Lunar Tides: Why on both sides of the Earth?

Tides: Why do they occur?

• Why do high tides occur on both sides of the earth, the side closest to the moon and the side farthest from the moon ?

• Newton applied the law of gravitation to understand high and low tides twice each day

• Tides are mainly due the differential pull of gravity by the moon across the earth, which varies with distance from the moon

Spring and Neap Tides

Tides• The side closer to the moon accelerates (tends to move)

towards it faster than the farther side, which lags behind. Relative to the center, the earth is stretched in opposite directions

• The Moon does NOT “lift” the water up on one side of the Earth closest to it!

• High and low tides ~ 12hrs; alternate ~ 6 hrs• Solar tides are about half as strong as lunar tides• When the sun and the moon are in line with the earth (line

of nodes), at new and full moon, the tidal effects add up and we have the strongest tides called Spring Tides

• When the moon is in quarter positions the effects tend to cancel out and we have the weakest tides, called Neap Tides

• Tidal forces slow down Earth’s rotation by ~ 0.0015 sec/century

Earth’s Rotation• The Sun sets in the “West” because the Earth rotates “East”, counterclockwise• How do we know the Earth rotates?• Foucault’s Pendulum (COSI)• Experiment: The pendulum swings independent of the motion of supporting platform• Foucault’s experiment with the long pendulum suspended from the dome of the Pantheon in Paris traced a full circle on the floor in one day• The period depends on the latitude; 24 hrs on the north pole but 34 hrs at 45 degrees N

Effects of the Earth’s Rotation• Movement along a meridian (N-S) is affected, like

trying to walk straight on the rotating platform of a carousel experience a sideways force

• Coriolis Force – due to linear motion relative to rotational motion

• Winds blowing north from the Equator veer rightward as they move closer to the Earth’s axis at the North Pole

• At the Equator the eastward velocity is 1700 Km/hr; at the poles it is 0

• As they move north, winds circle and spiral around low-pressure areas Cyclones

Coriolis Force• Object moving north from the equator moves

rapidly eastward (right) due to:

1. An eastward velocity which gets higher relative to the Earth’s surface as it moves northward

2. Gets closer to the Earth’s axis; therefore the rotational speed increases, like that of an ice skater pulling arms inward

• Conservation of angular momentum:

L = m v r (mass x velocity x radius)

remains constant if r decreases then v must increase

Conservation of angular momentum says that product of radius r and momentum mv must be constant radius times rotation rate (number of rotations per second) is constant

Angular Momentum

Angular Momentum

• All rotating objects have angular momentum

• L = mvr ; acts perpendicular to the plane of rotation

• Examples: helicopter rotor, ice skater, spinning top or wheel (experiment)

• Gyroscope (to stabilize spacecrafts) is basically a spinning wheel whose axis maintains its direction; slow precession like the Earth’s axis along the Circle of Precession

Conservation of Angular Momentum

• Very important in physical phenomena observed in daily life as well as throughout the Universe. For example,

• Varying speeds of planets in elliptical orbits around a star

• Jets of extremely high velocity particles, as matter spirals into an accretion disc and falls into a black hole

Relativistic1 Jet “From” Black Hole

1. “Relativistic velocities are close to the speed of light