How Does Gravity Affect Time and Distance in Space Travel?

[Mayankv1994]

I'm feeling so frustrated that I typed out a whole detailed write up & it got washed off. Damn it.

1. How does gravity dilate time? I've been trying to get a conceptual answer that is easy to understand, for I have no background in physics whatsoever & am reading up out of interest.
Today however I started to wonder if the question itself was wrong, & that if I should be asking myself how gravity dilates/warps spacetime, since time isn't absolute.

2. Let us say an object travels from point A to B in space at Y Km/h, reaching B in X seconds. Let us also assume the object has traveled throughout its journey in linear motion, without being gravitationally interrupted/deviated from it's pathway.
If this same object were to travel from the same point A to B in space at Y Km/h, this time however being interrupted at some point by the gravitational pull of a body of mass, deviating off path, and into orbit of the body of a considerable mass. The speed & angle of this object however allows it to escape the the gravitational pull of this large body, to get back on track and reach point B. Due to momentary deviation, the interrupted object would obviously have taken a slightly curved path, meaning that it would have traveled a longer distance in reaching B, & since the speed was the same for the interrupted & uninterrupted object, the interrupted object would've taken a longer period of time to reach point B.
I was not satisfied with this conclusion of mine, due to the fact that it has been said that gravity dilates time (hence the 1st question to understand this whole concept), & since the interrupted object was affected by the gravitational pull of the large body. Shouldn't this mean that my above conclusion that the interrupted object would've taken a longer period of time to reach B would've been wrong, since time has been dilated at some point, making the factor of time uncomparable?

P.S. I would appreciate it if I could get a non-mathematical answer, though I would be able to understand the basic stuff (I do advanced maths).

Thank you so very much.

Cheers, & happy new year.

 

[Mayankv1994]

This is a drawn picture explaining difference in distance traveled when interrupted

 

[magic_claw93]

First of all, the picture you drew is impossible, because if a planet (or a body) was to interfere with the object, then the object will deviate from the path ITSELF.
But, theoretically speaking for your case, if it was to happen that way, gravity will be too weak to actually dilate time.
I am in no ways a Physics major or minor, but I remember something about gravity affecting the SPEED of the object which dilates time. For example, a black hole is a point of "infinite" gravity, which accelerates the object subject to its event horizon indefinitely to the point of "passing" speed of light. In this case, the speed itself will be the factor in dilating time as the universe wants you to stay within the boundaries of light speed; space will slow down time as to make the speed slower (time is in denominator).
This is a very crude (and possibly highly incorrect), but this is my understanding of the relationship between speed, gravity, and time.

 

[Mayankv1994]

Yes I already knew that dilation is a sort of an adjustment made to ensure that the boundary (speed of light) isn't crossed.
I also understand that this it is highly unlikely that such a scenario as shown in the picture will ever be possible though just for theory sake I came up with it. How can you say that gravity would be too weak too dilate time in this case? If you were to travel at a certain speed & at a certain angle through the gravitational radius of a black hole for example, you would be able to escape being sucked in. If this is possible, why wouldn't it be possible the way I put it in my question?