Exploring the Solar System Study Guide

Gravity and Orbits

Gravity is the physical force that makes the objects of the universe. Gravity unites the stars, gas clouds, and other forms of matter into galaxies. Gravity condenses gas clouds into stars and planets.

In the late 1600s, Englishman Isaac Newton defined the law of gravity, or Newton's law, which he used to mathematically describe both the orbit of the moon and the fall of an apple to Earth. Newton's law was modified by Einstein's theory of relativity, but these modifications come into play in scales of space-time and levels of detail that need not concern us here. Here we look at our own solar system.

Newton described the force of gravity in one of the most important equations ever written in the history of physics. If F is the force of gravity, G is a constant needed to equalize the units of the equation, M₁ is the mass of one object, M₂ is the mass of a second object, and D is the distance between the objects, then:

It is crucial that you understand the general meaning of this equation. The force of gravity between two objects is proportional to the mass of each of them (because the two masses are multiplied in the equation). So if either M₁ or M₂ doubles, then the force of gravity doubles. What happens to the force of gravity if both M₁ and M₂ double (see the practice questions)? Which object in the solar system contributes most to the force of gravity in all the other objects in the solar system?

The answer is the sun, because it has the biggest mass. Note also that the force of gravity gets weaker as the square of distance between two masses increases (because distance is in the denominator of the right hand side of the equation). This is the famous inverse square aspect of the Law of Gravity. In other words, if the distance between two objects is increased by a factor of 3, the force of gravity decreases to (compute: ) of its original value.

Newton was able to use the law of gravity to compute the shapes of the orbits of the planets. He found that the shapes were ellipses. Decades before Newton, Johannes Kepler had discovered by analyzing data on how the planets moved in the sky that the planets travel in ellipses. But not until Newton's law of gravity was it understood why the planets orbit in ellipses.

A planet and the sun are linked to each other by the gravitation force F (see Figure 2.2). Note that the shape of the planet's orbit is an ellipse. An ellipse has a major axis that is longer than its minor axis. That means that the planet is not exactly the same distance away from the sun at each point during the year, as it would be if the orbit were a perfect circle. In the case of our planet, Earth is about 3% closer to the sun in the time of year we call January than it is during July. That's because Earth's orbit is an ellipse. Also note in this diagram how the force of gravity works on the planet to keep the planet in orbit, countering the planet's inertia, its tendency to remain in its forward line of motion (roughly, its momentum, its velocity times its mass), which tends to shoot the planet off into space. This concept is described next in the text.

If you attach a rock to a string and then spin the rock around your head, the rock stays in orbit around you. Now what if you were to cut the string during this motion? The rock would fly away. With the string intact, the rock stays in orbit because two forces are in balance: The tendency for the rock to fly away is balanced (controlled) by the force of tension in the string.

The rock on a string can be used as an analogy to the situation in the solar system between a planet and the sun. Gravity is like the string. Earth is moving at close to 20 miles per second in a direction tangent to its orbit (see Figure 2.2, a tangent to a circle is a line perpendicular to a radius). For an object as massive as the earth, that is a lot of momentum. But gravity also pulls the earth toward the sun. What is the result of the momentum and gravity? Earth is made to travel in a closed loop, in a balance between its linear momentum and the gravitational pull toward the sun. One final important fact: As they move in their elliptical orbits, planets travel faster when they are closer to the sun than when they are farther away.

Rocky and Gaseous Planets

When the gas cloud condensed to become our sun between 5 and 4.5 billion years ago, the planets also condensed. The solar system has nine planets, plus the belt of asteroids between Mars and Jupiter. In the first few million years after the sun ignited, it gave off intense flares in the vast distances of space, which stripped the planets closest to the sun of their gases hydrogen and helium. The solar system was left with its most significant pattern: the difference between the inner and outer planets. Thus, although the planets probably began with roughly the same chemical com positions, the violent activity of the newborn sun left the inner planets as mostly rock.

The planets closest to the sun (the inner, or terrestrial planets) are rocky (Mercury, Venus, Earth, and Mars). Note that this doesn't mean that they don't have some gases; Venus and Earth, for example, have substantial atmospheres. One property of planets is their average density, which is their mass per unit volume. The density of the rocky planets is between 4 and 5.5 grams per cubic centimeter. (For comparison, the density of water is 1 gram per cubic centimeter.)

The planets farthest from the sun are sometimes called the Jovian planets, or just outer planets, or gaseous planets. They are Jupiter, Saturn, Uranus, Neptune, and Pluto. Their density varies from about 0.7 to 2 grams per cubic centimeter. Jupiter, for example, at 1.3 grams per cubic centimeter, is 98% hydrogen and helium and only 2% of the heavy elements that are most of Earth's mass. The density of Saturn, as another example, is less than that of water, which means that if you could find an ocean big enough to fit it, Saturn would float.

What follows is a list of the planets, in order, starting with the planet closest to the sun—Mercury. Data is given on each planet's diameter relative to that of the earth (we'll call the earth's diameter = 1, which is 12,756 kilometers). Data is also given on each planet's distance from the sun, relative to the earth's distance (Earth distance = 1, which is 150 million kilometers, or 93 million miles from the sun). Note also that each planet's period of revolution around the sun is given in Earth years. A few additional observations about each planet will also be made at the end of each section.

Mercury. Diameter = 0.38. Distance = 0.39. Period of revolution = 0.24 years. Mercury is heavily cratered, with virtually no atmosphere, like our moon.

Venus. Diameter = 0.95 (almost the same size as Earth!). Distance = 0.72. Period of revolution = 0.62 years. Venus has thick clouds and is extremely hot, partly because it is closer to the sun but mostly because the atmosphere is about 600 times more massive than that of Earth and is mostly carbon dioxide. This amount of CO₂ produces an intense greenhouse effect, which is a property of a planet's atmosphere that keeps, in the case of Venus, the planet hot. No water vapor or oxygen exists in the atmosphere.

Earth. Diameter = 1 (by definition). Distance = 1 (by definition). Period of revolution - 1 year (by definition, our year equals the time for the earth to go once around the sun). We'll be talking a lot about Earth in the rest of this book, so for now, let's just note it's the third planet from the sun, and because it's rocky, it's sometimes called the third stone from the sun.

Mars. Diameter = 0.53. Distance = 1.52. Period of revolution = 1.88 years. In 2004, the United States (NASA) successfully deployed two new rovers on the surface of Mars. The rovers have analyzed minerals and have concluded, through multiple lines of evidence, that Mars was once wet. Rivers flowed, and there was possibly a shallow ocean. The atmosphere is very thin and the average temperature at the equator is about the same as that of Antarctica on Earth. Burr!

Asteroid belt. Asteroids are chunks of rock of various sizes, between the orbits of Mars and Jupiter. There are millions of asteroids. Some have irregular orbits, and a few have almost certainly smashed into the Earth at several times in Earth's long history.

Jupiter. Diameter =11.2. Distance = 5.2. Period of revolution = 11.9 years. Jupiter is famous for its large moons and the bands across its surface, which are weather patterns.

Saturn. Diameter = 9.4. Distance = 9.5. Period of revolution = 29.5 years. Saturn is famous for its rings, a spectacle that can be seen even through a home telescope.

Uranus. Diameter = 4.06. Distance = 19.1. Period of revolution = 84 years. It has recently been discovered that Uranus also has rings, much fainter than those of Saturn.

Neptune. Diameter = 3.9. Distance = 30.0. Period of revolution =165 years. Neptune was named after the Roman god of the sea.

Pluto. Diameter = 0.47. Distance = 39.4. Period of revolution = 248 years. This most distant planet (so far) is smaller than Earth, and its diminutive size among the giants of the Jovian outer planets have led some to question whether it should even be called a planet.

Comets. These balls of ice and rock occur in great numbers in several zones out beyond the planets. Occasionally, a comet is perturbed into an irregular orbit that is so highly elliptical that it can be brought closer to Earth at its closet point than it normally would. It is certain that comets, like asteroids, have smashed into Earth at times in its history.

Here's a key fact regarding the time it takes each planet to cycle in its orbit once around the sun: The farther the planet is from the sun, the longer its year. The "year" of each planet has nothing to do with its size; it has only to do with its distance from the sun. Also, note that because the gaseous planets retained much of their original gases from the cosmic gas cloud that condensed to form the solar system, the gaseous plan ets are larger than the four inner, rocky planets. (Pluto is the exception, as was already discussed.)

Phases of the Moon

Though it was once thought that the moon might have condensed separately around the earth, the following scenario is now known to be true (from multiple lines of evidence). A few hundred million years after the formation of the earth, a rogue body about the size of Mars and having an odd orbit around the sun, smashed into the earth. Material from both the colliding body and the earth flew off and condensed around the earth to form the moon. The moon was much closer at that time and has been slowly moving away from the earth ever since.

The moon revolves around the earth in 29.5 days, from which we derive the calendar division called our month. The moon keeps its same face to the earth during this revolution. The side of the moon facing away from the earth, often referred to as the "dark" side of the moon, is not really dark. It's just that we never see it from Earth. Both "our" side of the moon and its "dark" side are lit by the sun and then go into shadow, as the moon goes through its phases.

Figure 2.4 shows the phases of the moon. It's great fun (I promise) to look at the moon in the sky and from its phase be able to sense where the moon is along its orbit, in relation to Earth and sun.

The moon's gravity is largely responsible for the oceans' tides—the rise and fall of sea level that we notice when we visit a beach for several hours or kayak in a marine bay. (To a lesser degree, the sun contributes to the tides as well.) The sun is less important because even though it's huge compared to the moon, it's also very far away. Tides are high at places on the earth that are either closest to the moon or on the opposite side of the earth from the moon. Therefore, two high tides and two low tides happen each day, with the low tides coming between each of the two high tides. The time interval from high tide to low tide, or from low tide to high tide, is about 6 hours.

The shapes of the coastlines and the local topography of the ocean's depths affect the exact timing of the tides locally. That is why we need tide tables that are specific to each locality. Furthermore, tides are particularly high and low when the moon and sun are in alignment with the earth, which occurs during either new or full moon.

The moon is also responsible for the exciting astronomical events we call eclipses. Two kinds of eclipses happen (see Figure 2.5). In the solar eclipse, the moon blocks out either a portion of the sun (a partial solar eclipse) or all the sun (a total solar eclipse). That can occur only during new moon and, for any particular city on Earth, only once in a great while.

The second kind of eclipse is the lunar eclipse, which occurs only at full moon, when the earth's shadow is cast upon the moon. Lunar eclipses can also be full or partial. The moon doesn't disappear completely during a full lunar eclipse but turns a deep reddish-brown in the night sky. Because the earth's shadow is so large, lunar eclipses can be seen more often from any place on Earth, but they are still special astronomical events worth watching.

Practice problems of this concept can be found at: Exploring the Solar System Practice Questions