IMPETUS THEORY

qoute from Buridan's "Quaestiones on Aristotle's Physics":

When a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the  direction in which the mover starts it, be it upwards, downwards, sidewards, or in a circle.  The implanted impetus increases in the same ratio as the velocity.  It is because of this impetus that a stone moves on after the thrower has ceased moving it.  But because of the resistance of the air (and also because of the gravity of the stone) which strives to move it in the opposite direction to the motion caused by the impetus, the latter will weaken all the time.   Therefore the motion of the stone will be gradually slower, and finally the impetus is so diminished or destoyed that the gravity of the stone prevails and moves the stone towards its natural place.  In my opinion one can accept this explanation because the other explanations prove to be false whereas all phenomenaa agree with this one.
Note that the implanted impetus is caused by a mover who imparts an initial velocity to a projectile; the impetus is proportional to the velocity:  in fact, Buridan gave it a mathematical formulation:

impetus = weight x velocity

Notes on figure illustrating ballistic trajectory of impetus theory vs. Aristotelian theory:

Three stages of projectile motion yield the ballistic curve in the illustration:
1. Initial stage.  Impetus is dominant.  Gravity is insignificant.  Motion is in a straight line in direction of impetus.
2. Intermediate stage.  Air resistance slows projectile.   Gravity recovers.   Path begins to deviate downwards. Path deviates downwards from straight line.  This part of the path was conceived as part of a great circle.
3. Last stage.   Impetus is completely spent.  Gravity alone draws projectile downwards.

Compare this with an Aristotelian trajectory:
1. Impetus comes from surrounding air, which receives it from the pusher (a catapult, for example). This results in a straight line trajectory, with decreasing velocity.
2. At a certain point, the force is exhausted so the projetile falls downwards in a straight line.
Is impetus theory a forerunner of Momentum, ala Galileo and Newton?

Yes and No.

Yes: Like momentum, impetus, once imparted to an object, will endure forever unless corrupted by an outside force.
With impetus theory, angels are not needed to push celestial spheres.  With an initial impetus, spheres would keep moving since there is no air resistance in the celestial realm.
No: Not like inertia: in modern inertia, rest and motion are equivalent.  But impetus has no meaning for a non-moving object.

No: In modern theory, we speak of both linear and angular (circular motion) momentum.  But angular motion requires a force to be maintained (in modern theory).

Buridan used impetus theory to explain LINEAR as well as CIRCULAR motion, i.e., these were essentially the same; impetus was the force that tended to uphold the INITIAL motion, whether straight or circular; this idea survived for 300 years until Galileo.
What does Impetus Theory mean for astronomy?  LIBERATION.
Freed from domination by Aristotle's laws of motion, astronomers can pursue new ideas.

We don't need angels to push celestial spheres around; as written by Buridan about celestial intelligences:

"one could imagine that it is unneccesary to posit intelligences as the movers of celestial bodies since the Holy Scriptures do not inform us that intelligences must be posited. For it could be said that when God created the celestial spheres, He began to move each of them as He wished, and they are still moved by the IMPETUS which He gave to them because, there being no resistance, the impetus is neither corrupted nor diminished."
This theory of heavenly motion is a radical break with the traditional view.  Traditionally, back to Aristotle, celestial and terrestrial phenomena were made of different stuff and so obeyed related but separate laws of physics;  the impetus theory enabled philosophers to include celestial motion into the same theory used to describe terrestrial motion.

Yet, though impetus theory appears sensible in many ways, it is in contradiction so many things that are observed.  Common sense says Aristotle might still be right.

So, even Buridan retains the traditional view of solid celestial spheres (not planets) being the objects in motion.

And Oresme ultimately believed that angles moved the celestial spheres.