What is the path of earth in 4-d space?

[Rishavutkarsh]

what is the path of Earth in 4-d space??

as i read in the brief history of time "let a plane be moving straight in 3-d world but we see it in a curved path on a 2-d Earth surface (mountain). can any1 tell how can we see the space curve as 2-d has not elevation??
moreover i used to think that bodies with mass curve the 4-d space like a paper weight (sun) curves a trampoline and object like Table tennis ball (earth) which try to move in straight path in 4-d space will be disturbed by their path and revolve around the center (as the Earth to sun) and will get closer and closer and will reach the center in some time (millions of year when talking about sun and earth) and in secs in our model (trampoline) .

Am i having a misconception?

 

[Dale]

as i read in the brief history of time "let a plane be moving straight in 3-d world but we see it in a curved path on a 2-d Earth surface (mountain). can any1 tell how can we see the space curve as 2-d has not elevation??

I am not familiar with this analogy, so I cannot comment.

moreover i used to think that bodies with mass curve the 4-d space like a paper weight (sun) curves a trampoline and object like Table tennis ball (earth) which try to move in straight path in 4-d space will be disturbed by their path and revolve around the center (as the Earth to sun) and will get closer and closer and will reach the center in some time (millions of year when talking about sun and earth) and in secs in our model (trampoline) .

Yes, this is correct. Most people on this forum do not like the trampoline analogy since it is a 2D spatial example whereas GR deals with curvature in 4D spacetime (3D space and 1D time). However, it seems that you understand that key difference and understand that it is an analogy for spacetime.

 

[phinds]

"path" I think has meaning only RELATIVE to something. That is, you have to have point of origin for a coordinate system. What reference point did you have in mind?

 

[Rishavutkarsh]

I am not familiar with this analogy, so I cannot comment.

it literally means that an plane for example moves straight above the mountain (3-d space) but is seen to move in curve according to 2-d because of up's and down's of mountain . my question is that how can the elevation of the mountain be seen in 2-d?

 

[Dale]

it literally means that an plane for example moves straight above the mountain (3-d space) but is seen to move in curve according to 2-d because of up's and down's of mountain . my question is that how can the elevation of the mountain be seen in 2-d?

It cannot, but the curvature of the 2D surface of the mountain can be measured purely within the 2D surface without ever referring to the altitude.