## If two planets were really close together and you were between them, how would t…

#### If two planets were really close together and you were between them, how would the gravitational force affect you? — MB & Class

If you were directly between the two planets, their gravitational forces on you would oppose one another and at least partially cancel. Which planet would exert the stronger force on you would depend on their relative masses and on your distances from each of them. If one planet pulled on you more strongly than the other, you would find yourself falling toward that planet even though the other planet’s gravity would oppose your descent and prolong the fall. However, there would also be a special location between the planets at which their gravitational forces would exactly cancel. If you were to begin motionless at that point in space, you wouldn’t begin to fall at all. While the planets themselves would move and take the special location with them, there would be a brief moment when you would be able to hover in one place.

But there is something I’ve neglected: you aren’t really at one location in space. Because your body has a finite size, the forces of gravity on different parts of your body would vary subtly according to their exact locations in space. Such variations in the strength of gravity are normally insignificant but would become important if you were extremely big (e.g. the size of the moon) or if the two planets you had in mind were extremely small but extraordinarily massive (e.g. black holes or neutron stars). In those cases, spatial variations in gravity would tend to pull unevenly on your body parts and might cause trouble. Such uneven forces are known as tidal forces and are indeed responsible for the earth’s tides. While the tidal forces on a spaceship traveling between the earth and the moon would be difficult to detect, they would be easy to find if the spaceship were traveling between two small and nearby black holes. In that case, the tidal forces could become so severe that they could rip apart not only the spaceship and its occupants, but also their constituent molecules, atoms, and even subatomic particles.

## In one of your answers, you said that the “water on the earth’s surface swells …

#### In one of your answers, you said that the “water on the earth’s surface swells up into two bulges: one on the side of the earth nearest the moon and one on the side farthest from the moon.” Can you explain why the water bulges up on the side farthest from the moon? — ST

To understand the two bulges, imagine three objects: the earth, a ball of water on the side of the earth nearest the moon, and a ball of water on the side of the earth farthest from the moon. Now picture those three objects orbiting the moon. In orbit, those three objects are falling freely toward the moon but are perpetually missing it because of their enormous sideways speeds. But the ball of water nearest the moon experiences a somewhat stronger moon-gravity than the other objects and it falls faster toward the moon. As a result, this ball of water pulls away from the earth—it bulges outward. Similarly, the ball of water farthest from the moon experiences a somewhat weaker moon-gravity than the other objects and it falls more slowly toward the moon. As a result, the earth and the other ball of water pull away from this outer ball so that this ball bulges outward, away from the earth.

It’s interesting to note that the earth itself bulges slightly in response to these tidal forces. However, because the earth is more rigid than the water, its bulges are rather small compared to those of the water.

## Lunar gravity is partly what causes oceanic currents. If we had more than one mo…

#### Lunar gravity is partly what causes oceanic currents. If we had more than one moon orbiting Earth, what [if anything], would happen to the oceans? — MS, St. Charles, Missouri

While the moon’s gravity is the major cause of tides (the sun plays a secondary role), the moon’s gravity isn’t directly responsible for any true currents. Basically, water on the earth’s surface swells up into two bulges: one on the side of the earth nearest the moon and one on the side farthest from the moon. As the earth turns, these bulges move across its surface and this movement is responsible for the tides.

If there were more than one moon, the tidal bulges would become misshapen. That is essentially what happens because of the sun. As the moon and sun adopt different arrangements around the earth, the strengths of the tides vary. The strongest tides (spring tides) occur when the moon and sun are on the same or opposite sides of the earth. The weakest tides (neap tides) occur when the moon and sun are at 90° from one another. Extra moons would probably just complicate this situation so that the strengths of the tides would vary erratically as the moons shifted their positions around the earth. Since the timing of the tides is still basically determined by the earth’s rotation, there would still be approximately 2 highs and 2 lows a day.

## What do engineers have to consider about waves when they are building bridges?

#### What do engineers have to consider about waves when they are building bridges? — K

There are two answers to this question because there are two possible interpretations of the word “waves.” If you mean waves in the water beneath the bridge, then naturally the engineers must plan for the forces exerted on the bridge by the moving water that flows around its surfaces. But a more interesting wave issue is waves in the bridge itself. The bridge’s surface can experience waves, just as a taut rope or a long beam can have waves running through it. For example, when a heavy object drops on the surface of the bridge, a ripple heads outward along the bridge surface and doesn’t stop completely until it reaches the ends of the bridge. In fact, the wave will reflect from various portions of the bridge and its effects may not disappear for many seconds after the incident that started the waves.

Most of the time, these waves aren’t important and can be ignored. But occasionally some special event will cause enormous waves to begin traveling through a bridge. The classic example was the Tacoma Narrows Bridge in Washington State that collapsed in 1940 when wind-driven waves in its surface ripped it apart. The entire collapse was captured on film and is a fascinating to watch. When a large group of soldiers crosses a footbridge, they are often instructed to break step so that their rhythmic cadence doesn’t excite intense waves that might damage the bridge. In general, modern bridges are engineered to dampen these waves—wasting their energy through friction or friction-like effects so that they die away quickly. While it might be fun to watch waves traveling along the surface of a bridge from a safe vantage point, you probably wouldn’t want to be on a bridge when it was experiencing strong ones.

## What causes the phases of the moon?

#### What causes the phases of the moon? — CH, Denver, Colorado

Except during an eclipse, one half of the moon’s surface is bathed in sunlight while the other half is in shadow. The phases of moon occur because we can only see half the moon at any moment and the fractions of lighted and shadowed moon that we see vary with about a four-week cycle—the lunar month. For example, when the moon is almost on the opposite side of the earth from the sun, we see only the lighted side of the moon and the moon appears full. When the moon is on the same side of the earth as the sun, we see only the shadowed side of the moon and it appears almost non-existent—a new moon. Each lunar month, our vantage point gradually evolves so that we see the new moon become a growing crescent moon, a half moon, a gibbous moon, and a full moon, a gibbous moon, a half moon, a shrinking crescent moon, and finally a new moon again. You can see this effect by illuminating a soccer ball with a bright flashlight and then walking around the soccer ball. You’ll see the phases of the soccer ball.

## Why are there two tides per day?

#### Why are there two tides per day? — JF

The tide is caused primarily by the moon’s gravity. Gravity is what keeps the moon and earth together as a pair—the moon and earth orbit one another because each is exerting an attractive force on the other. While they are effectively falling toward one another as the result of this gravitational attraction, their sideways motion keeps them from smashing together and they instead travel in elliptical paths around a common center of mass. But the moon’s gravity is slightly stronger on the near side of the earth than it is on the far side of the earth. As a result, the water on the near side of the earth bulges outward toward the moon. The water on the far side of the earth also bulges outward because the earth itself is falling toward the moon slightly faster than that more distant water is. The distant water is being left behind as a bulge.

There are thus two separate tidal bulges in the earth’s oceans: one on the side nearest the moon and one on the side farthest from the moon. But the earth rotates once a day, so these bulges move across the earth’s surface. Since there are two bulges, a typical seashore passes through two bulges a day. At those times, the tide is high. During the times when the seashore is between bulges, the tide is low. Because the moon moves as the earth turns, high tides occur about 12 hours and 26 minutes apart, rather than every 12 hours. Since local water must flow to form the bulges as the earth rotates, there are cases where the tides are delayed as the water struggles to move through a channel. However, even in those cases, the high tides occur every 12 hours and 26 minutes. The sun’s gravity also contributes to the tides, but its effects are smaller and serve mostly to vary the heights of high and low tide.

## Why is it that the times at which the moon sets and rises change so much from da…

#### Why is it that the times at which the moon sets and rises change so much from day to day?

The moon orbits the earth about every 27.3 days, so its position relative to the sun changes from day to day. Because of the moon’s movement around the earth, the moon rises and sets about 1 hour later every day. When the moon is on the sun side of the earth, it rises at sunrise and sets at sunset. Fourteen days later, when the moon is on the side opposite the sun, it rises at sunset and sets at sunrise.

## How does a tsunami form and how far does it go when it hits land?

#### How does a tsunami form and how far does it go when it hits land? — JM, Berkley, MI

A tsunami is simply a giant surface wave on water. Surface waves have several important characteristics, one of which is wavelength—that is, the distance between one crest and the next. The longer its wavelength, the faster a surface wave moves and also the deeper it extends below the surface of the water. In general a surface wave extends downward about one wavelength, so that if the crests are 100 meters apart, the wave is about 100 meters deep.

The wavelength of a tsunami is enormous—hundreds or even thousands of meters. As a result, a tsunami travels hundreds of kilometers per hour and extends downward deep into the ocean. Because it disturbs so much water, it carries a great deal of energy and it delivers this energy to the shore when it hits. Tsunamis are normally created by earthquakes or volcanic eruptions that sudden shift the supporting surfaces of a large amount of water. The water experiences a sudden impulse when the land or seabed shifts and a wave is emitted. You can launch a similar wave simply by shaking the end of a basin of water. But when a large region of land or seabed moves, the wave that’s launched has a very long wavelength and tremendous energy. This tsunami heads off with enormous speed until it encounters the gradual shallowing of a seashore. There it becomes deformed because the lack of water in front of it causes its crest to become incomplete. Eventually the tsunami breaks in churning surf. The height of this breaking wave crest and the distance it travels onto shore before it stops depends on the total energy of the tsunami, but heights of 10 or 20 meters are not uncommon. Such waves can travel hundreds of meters up a beach or oceanfront if the slope is sufficiently gradual.

## What causes undertows?

#### What causes undertows?

When a wave breaks and then rushes up the beach, it leaves the water on the beach with excess gravitational potential energy. That’s what’s left of the wave’s energy. The water accelerates back down the beach and returns to the sea. This returning flow of water tends to go under the sea’s surface, probably because of the water’s circular motion in waves. Remember that the water in a wave travels in a circle, always moving forward (in the direction of the wave’s motion) when it’s at its highest point and backward (away from the direction of the wave’s motion) when it’s at its lowest point. I suspect that the returning flow of water from the beach joins this backward moving low water. When this low-lying returning water flows past you, it tends to sweep you along with it, hence the name undertow.

## What would happen if the moon instantly disappeared? (Tidal waves, earthquakes,….

#### What would happen if the moon instantly disappeared? (Tidal waves, earthquakes,…?)

The moon’s gravity affects both the earth’s path through space and the earth’s shape. If the moon were to disappear, the earth’s path would change but probably not enough to cause a noticeable difference. The earth and the moon normally orbit one another but the moon, which has much less mass than the earth, does most of the moving. Without the moon, the earth would just orbit smoothly around the sun. As for the earth’s shape, the only part of the earth that responds noticeably to the moon’s gravity is the water on its surface. The tides are caused mostly by the moon’s gravity. Without the moon, the tides would be much smaller and caused only by the sun’s gravity. Thus, in the long run, you would probably have trouble telling that the moon was gone without looking overhead—the earth’s path wouldn’t change much and you would have to look carefully to see the effect on the earth’s oceans.

However, in the moments following the moon’s disappearance, there might be some dramatic waves and a few stress-related earthquakes. The oceans and the earth’s crust do experience substantial stresses due to the unevenness of the moon’s gravity (it’s stronger on the side of the earth nearest the moon than it is on the side of the earth farthest from the moon). But I doubt that the sudden change in stress caused by having the moon disappear would do more than temporarily flood a few coastal cities. One last effect worth noting is that the precession of the equinoxes, a 26,000 year process that shifts the earth’s rotational axis in space and causes the stars that are overhead at night during a particular season to change gradually, is driven by the moon’s gravity and would disappear if the moon were to disappear.