters? Commented Feb 13, 2015 at 13:21
• Orbital speed is speed around the Sun. Did you mean rotation period? Commented Feb 13, 2015 at 16:17
• You can't change orbital period (or speed) for a distance , as these have a fixed relation T^2 = R^3. If you do, the planets won't be in orbit. Commented Feb 14, 2015 at 0:15
• If you reduce the mass of the sun to earth's, it goes out. If you change Earth's size to be that of the sun, it collapses into a black hole. Commented Feb 14, 2015 at 0:18

The first thing that would happen is that it would wreak havoc with every orbit in the solar system.

The orbits of the planets around the sun have their focal point very close to the sun's centre because the sun is so very much more massive than anything else in the solar system.

In a binary system (two objects of somewhat similar mass), the orbit of the two objects will be relatively stable with a focal point between the two objects; technically, the focal point will be at the common center of mass, which iff the two objects have identical mass should be at the center of an imaginary line drawn between the two objects' centers. Besides binary stars, in our immediate neighborhood Pluto and Charon form a binary system.

(In fact, perturbations in the star due to planets tugging on it is one of the techniques used to detect exoplanets.)

A trinary system (three objects) is more involved, and less likely to be stable, but follows the same principle: all objects orbit the common center of mass. I think we have some questions here on the site about planets in binary star systems.

By the time you move into systems with more than three objects (especially if those objects are of similar mass), you are heading straight into the unknown. While examples of systems of more than three stars exist (even triple star systems with planets, like Gliese 667), these consist of bodies of dissimilar mass. I have serious doubts that a system consisting of more than three bodies of similar mass even can be stable in a natural environment.

If all bodies in the solar system were somehow magically changed to have the same mass, that would upset the center of mass in the solar system. Everything would then start orbiting around the new center of mass, with likely increasing perturbations due to the changes in the location of the center of mass as the objects orbit the location of the center of mass.

The solar system would look massively different, and both the sun as well as planets would likely be ejected in various directions on either hugely different orbits, or on escape trajectories. Either way would be a Bad Thing.

So the amount of sunlight reaching Earth in this scenario is likely to be (at least among) the least of your problems.

• Also remember that Newton and Kepler tell us objects orbiting at different distances must have different speeds. If all the planets moved at the speed of Earth, they would all end up in highly elliptical orbits, with the closest coming even closer to the Sun, and the furthest being ejected from the solar system altogether. Commented Feb 14, 2015 at 0:33

If you want everything to be perfect you should just get rid of the solar system and take your planet interstellar. It would be easier than rearranging a solar system. Still implausible, but much easier.

You would then wrap the planet in reflective foil illuminated by ground based fusion powered lamps. The foil would be suspended by the reflectivity not being quite 100% resulting in the air below and inside the multi-layered structure being heated. This could be aided with some helium gas bags. The altitude would be somewhere in the stratosphere. Maybe 30 to 40 kilometres. So to people below it would look like the sky. The structure would be kept together by similar fibers to those that are considered for space elevators.

The major benefits of this, in addition to removing the need for the untidy and flawed solar system, would be that since the light supply is controllable, the sky can be used to project the words of the great leader in letters of fire. Also it might be possible to use the sky to reflect lasers and make any settlements with dissidents and traitors "spontaneously" combust.

If the masses of every celestial object in the solar system was he same orbits would be thrown completely out. Currently the sun makes up about 99.8% of the solar systems mass, it is because of this that the planets orbit it. For the Sun to still function as a star it would still need to be in the order of the size it is now (the sun is a small to medium sized star). This means that all the other planets would have to be up-scaled to the size of the sun. Now those would be some large planets. The orbits would no longer function as all masses have a gravity (so everything would pull on everything else with the same force as $m_1$ and $m_2$ are the masses)

$$F=G\frac{m_1 m_2}{r^2}$$

Gravity is also dependant on distance ($r$ is the distance between the centre of the masses) so if all the distances were the same too I would have to make a guess that everything would just be pulled together into one large mass positioned at the 'centre' of all the masses.

• If Earth were instantly inflated to Sun size but its composition is the same, this hugely massive 860000 mile wide ball of mostly iron would either collapse to a black hole or blow up into a Supernova. Take your pick. Commented Feb 14, 2015 at 0:22

There is a valid pattern for this. You can find it in the description in the article Klemperer Rosette.

The term "Klemperer rosette" (often misspelled "Kemplerer rosette") is often used to mean a configuration of three or more equal masses, set at the points of an equilateral polygon and given an equal angular velocity about their center of mass. Klemperer does indeed mention this configuration at the start of his article, but only as an already known set of equilibrium systems before introducing the actual rosettes.

So basically you can have all of your bodies orbiting their shared center of mass. There are three significant issues:

1. It is extremely unlikely that this would occur naturally, requiring active alien or creator intervention.
2. The bodies either need to have identical masses, or alternate heavy/light masses in an even configuration.
3. Your "sun" likely won't provide enough light, so you'll probably need an artificially increaseed light source.

Edit: I suspect you could have the sun still be in the shared center, but I do not know for certain. I know you could have the sun as an equal-mass object sharing the orbit with the other objects, though.

• He's intending each planet to be at different distances from the center. Commented Feb 14, 2015 at 0:17
• Ah, I misread "Apart from that, I want the distance between the orbits to be exactly same for each planet". So yeah, this won't work then. Commented Feb 14, 2015 at 18:13