Please explain the paths that planets take in regards to spacetime.

[Dusty_Matter]

Do planets follow the curvature of spacetime as they orbit, or what is their path considered to be?

 

[Kevin_Axion]

Yes, they follow the curvature of space-time, particularly from the host star.

 

[Rick88]

To visualise it try something like this:
place something heavy on your bed so that it "sinks" a little.
Take a little ball and let it go in a straight path near the heavy object. It will start orbiting the heavy object (some trial-and-error might be ended to give the ball the right velocity so that it doesn't shoot out of the orbit).

Of course it would "collapse" into the heavy object after a while due to energy being lost to friction and air resistance.R.

 

[Dusty_Matter]

Okay, I thought that light followed the curvature of spacetime. The sun bends light only very slightly. Light would never follow the orbit of Mercury, or any other planet out to Neptune. Light would essentially travel in a straight line.

So then does light follow the curvature of spacetime? If light does, then the planets cannot. If planets do, then light does not. Which one follows the curvature of spacetime?

 

[yenchin]

Both light and planets follow the curvature of spacetime. If you want example of light to exhibit similar property of orbiting a gravitational body (albeit unstable one), look at "photon orbit" need a black hole.

The details can only be worked out if you go through the math.

 

[Pengwuino]

They both follow general relativity. The thing with a photon is that it CAN orbit a massive body. The body just needs to be extremely massive! Imagine a rogue asteroid zooming into our solar system at some tremendous speed and its closest approach to the Sun is something like the distance from Earth to the Sun. If it is going very fast and is at a great distance from the Sun, wouldn't it make sense that the Sun wouldn't be able to capture it in orbit? The analogy isn't mean to explain why photons aren't captured most of the time, simply why massive objects don't always have to be captured in a stars orbit.

 

[Kevin_Axion]

Pengwuino is referring to the photosphere of a black hole, the place where light is in orbit around a black hole. It is approximately 1.5 times the Schwarzschild Radius for a non-Kerr black hole.

 

[Dusty_Matter]

No, I am not asking if light can orbit a massive object. I am asking about the curvature of spacetime and if planets follow explicitly the curvature of spacetime as light does. It is understood that light follows the curvature of spacetime. Planets hardly bend spacetime at all. Most stars (like our own) bend spacetime by only a little. Black holes bend it a lot, and so do massive galaxies.

But light does not circle our sun in a loop with a radius of 93 million miles. Spacetime is practically straight, and light travels in a straight enough path, so our planet, and all the other planets cannot follow the curvatures of spacetime. What are the paths called then that planets take if they do not follow the curvature of spacetime?

 

[Chronos]

See, for example, Einsteins explanation on the orbit of mercury:
http://theory.uwinnipeg.ca/mod_tech/node60.html

 

[Jonathan Scott]

You're clearly only thinking about the curvature of spacetime with respect to space, not with respect to both space and time.

The space component of the curvature of spacetime in affects objects proportionally to the square of their speed, v²/c². It has no effect on objects at rest.

Spacetime is also curved by the same amount with respect to time, and this affects all objects, including those at rest. If you plot against time the radial distance between a test object initially at rest and a gravitational source, then if space and time are measured in equivalent units, the curvature of that line is the same as the corresponding curvature of space. On its own, the curvature with respect to time has a similar effect to the Newtonian acceleration.

A light beam or a material object traveling near c is accelerated both by the curvature with respect to space and by the curvature with respect to time, so it is accelerated by twice the Newtonian acceleration.

 

[Dusty_Matter]

Thank you Jonathan Scott,

The explanation is a bit over my head, but thanks anyway.