Outline
• Orbital Motion & Gravity
• Newton’s Universal Law of Gravitation
• Surface Gravity & Weight
(A) A cannon on a mountain peak fires a projectile. If
the projectile is fired faster, it travels farther before
hitting the ground. (B) At a sufficiently high speed,
the projectile travels so far that the Earth’s surface
curves out from under it, & the projectile is in orbit.
Gravity produces a force of attraction (green arrows)
between bodies. The strength of the force depends on the
product of their masses, m & M, and the square of their
separation, d. G is the universal gravitational constant.
Astronaut John Young making a jumping salute at the Apollo
16 lunar landing site near Descartes Crater. Despite a total
mass of over 170 kg (~370 pounds) in his space suit, he
easily jumps up because of the Moon’s weak gravity.
Center of Mass
The terms "center of mass" and "center of gravity" are used
synonymously in a uniform gravity field to represent the
unique point in an object or system which can be used to
describe the system's response to external forces and
torques. The concept of the center of mass is that of an
average of the masses factored by their distances from a
reference point. In one plane, that is like the balancing of a
seesaw about a pivot point with respect to the torques
produced.
Key Terms
• g: the acceleration due to gravity at Earth’s
surface—about 9.8 m/s2.
• G: Newton’s gravitational constant, which
allows us to determine the force between objects
if we know their masses & separation.
• newton (N): the standard unit of force in the
metric system.
• Surface gravity: the acceleration an object will
experience near the surface of a planet (or other
body) because of the planet’s gravitational
pull.
Law of Gravity
• A description of the gravitational force
exerted by one body on another. It is
proportional to the product of their masses
(M, m) & the inverse square of their
separation (d):
FG = M ×m
G d2
G = 6.67×10-11 m3-kg-1-s-2