orbitAni.gif (28043 bytes)

The Gravitational Field

falling.gif (39437 bytes)


Previously Asked Questions

Q:     "Why is it that if the mass of the earth increased, your weight would correspondingly increase, but if the mass of the sun increased, your weight would not be affected at all?  How does gravitational force works on this situation?"

A:    It is not true that the weight of a person on the surface of planet Earth is not affected by the mass of the sun or of any other celestial object.  We usually disregard the attraction of object at the earth's surface by other celestial bodies in the universe.  Within the limits of this approximation, the weight of an object at the earth's surface is determined only by the force of attraction applied on it by the mass of the earth.  If the mass of the earth is increased (without changing the radius of the earth - this radius representing the distance between the center of mass of the object and the center of mass of the earth) then the gravitational force of attraction of the body by the earth is increased proportionally: 

F = G (mobject * m earth) / r2

Q:     What must the separation be between a 5.0 kg particle and a 2.5 kg particle be in order for their gravitational attraction to be 3.0 X 10-12 N?

A:    The force between the two particles is given by the equation 14-1.gif (169 bytes) where m1 and m2 are the masses, r is the distance of their separation, and G is the universal gravitational constant 6.67 m3 / (s2 kg).

Now we need to solve for r

r 2 = (G m 1 m2 ) / F  =>  equ1.gif (294 bytes)

Now we plug in the values and solve for r:

    equ2.gif (1924 bytes)       

                                                                                         r = 16.7 meters

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Kepler's Laws

The Law of Orbits
    All planets move in elliptical orbits, with the sun at one focus.

The Law of Areas
A line that connects a planet to the sun sweeps out equal areas in equal times.

The Law of Periods
    The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

        14-31.gif (298 bytes)


Newton's Law of Gravitation

14-1.gif (169 bytes)

Superposition principle
14-5.gif (183 bytes) 14-4.gif (209 bytes)
Gravitational Acceleration
14-11.gif (125 bytes) 14-12.gif (180 bytes)
Gravitation within a Spherical Shell 14-18.gif (211 bytes)
Gravitational Potential Energy 14-20.gif (191 bytes)
Potential Energy of a System 14-21.gif (577 bytes)
Escape Speed 14-26.gif (254 bytes)
Law of Periods 14-31.gif (298 bytes)
Energy in Planetary Motion
14-20.gif (191 bytes) 14-42.gif (202 bytes)
14-40.gif (197 bytes) 14-44.gif (205 bytes)

[Top] [Previously Asked Questions] [References]

Mechanics List of Topics

Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of
Rigid Bodies
Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical
Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves
Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy
and Work
Circular Motion of Point-Mass Objects Equilibrium Sound