Effect on orbit of Earth due to decreasing gravitational force of the Sun What would happen to the motion of the earth, if the gravitational force of sun on earth starts decreasing uniformly with time?  
What path would the earth follow? 
Note
Consider Earth's orbit to be circular initially.
 A: Because the Earth orbits the sun in a uniform circular path (in this problem), the gravitational force from the Sun acts as the Centripetal force on the Earth.  The Centripetal force pulling the Earth towards the Sun combined with Earth's own velocity produces a curved motion around the Sun.
To examine the effects of decreasing this gravitational / centripetal force, we have to use the basic formula for centripetal force.  Here it is:
Fc = mv^2 / r
In this formula, Fc has a direct-square relationship with velocity and an inverse relationship with r (which is the distance between the Earth and the Sun).  So, a decrease in Fc would either cause the Earth's velocity to decrease slightly or it would cause the distance to increase.
When you think about it, this makes sense.  A decrease in the Sun's pull of the Earth towards it would allow the Earth to "get free" a bit and move farther away.  At the same time, Earth's velocity would have to decrease slightly in order to not reach an escape velocity of the Sun's gravitational pull.  If there is less centripetal force pulling on the Earth, it would take less velocity for the Earth to fling out of orbit, so the Earth has to compensate for this.
The type of motion would remain the same though (assuming we started off with uniform circular motion).  Earth's orbit would still be circular around the sun, it would just be a larger circle and would go slightly slower in its orbit.
