Wikipedia says that :
"Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a circular motion"
and this is confirmed in some threads, for example here
"...a force acting perpendicular to the velocity will merely change its direction. In an object moving in a low-eccentricity orbit, the gravitational force is always nearly perpendicular to the velocity, so there isn't a large speed change."
But we also know that a perpendicular force always causes an acceleration according to the rule of addition of forces. If the centripetal force is greater :
the resulting vector is near the perpendicular, if the centripetal force is in perfect balance the resulting vector should point exactly at 45°.
Can you please explain why this doesn't apply to an orbiting body? Can you clearly specify what is the real trajectory of the body in a circular orbit, is it a perfect circle or is it more like a sawtooth motion,
and it moves tangentially and then it is brought back on track by the centripetal force?
I actually took the image from the question which is considered a duplicate: it shows vector addition between the tangential and centripetal vector, and shows that, when the latter is greater than v^2/r the body accelerates and the resultant direction is at about 70°. I am taking that as the basis of my own question:
If that answer is correct, and we just change the centripetal acceleration to exactly v^2/r, why shouldn't this scheme be appropriate anymore? If we use the same logic and rules, the body will accelerate less (* 1.41) and the resultant will make an angle of 45° with the tangent vector , but it should still accelerate. Since everybody says it doesn't, why so? what is the difference ?
The sawtooth pattern is, of course, infinitesimally small, but yet it should be there, else the vector would not be tangential and we know it is, since if you cut the string of an orbiting body, it flies off at a tangent. Doesn't that imply the the motion of the body is always in a straight line?