Chapter 10 - Gravity and Motion. Newton’s First Law of Motion. A body continues in a state of rest or uniform motion in a straight line unless made to change that state by forces acting on it. The natural behavior of objects is to continue to move however they have been moving (inertia).
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Path followed by the Moon
F = G M m / r2 where
F is the gravitational force (in newtons)
M, m are the masses of the attracting bodies (in kilograms)
r is the distance between the (centers) of the bodies
G is a proportionality constant that depends on units
G = 6.67 x 10-11 N m2 / kg2
Example: Calculate the force of gravity exerted by the Earth on a 7-kg bowling ball.
Solution:F = GMm/r2
G = 6.67 x 10-11 Nm2/kg2
M = MEarth = 6 x 1024 kg
m = Mball = 7 kg
r = distance between centers = radius of Earth = 6,378,000 m
F = (6.67 x 10-11)(6 x 1024)(7)/(6,378,000)2 N
= 68.9 N (kg and m units all cancelled out)
Example: If the bowling ball from the previous example is dropped, how fast will it accelerate?
Solution:a = F/m
F = 68.9 N
m = 7 kg
a = (68.9)/(7) = 9.8 m/s2
The Earth also feels the force of 68.9 N but accelerates much less (essentially zero acceleration) because of its far larger mass.
Galileo did experiments that easily proved this was not true (although that he did the experiments/demonstration at the Leaning Tower of Pisa is believed to be a myth).Galileo’s Experiment
Perturbed orbit due to Jupiter
G = gravitational constant
M = mass of planet
R = radius of planet
G = 7 x 10-11 m3/(kg s2)
m = 6 x 1024 kg
r = 6 x 106 m
vesc2 = 2 (7e-11) (6e24) / (6e6) m2/s2
= 11,832 m/s
= 11,832 m/s (1 km/1000 m) = 11.8 km/s