The way I see it: Assuming space is a perfect vacuum, a satellite should stay in circular orbit with CONSTANT RADIUS around earth forever but I think the radius should gradually decrease for the following reason. Are my thoughts wrong? A satellite in circular orbit has a tangential velocity which earth people have provided it. But, it has no tangential acceleration as the tangential velocity is constant. Now, the Earth is continuously exerting a force of attraction towards the center which is also the NET force on the satellite. This force creates a component of velocity towards earth that is increasing by a factor of 9.8 per second So, if this 'centripetal velocity' is increasing but the tangential velocity is constant shouldn't this radius of the circular orbit eventually decrease?
2 Answers
Forget about the Earth-Satellite system, your question is much simpler: you are asking about circular motion in general.
It is a basic notion that, for a uniform circular motion, a centripetal acceleration is required. This acceleration changes the direction of the velocity, but not its modulus.
Because acceleration is the change in velocity, but vectors!
$$\vec{a}=\frac{\Delta\vec{v}}{\Delta t}$$
A vector can change if the modulus changes, but also if the direction changes.
A perpendicular acceleration does not change the speed, it only changes direction of motion. This is a basic thing you must learn before you study any dyunamics. Kinematics are more fundamental.
You are correct that the Earth is constantly pulling orbiting satellites toward it. But because of their lateral velocity, they are able to 'miss' hitting into the Earth.
See the section "The 'weightless astronaut' paradox in this link. I also like the quote at the beginning as it turns your question into a statement of fact.
Being in orbit is like being infatuated – you are constantly falling, but you aren’t getting closer.
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1$\begingroup$ +1 for the last quote :P sums it up neatly $\endgroup$ Commented Jul 22, 2020 at 1:44