Tidal Forces

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Tidal Forces

• Section 19.2
• By Greg Potember

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Basic Point-Mass Gravitational Forces

• Assuming Spherical Symmetry

A
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Basic Point-Mass Gravitational Forces

• Assuming Spherical Symmetry

A
B
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Basic Point-Mass Gravitational Forces

• Assuming Spherical Symmetry

A
B
Force of B on A
Force of A on B
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A
B
Force of B on A
Force of A on B
Radius r
M
m
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Gravitation Forces on Large Objects
A
r
R
B
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What is
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Differential Force is Tidal Force

• Creates a bulge in water and land masses
• In land, creates small deformations
• Earth- 10 cm Bulges
• Moon- 20 m Bulges
• In water, creates tides
• Two high tides every 24 hours 53 minutes

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Where are the bulges?

• Earths bulges do not line up with Earth-Moon
  axis
• Moons bulge occurs on one side

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Analyzing ?F
r
R
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Analyzing ?F
r
R
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Pulling r2 out of the denominator...
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Using a combination of approximations and
algebra...
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R
?
r
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Tidal bulges create Torque
Creates Torque on Earth
and
Alters Orbital Path
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Torque Effects

• Creates Drag
• Earths Rotational Kinetic Energy is slowly
  decreasing
• Moon has complete 11 Synchronous Rotation

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The Suns Effects
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Roche Limit
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Roche Limit
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Roche Limit
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Roche Limit
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Roche Limit
We assume the differential force is greater than
the Force of gravity holding the moon together
Gravitational Acceleration lt Differential
Acceleration
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Roche Limit
We assume the differential force is greater than
the Force of gravity holding the moon together
Gravitational Acceleration lt Differential
Acceleration
In terms of Densities
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Example 19.2.1 p. 724

• Saturns Density 687 kg/m3
• Saturns Radius 6.03x107 m
• Moon Density 1200 kg/m3
• Remember
• What is the Roche Limit radius?

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Example 19.2.1 p. 724

• Saturns Density 687 kg/m3
• Saturns Radius 6.03x107 m
• Moon Density 1200 kg/m3
• r 1.23 x 108 m