Does the earth move at a constant speed around the sun?

Explanation

The force of gravitation toward the sun will have two effects on the earth's motion:  it will cause the path to curve and it will cause the Earth to increase its speed (since the force is pulling forward as well as to the side).

Consider the motion of the earth when it is halfway around its orbit from where it is shown in the figure.  In this case, the force will still cause the planet's path to curve, but now the force will also slow down the earth.