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My reasoning is that the velocity of the earth is constantly changing. As the sun pulls the earth's orbit into an ellipse, the direction component of velocity is being changed. Therefore velocity is changing.

It's easy to work out the centripetal acceleration from classical mechanics, but I'm trying to explain it intuitively.

Their reasoning is as follows:

-The direction component of all the infinitude of velocity vectors during the earth's orbit cancel out. (for every one pointing in direction X, there's another one, half a year later, pointing in direction X + pi, etc.)

-Since the direction components all cancel out, the velocity is reduced to the constant speed.

-Since the speed is constant, the acceleration is zero.

I need a little help explaining why that reasoning is flawed. I'm pretty much at my limit of ability to explain things.