I am a high school student. I saw the latest Indian spacecraft "CHANDRYAANN 2", which was in orbit around the Earth for 14 days.....
I am so curious to know how a spacecraft changes its orbit. I have done some research on Google and it says "velocity first increases then decreases"; I do not know why the velocity increases. Can anyone explain this if I have read it correctly?
To answer your title question: By using its engines.
However you seems to be quite puzzled by the fact that velocity of an object can decrease and increase over the course of an orbit.
If the orbit is perfectly circular, the speed will always remain the same (until thrusters are used).
However, as is the case with Chandrayaan-2, most orbits are elliptical (so they have a high altitude and a low altitude points)
On an elliptical (i.e., not circular) orbit, the altitude curve looks a bit like this (1):
_ _ _
/ \ / \ / \
/ \ / \ / \
_/ \_/ \_/ \...
The altitude of the spacecraft goes up and down. When the spacecraft altitude increases, it slows down, and when the spacecraft altitude decreases, it accelerates.
This is exactly the same as riding over small hills on a bicycle (except there is no friction so you don't need to pedal at all).
[1]: It's a bit more complicated, since the altitude change is not linear with time, but you get the idea.
After reading all your answers I'd like to summarise the situation.
The black circles are the circular orbits and the red ellipse is the transfer orbit.
Consider a spacecraft in the elliptical orbit. At the point P the velocity is greater than the circular orbital velocity, and that's why the distance from the centre increases. And at the point A the velocity is less than the orbital velocity, which is why the spacecraft falls back towards the centre.
So if you start at the inner circular orbit then at the point P you have to increase your velocity to change to the red elliptical orbit. When you get to the point A your velocity has fallen because you slow down as you move away from the centre. So you now have to increase your velocity once again to change to the outer circular orbit.
So there are three changes to the velocity:
you fire your engines at point P to increase velocity
your velocity decreases as you coast away from the Sun
you fire your engines at point A to increase velocity again
So in fact both times you fire you engine it is to increase your velocity. The total velocity change is the sum of the two increases when you fire your engine minus the decrease that happens as you coast away from the Sun.
To simplify the explanation and terminology, let's consider the case of a spacecraft orbiting Earth.
All orbits are elliptical, with the center of mass of the system (Earth, in our example) at one focus. Circular orbits are a special case where the ellipse has no eccentricity and the focii are coincident.
The orbit of our spacecraft has a perigee (closest point to Earth) and apogee (farthest point from Earth). As an aside: the terms "perigee" and "apogee" are used specifically for orbits around Earth; around an unspecified object, we use the terms "periapsis" and "apoapsis". As our spacecraft completes one orbit around Earth, it will pass through perigee once, and apogee once.
Kepler worked out that an object in orbit (our spacecraft) will not travel at a uniform speed, but instead carve equal areas in equal time as it orbits. This means that it will have its highest speed at perigee and lowest speed at apogee. A truly circular orbit is a special case where its speed actually is uniform.
Let's consider a spaceship in a circular orbit. It wants to climb to a higher orbit. It briefly fires its engine to speed up along its current trajectory. It is now no longer in circular orbit; it is now at the perigee of an elliptical orbit, and as it travels to apogee, it must slow down. If it does nothing else, it will return to that same perigee point after one complete orbit. On the other hand, when it gets to the apogee point, it can fire its engine again to speed up again. This will raise the perigee point; the right change in speed at apogee will raise the perigee to make the orbit circular again, at the new altitude.
The "velocity increases then decreases" would refer to either an interpretation of Kepler's second law, or what typically happens when a spacecraft makes an adjustment to its orbit, such as I've described.
Imagine your spacecraft is on elliptical orbit around space body. The body is inside ellipse (in the focus, if more specifically). When spacecraft is on the vertex of ellipse and speed up in direction of movement, another vertex of trajectory is moving far from body. Vice versa, if the spacecraft is braking (by turning engines forward and burning) in the one vertex, second vertex moves to the space body.
This is simplest scenario, without orbit precession and other things, but it illustrate the idea.
If you really want to know, just find demo of Kerbal Space Program game, it will help for sure.
