# PHY 101 Chapter Notes - Chapter 12: Hohmann Transfer Orbit, Roche Limit, Gravitational Lens

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**preview**shows page 1. to view the full**4 pages of the document.**● 12-1 Newton’s Law of Universal Gravitation

● gravity- the weakest fundamental force of nature; it is

responsible for the motion of the sun, moon, earth and

planets

● Newton’s Law of Universal Gravitation: F= G(m1m2)/r;

the force of gravity between any two point objects is mass m1

and m2 is attractive and of magnitude F given by the above

equation

○r is the distance between the masses, and G is the

universal gravitation constant; G= 6.67 * 10-11

N*m2/kg2

● each mass experiences a force of the same magnitude but in

opposite directions, the force between two objects forms an

action reaction pair

● according to Newton’s law, all objects in the universe attract

all other objects in the universe by way of gravitational

interaction

● In general, gravitational forces are only significant when large

masses are involved

● The force of gravity decreases with distance; F varies as 1/r2,

it has an inverse square dependence on the distance

● Gravity never completely vanishes; the force of gravity

between two masses also depends on the product of the

masses

● Superposition: when a given mass is acted on by

gravitational interactions with a number of other masses and

the net force acting on it is simply the vector sum of each of

the forces individually

● 12-2 Gravitational Attraction of Spherical Bodies

● Newton’s law applies to point objects and using it to find the

force of gravity for objects of a finite size can be difficult

● Uniform Sphere

○The net force exerted by the sphere on mass m is the

same as if all the mass of the sphere were

concentrated at its center; F= G(mM/r2)

○The force the earth exerts on a mass m is F= m(GMe/Re2)

where Me and Re are the mass and radius of the earth

○m(GMe/Re2) = mg; g= GMe/Re2; this equation can be used

to find the acceleration due to gravity on other objects

in the solar system by using the mass and radius of that

planet

○r is the distance from the center of one object to the

center of the other

● Weighting the Earth

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