1. Tidal Forces
Section 19.2
By Greg Potember

2. Basic Point-Mass Gravitational Forces
Assuming Spherical Symmetry A

3. Basic Point-Mass Gravitational Forces
Assuming Spherical Symmetry A B

4. Basic Point-Mass Gravitational Forces
Assuming Spherical Symmetry A B
Force of B on A
Force of A on B

5. A B
Force of B on A
Force of A on B
Radius r M m

6. Gravitation Forces on Large Objects

7. What is

8. 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

9. Where are the bulges?
Earth’s bulges do not line up with Earth- Moon axis
Moon’s bulge occurs on one side

10. Analyzing ΔF r R

11. Analyzing ΔF r R

12. Pulling r^2 out of the denominator...

13. Using a combination of approximations and algebra...

16. R θ r

17. Tidal bulges create Torque
Creates Torque on Earth
and
Alters Orbital Path

18. Torque Effects Creates Drag
Earth’s Rotational Kinetic Energy is slowly decreasing
Moon has complete 1:1 Synchronous Rotation

19. The Sun’s Effects

20. Roche Limit

21. Roche Limit

22. Roche Limit

23. Roche Limit

24. Gravitational Acceleration < Differential Acceleration
Roche Limit
We assume the differential force is greater than the Force of gravity holding the moon together Fd Fg
Gravitational Acceleration < Differential Acceleration

25. Gravitational Acceleration < Differential Acceleration
Roche Limit
We assume the differential force is greater than the Force of gravity holding the moon together Fd Fg
Gravitational Acceleration < Differential Acceleration
In terms of Densities:

26. Example 19.2.1 p. 724 Saturn’s Density = 687 kg/m^3
Saturn’s Radius = 6.03x10^7 m
Moon Density = 1200 kg/m^3
Remember:
What is the Roche Limit radius?

27. Example 19.2.1 p. 724 Saturn’s Density = 687 kg/m^3
Saturn’s Radius = 6.03x10^7 m
Moon Density = 1200 kg/m^3
r = 1.23 x 10^8 m