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It is often said that planets follow a "straight line" through space time. The argument goes that a star like our sun curves space, and the planets follow this path. The argument is also made that light is bent around suns because of this space curvature.

But here's the question: planets and asteroids and space dust will all follow the same orbit (if at the same distance from the sun) regardless of mass. But light doesn't follow the same path. If we explain both light bending and planet orbitals by "the sun curves space," then what is the mechanism by which masses follow a different curved path than that which light follows?

Qmechanic
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Ralph Berger
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3 Answers3

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If a massive object would move close to the speed of light and pass at the same distance of the Sun it should describe the same orbital as light.

my2cts
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The only difference is that masses move slower than light, while light moves at the speed of light (duh). As it turns out, this is a very significant difference. One of the consequences of relativity is that speeds below $c$ are not very different as far as the mathematical formulation goes, because you can move to a different reference frame and from your perspective these speeds will change. The speed of light, however, looks the same to everyone, so light behaves quite differently from not-light.

Mathematically, the four-velocity of a massive object such as a planet (no matter its speed) is a unit vector in four-dimensional spacetime. The four-velocity of light, however, has zero norm (though it is not the zero vector). This puts it into a different category.

Javier
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Imagine two asteroids, both at the same distance from the sun, both with velocity vectors pointing perpendicular to the distance axis to the sun. If one asteroid has a larger initial velocity that the other, it will follow a different path than the other.

While the trajectories of the asteroids do not depend on their masses, the trajectories certainly do depend on their initial velocities.

There are many "straight lines in space time" that start at the same point and then go in different directions. The difference between these divergent lines is that they start with different initial velocities.

user1379857
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