Tides

Question 1

For the tide analysis we distinguish two different theories:

Answer 1

• The theory of equilibrium after Newton
• The harmonic analysis after Laplace

Question 2

The theory of equilibrium after Newton

Answer 2

The theory of equilibrium by Newton describes the tide as a result of the gravitational attraction between two ideal celestial bodies of masses m1 and m2 with the distance r to each other:

Force of attraction = Gm1m2/r^2

The attraction forces counteract centrifugal forces, as two celestial bodies are moving around a common center. The centrifugal forces on the celestial body of mass m1 and the distance e1 for common centroid can be calculated to:

Centrifugal Force = m1omega^2e1

The difference between attraction and local centrifugal force determines the tide generating force.

Question 3

Harmonic Analysis after Laplace

Answer 3

Since the theory of equilibrium by Newton assumes an ideal celestial body with a constant water level above, the harmonic analysis of the tides after Laplace has been established, describing the tide as a summation of individual oscillation components of the amplitudes ai and phase Φi.

Question 4

Which statements apply to the theory of equilibrium after Newton?

Answer 4

-A uniform water coverage of the earth is assumed.
-Dynamic effects and friction are not considered.
-The tide-generating forces are created due to the forces of the celestial bodies (forces of attraction and centrifugal forces)

Question 5

How does the gravitational attraction between to masses relate to the distance between those two masses?

Answer 5

antiproportional to the square of the distance between the two masses

Question 6

The centrifugal forces on the planets depend on

Answer 6

-the distance to the common center
-the rotational speed around the common center
-the mass of the celestial body

Question 7

Astronomical frequencies and periods

Answer 7

solar day: 24h
lunar day: 1,03 MSD
tropical month: 27,32 MSD
tropical year: 365,24 MSD
julianic year: 8,85 years
nodaltide: 18,61 years
perihelion: 20900 years

MSD= mean solar day =24h

Question 8

Full moon, new moon, half moon and their meaning for the different tides

Answer 8

Full moon: spring tide (superposition of lunar and solar tide)
new moon: spring tide (superposition of lunar and solar tide)
half moon: neap tide (lunar and solar tide partially cancel each other out)

Question 9

Tidal Form Factor F

Answer 9

F=(K1+O1)/(M2+S2)

Question 10

Form factor ranges and corresponding form names

Answer 10

F=0-0,25: semidiurnal form
F=0,25-1,50: mixed, predominantly semidiurnal form
F=1,50-3,00: mixed, predominantly diurnal form
F>3: diurnal form