Download File

Gravitation
Gravitation vs. Gravity
 All objects near the surface of Earth accelerate toward
Earth at a rate of 9.8m/s2 regardless of their mass and
assuming there is no air resistance.
 The force of gravity can be found two different ways
depending on the location of the object relative to
Earth.
 Near the surface F=mg where rearranging for g, we get
g=F/m. Therefore a m/s2 is equivalent to a N/kg. In
addition to acceleration, this is the gravitational field
strength. Just like electric field is a N/C. g is the
amount of force felt per kg of mass.
Alternate Calculations
 This holds true at the surface of Earth and at any
distance away from Earth.
 r is the distance between the centers of mass of each
object.
 At very large distances, the radius of Earth itself is
negligible.
Combining the two
 Substituting mg for F gives us
 mg=(GMm)/r2
 g = (GM)/ r2
 Use this to solve for the acceleration due to gravity on
any planet where M is the mass of the planet and r is
the radius of the planet.
Orbiting objects
 Any object orbiting another object is NOT weightless.





Gravitational fields are everywhere in space due to
masses in space. Therefore objects in space have weight.
These objects are in freefall. But as they fall toward a
planet, the surface of the planet curves away from them
so they can never reach the surface.
Orbiting objects are undergoing UCM where Fc=mv2/r
Centripetal force has to be caused by something and in
this case it is gravity.
mv2/r = (GMm)/r2
v = √(GM/r) This is the orbital velocity of an object in in
a geosynchronous orbit.
Gravitational Forces
 These are vectors and should following the same rules
for vectors when investigating multiple masses
interacting.
 Solve for components and find the resultant.