Quote by hermy
i recently read A Brief History of Time. it says that the orbits of planets may seem elliptical, but are actually straight in spacetime. so how does that happen?? how does spacetime curve?? here does time refer to imaginary time??? and what do we really mean by imaginary time? is it taken that way just for mathematical convenience?

My $0.02 worth...
To your last question, imaginary time, yes this is a mathematical convenience.
The use of the word "straight" here is not quite right. The analogy is this picture you and another person walking south from the north pole starting in slightly different directions. You both begin moving away from each other but by the time you reach the equator you're distance apart stops growing and starts shrinking until as you reach the south pole you meet. You are walking "straight" in the sense that you neither turn left nor right but your paths are curved in the sense that the distance between you doesn't change uniformly. This is because the surface of the earth is not flat but curved... i.e. curved 2dimensional space.
In SR space and time are components of 4dimensional spacetime so you can imagine objects traveling at different velocities as traveling in different spacetime directions (at a rate of one spacetime unit per propertime unit.) In GR this spacetime is curved so as you "walk" in spacetime your direction=velocity can change. You are accelerated relative to other object's paths.