Lecture 18
Donut Theorem:
a = acceleration
v = velocity
R = radius
a = v
2
/R
To calculate acceleration of a planet’s orbit, use
v = 2
π
R/t
and plug into Donut Theorem equation.
Newton’s Great Idea: The gravitational force between two
objects is
proportional to their masses
, and decreases
inversely as the square of the distance between them
.
F = Gm
1
m
2
/R
2
G =
some number
m
1
= mass of object 1
R =
distance between the objects
m
2
= mass of object 2
They both feel the same force,
F
, tugging on them.
Comparing accelerations towards Earth’s surface:
a
1
/a
2
= (R
2
2
/R
1
2
)
Where R = the respective distance of the object from the earth’s surface.
THINGS TO KNOW ABOUT LECTURE #19 SLIDES:
*
Newton's Laws work well over a wide range of subjects...BUT Einstein's Theory of General
Relativity is better. Incorporates Newton's Laws, but with new features; passes all experimental
tests and governs our study of the universe
*
Predicted acceleration of the Moon: a = 2.76 x 10-4 g, or a = 2.7 x 10-3 m/s2. Actual
acceleration of the Moon (from donut theorem): a = 2.7 x 10-3 m/s2. Agreement between

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- Spring '09
- RobertKirshner
- Mass, General Relativity, Celestial mechanics