1. Check option A:

A planet revolving around the sun generally moves in an elliptical orbit. By Kepler’s second law, the planet moves faster when it is nearer the sun and slower when it is farther away. So its linear speed does not remain constant.

Hence, A is incorrect.

2. Check option B:

When a body falls toward the earth, actually both the body and the earth move toward their common center of mass. But since the mass of earth is extremely large compared to the falling body,

$a_{\text{earth}} = \frac{F}{M_{\text{earth}}}$

is extremely small, so the displacement of earth is negligible.

Hence, B is correct.

3. Check option C:

For a satellite in a given circular orbit, the radius is constant. Its speed is

$v = \sqrt{\frac{GM}{r}}$

Since $G$, $M$, and $r$ are constant, the speed remains constant.

Hence, C is correct.

4. Check option D:

For a planet revolving around the sun in an elliptical orbit, the gravitational force is conservative. Therefore, the total mechanical energy remains constant:

$E = K + U = -\frac{GMm}{2a}$

where $a$ is the semi-major axis of the ellipse. Thus total energy is constant throughout the motion.

Hence, D is correct.

5. Conclusion:

The only incorrect statement is:

$\boxed{A}$