It would work the same, but measure the same mass as different weights depending on the planet. On the gas giants it would be hard to find a place to set it.
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Yes, a spring scale would work on other planets because it measures gravitational force by stretching a spring. The reading on the scale may vary depending on the strength of gravity on that particular planet.
Using the same scale for both planet size and distance from the sun would result in planets being spaced too far apart from each other compared to their actual distances. This would lead to an incorrect representation of the relative distances between planets in our solar system. It is better to use separate scales for size and distance to accurately depict the vastness of space.
Gravity holds almost everything together; the planets, our solar system, essentially everything 'big' in our universe. For Earth, if gravity was suddenly 'switched off', the Earth would expand as everything that was densely held together by gravity suddenly separates. The atmosphere would dissipate, everything would turn into a giant chaotic cloud of matter. On the atomic scale however not much would change. Atoms would still exist, as would molecules and probably some collections of them too. On such a small scale where everything is so close together and mass is so insignificant gravity is not as significant a force as it is in our day to day lives. At this scale we get what are called the 'strong' and 'weak' nuclear forces taking control along with electrostatic forces, holding the atomic nuclei together and keeping electrons orbiting, and other very important things. So if we did not gravity, we would cease to exist. But on the atomic scale not much would change.
The accurate representation of the solar system orbits to scale would show the planets orbiting the sun at varying distances, with the inner planets closer to the sun and the outer planets farther away. The orbits would be elliptical in shape, with each planet following its own path around the sun. The distances between the planets would also be accurately depicted to scale, showing the vastness of space between them.
The forcetat drives all large scale motion (from cars to planets and suns) is GRAVITY, the gravitational force. The reason it is so important on large scale is that, unlike other forces, it is always attractive. Electromagnetism, though stronger than gravity, is sometimes attractve and sometimes replulsive and these tend to cancel each other out.
If someone is trying to make a model of the solar system, and the goal is to represent it as it is, scaled-down of course, then there will be one very big problem. The problem would be exactly the scaling. The Sun is significantly larger than any of the planets in the solar system. While the planets