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# GRAVITY EXPLAINS THE MOTIONS OF THE PLANETS

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Gravity is the name given to the force of attraction between any two masses. It is the force that attracts all objects to Earth, giving them weight. It draws objects downward, toward the center of Earth. If the object were on the moon, a much smaller mass than Earth, the force would be six times less and its weight would be one sixth of its weight on Earth. English physicist, astronomer, and mathematician Isaac Newton was the first person to realize that gravity is a universal force, acting on all objects, and that it explains the movement of planets.

“To myself I am only a child playing on the beach, while vast oceans of truth lie undiscovered before me.” Isaac Newton

## Describing orbits

The shapes of the orbits of the planets were already well-known in Newton’s time, based on the three laws of planetary motion introduced by Johannes Kepler. Kepler’s first law stated that these orbits were ellipses, with the sun at one focus of each ellipse. The second law described the way that planets moved along their orbits more quickly when they were close to the sun than when they were farther away. The third law described the relation between the time taken to complete one orbit and the distance from the sun: the time taken for one orbit, squared, was equal to the cube of the average distance between the planet and the sun. For instance, Earth goes around the sun in one year, while Jupiter is 5.2 times farther away from the sun than Earth. 5.2 cubed equals 140, and the square root of 140 gives the correct figure for one Jupiter year: 11.86 Earth years.

However, although Kepler had correctly discovered the shapes and speeds of planetary orbits, he did not know why the planets moved as they did. In his 1609 book Astronomia Nova, he suggested that Mars was being carried around its orbit by an angel in a chariot. A year later, he had changed his mind, suggesting that the planets were magnets and were being driven around by magnetic “arms” extending from the spinning sun.

## Newton’s insight

Before Newton, several scientists, including Englishman Robert Hooke and Italian Giovanni Alfonso Borelli, suggested that there was a force of attraction between the sun and the individual planets. They also stated that the force decreased with distance. On December 9, 1679, Hooke wrote to Newton saying that he thought the force might decrease as the inverse square of distance.

However, Hooke did not publish the idea and did not possess the mathematical skills to fully demonstrate his proposition. By contrast, Newton was able to prove rigorously that an inverse square law of attractive force would result in an elliptical planetary orbit.

Newton used mathematics to demonstrate that, if the force of attraction (F) between the sun and the planets varied precisely as an inverse square of the distance (r) between them, this fully explained the planetary orbits and why they follow Kepler’s three laws. This is written mathematically as F ∝ 1/r2. It means that doubling the distance between the objects reduces the strength of the attractive force to a quarter of the original force.

## The Great Comet

Newton was a shy, reclusive man, and reluctant to publish his breakthrough. Two things forced his hand. The first was the Great Comet of 1680, and the second was the astronomer Edmond Halley.

The Great Comet of 1680 was the brightest comet of the 17th century—so bright that for a short time it was visible in the daytime. Two comets were seen: one that was approaching the sun in November and December 1680; and another that was moving away from the sun between late December 1680 and March 1681. As with all comets at the time, its orbit was a mystery, and the two sightings were at first not widely recognized as the same object. Astronomer John Flamsteed suggested that the two sightings might be of the same comet, which had come from the outer edge of the solar system, swung around the sun (where it was too close to the sun to be seen), and moved out again.

Halley was fascinated by the mysterious form of cometary orbits, and traveled to Cambridge to discuss the problem with his friend Newton. Using his law that related force to acceleration and his insistence that the strength of the force varied as the inverse square of distance, Newton calculated the parameters of the comet’s orbit as it passed through the inner solar system. This breakthrough intrigued Halley so much that he went on to calculate the orbits of 24 other comets, and to prove that one comet (Halley’s comet) returned to the sun around every 76 years. Perhaps more importantly, Halley was so impressed by Newton’s work that he strongly encouraged him to publish his findings. This resulted in the book Philosophiae Naturalis Principia Mathematica, published in Latin on July 5, 1687, in which Newton describes his laws of motion, his gravitational theory, the proof of Kepler’s three laws, and the method he used to calculate a comet’s orbit.

In his book, Newton stressed that his law was universal—gravity affects everything in the universe, regardless of distance. It explained how an apple fell on his head in the orchard of Woolsthorpe where his mother lived, the tides in the seas, the moon orbiting Earth, Jupiter orbiting the sun, and even the elliptical orbit of a comet. The physical law that made the apple fall in his yard was exactly the same as the one that shaped the solar system, and would later be discovered at work between stars and distant galaxies. Evidence was all around that Newton’s law of gravitation worked. It not only explained where planets had been, but also made it possible to predict where they would go in the future.

## Constant of proportionality

Newton’s law of gravitation states that the size of the gravitational force is proportional to the masses of the two bodies (m1 and m2) multiplied together and divided by the square of the distance, r, between them. It always draws masses together and acts along a straight line between them. If the object in question is spherically symmetrical, like Earth, then its gravitational pull can be treated as if it were coming from a point at its center. One final value is needed to calculate the force—the constant of proportionality, a number that gives the strength of the force: the gravitational constant (G).

Newton’s law of universal gravitation shows how the force produced depends on the mass of the two objects and the square of the distance between them.

## Measuring G

Gravity is a weak force, and this means that the gravitational constant is rather difficult to measure accurately. The first laboratory test of Newton’s theory was made by the English aristocrat scientist Henry Cavendish in 1798, 71 years after Newton’s death. He copied an experimental system proposed by the geophysicist John Michell and successfully measured the gravitational force between two lead balls, of diameters 2 and 12 in (5.1 and 30 cm). Many have tried to refine and repeat the experiment since. This has led to a slow improvement in the accuracy of G. Some scientists suggested that G changed with time. However, recent analysis of type 1a supernovae has shown that, over the last nine billion years, G has changed by less than one part in 10 billion, if at all. The light from distant supernovae was emitted nine billion years ago, allowing scientists to study the laws of physics as they were in the distant past.

“Nature and Nature’s laws lay hid in night: God said, “Let Newton be!” and all was light.” Alexander Pope

## Seeking meaning

Like many of the scientists of his time, Newton was deeply pious and sought a religious meaning behind his observations and laws. The solar system was not regarded as a random collection of planets, and the sizes of the specific orbits were thought to have some specific meaning. For example, Kepler had sought meaning with his notion of “the music of the spheres.” Building on ideas first put forward by Pythagoras and Ptolemy, Kepler suggested that each planet was responsible for an inaudible musical note that had a frequency proportional to the velocity of the planet along its orbit. The slower a planet moved, the lower the note that it emitted. The difference between the notes produced by adjacent planets turned out to be well-known musical intervals such as major thirds.

There is some scientific merit behind Kepler’s idea. The solar system is about 4.6 billion years old. During its lifetime, the planets and their satellites have exerted gravitational influences on each other and have fallen into resonant intervals, similar to the way musical notes resonate. Looking at three of the moons of Jupiter, for every once that Ganymede orbits the planet, Europa goes around twice and Io four times. Over time, they have been gravitationally locked into this resonance.

## The three-body problem

The solar system as a whole has fallen into similar resonant proportions to Jupiter’s moons. On average, each planet has an orbit that is about 73 percent larger than the planet immediately closer to the sun. Here, however, there appears a difficult mathematical problem, and one that Newton had grappled with. The movement of a low-mass body under the gravitational influence of a large-mass body can be understood, and predicted. But when three bodies are involved, the mathematical problem becomes exceedingly difficult.An example of a three-body system is the moon-Earth-sun. Newton thought about this system but the mathematical difficulties were insurmountable, and human knowledge of where the moon will be in the distant future is still very limited. Variations in the orbit of Halley’s comet are another indicator of the influence of the gravitational fields of the planets operating in addition to the gravitation of the sun. Recent orbits have taken 76.0, 76.1, 76.3, 76.9, 77.4, 76.1, 76.5, 77.1, 77.8, and 79.1 years respectively due to the combined gravitational influence of the sun, Jupiter, Saturn, and other planets on the comet.

“I have not been able to discover the cause of these properties of gravity from phenomena, and I frame no hypotheses.” Isaac Newton

## Shaping the planets

While Newton searched for religious meaning in his scientific work, he could find none behind his theory of gravity. He did not discover the hand of God setting the planets in motion, but he had found a formula that shaped the universe.

The action of gravity is key to understanding why the universe looks as it does. For instance, gravity is responsible for the spherical shapes of the planets. If a body has sufficient mass, the gravitational force that it exerts exceeds the strength of the material of the body and it is pulled into a spherical shape. Astronomical rocky bodies, such as the asteroids between the orbits of Mars and Jupiter, are irregular in shape if they have a diameter of less than about 240 miles (380 km) (the Hughes-Cole limit).

Gravitation is also responsible for the size of the deviations from a sphere that can occur on a planet. There are no mountains on Earth higher than the 5.5 miles (8.8 km) of Mount Everest because the gravitational weight of a taller mountain would exceed the strength of the underlying mantle rock, and sink. On planets with lower mass, the weight of objects is less, and so mountains can be bigger. The highest mountain on Mars, for instance, Olympus Mons, is nearly three times as high as Everest. The mass of Mars is about one-tenth that of Earth, and its diameter is about half Earth’s. Putting these numbers into Newton’s formula for gravitation, this gives a weight on the surface of Mars of just over one-third that on Earth, which explains the size of Olympus Mons.

Gravity thus also shapes life on Earth by limiting the size of animals. The largest land animals ever were dinosaurs weighing up to 40 tons. The largest animals of all, whales, are found in the oceans, where the water supports their weight. Gravity is also responsible for the tides, which are produced because water bulges toward the sun and moon on the side of Earth nearer to them, and also bulges away from them on the other side where their gravitational pull is weaker. When the sun and moon are aligned, there is a high spring tide; when they are at right angles, there is a low neap tide.

“The motions of the comets are exceedingly regular, and they observe the same laws as the motions of the planets.” Isaac Newton

## Escape velocity

Gravity profoundly affects human mobility. The height a person can jump is determined by the gravitational field at ground level. Newton realized that the strength of gravity would affect the ease of travel beyond the atmosphere. To break free from Earth’s gravitational pull, it is necessary to travel at 25,020 mph (40,270 km/h). It is much easier to get away from less massive bodies
such as the moon and Mars. Turning the problem around, this escape velocity is also the minimum velocity that an incoming asteroid or comet can have when it hits Earth’s surface, and this affects the size of the resulting crater. Today, gravity is held to be most accurately described by the general theory of relativity proposed by Albert Einstein in 1915. This does not describe gravity as a force, but instead as a consequence of the curvature of the continuum of spacetime due to the uneven distribution of mass inside it. This said, Newton’s concept of a gravitational force is an excellent approximation in the vast majority of cases. General relativity only needs to be invoked in cases requiring extreme precision or where the gravitational field is very strong, such as close to the sun or in the vicinity of a massive black hole. Massive bodies that are accelerating can produce waves in spacetime, and these propagate out at the speed of light. The first detection of one of these gravitational waves was announced in February 2016.

## ISAAC NEWTON

Isaac Newton was born on a farm in Woolsthorpe, Lincolnshire, on December 25, 1642. After school in Grantham, he attended Trinity College Cambridge, where he became a Fellow and taught physics and astronomy. His book Principia set out the principle of gravity and celestial mechanics. Newton invented the reflecting telescope; wrote theses on optics, the prism, and the spectrum of white light; was one of the founders of calculus; and studied the cooling of bodies. He also explained why Earth was oblate (a squashed sphere) in shape and why the equinox moved, and formalized the physics of the speed of sound. He spent much time on biblical chronology and alchemy. Newton was at various times President of the Royal Society, Warden and Master of the Royal Mint, and member of parliament for Cambridge University. He died in 1727.

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# A LABORATORY ON MARS

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In August 2012, the Mars Science Laboratory Rover, better known as Curiosity, landed on Mars. This 2,000-lb (900-kg) wheeled vehicle, which is still roaming the Martian surface, is a mobile laboratory equipped to conduct geological experiments aimed at figuring out the natural history of the red planet. It is the latest robot explorer to reach Mars, and the largest and most advanced in a long line of rovers sent to explore other worlds.

“Mars has been flown by, orbited, smacked into, radar-examined, and rocketed onto, as well as bounced upon, rolled over, shoveled, drilled into, baked, and even blasted. Still to come: Mars being stepped on.” Buzz Aldrin

## Wanderers

The potential of rovers in space was clear as far back as 1971, when Apollo 15 carried a four-wheel Lunar Roving Vehicle to the moon. This agile twoseater widened the scope of lunar exploration for the last three Apollo missions. For instance, during the first moon landing in 1969, Neil Armstrong and Buzz Aldrin spent just two and a half hours moonwalking, and the farthest they moved from their lunar module was 200 ft (60 m). By contrast, however, in the final Apollo moon mission, Apollo 17, in 1972, the crew of two—Eugene Cernan and Harrison Schmitt—spent more than 22 hours outside. In their rover, they covered 22 miles (36 km) in total, with one drive taking the pair 4.7 miles (7.6 km) from their spacecraft. The Lunar Roving Vehicle, or moon buggy, was used to collect rocks. The six Apollo missions returned to Earth with 840 lb (381 kg) of them.

Analysis of these rocks revealed much about the history of the moon. The oldest were about 4.6 billion years old, and their chemical composition clearly showed a common ancestry with rocks on Earth. Tests revealed no evidence of organic compounds, indicating that the moon has always been a dry and lifeless world.

## Lunokhod 1

The Soviet lunar program, which began in the early 1960s, relied on unmanned probes to explore the moon. Three of the Soviet Luna probes returned with a total of 11.5 oz (326 g) of rock. Then, in November 1970, the Soviet lander Luna 17 arrived at a large lunar plain called the Sea of Rains (many lunar areas are named after the weather conditions they were once thought to influence on Earth). Luna 17 carried the remote-controlled rover Lunokhod 1 (Lunokhod means “moonwalker”). This was the first wheeled vehicle to traverse an extraterrestrial world, arriving about eight months before the first Apollo buggy. The concept behind it was simple—instead of sending moon rocks to Earth, the rover would do the analysis there.

## Remote-controlled explorer

The Lunokhod rover was 7½-ft (2.3-m) long and resembled a motorized bathtub. The wheels were independently powered so that they could retain traction on the rough lunar terrain. Lunokhod was equipped with video cameras that sent back TV footage of the moon. An X-ray spectrometer was used to analyze the chemical composition of rocks, and a device called a penetrometer was pushed into the lunar regolith (soil) to measure its density. Lunokhod was powered by batteries that were charged by day using an array of solar panels that folded out from the top of the rover. At night, a source of radioactive polonium inside the machine acted as a heater to keep the machinery working. The rover received commands from controllers on Earth about where to go and when to perform experiments. A human might have done a better job, but rovers could stay in space for months on end, and did not require food and water from Earth.

Lunokhod 1 was designed to work for three months, but lasted almost 11. In January 1973, Lunokhod 2 landed in the Le Monnier Crater on the edge of the Sea of Serenity. By June, Lunokhod 2 had traveled a total of 24 miles (39 km), a record that would stand for more than three decades.

“Over time you could terraform Mars to look like Earth … So it’s a fixer-upper of a planet.” Elon Musk

## Martian walker

As Lunokhod 1 was exploring the moon, the Soviet space program was eyeing an even greater prize: a rover on Mars. In December 1971, two Soviet spacecraft, code-named Mars 2 and Mars 3, sent modules to land on the red planet. Mars 2 crashed, but Mars 3 made a successful touchdown—the firstever landing on Mars. However, it lost all communications just 14.5 seconds later, probably due to damage from an intense dust storm. Scientists never found out what happened to Mars 3’s cargo: a Prop-M rover, a tiny 10-lb (4.5-kg) vehicle designed to walk on two ski-shaped feet. It was powered through a 50-ft (15-m) umbilical cord, and once on the surface was designed to take readings of the Martian soil. It is unlikely that the Prop-M ever carried out its mission, but it was programmed to operate without input from Earth. A radio signal between the moon and Earth travels in less than 2 seconds, but a signal to or from Mars takes between 3 and 21 minutes to arrive, varying with the planet’s distance from Earth. For a Martian rover to be a successful explorer, it needed to work autonomously.

## Bounce down

In 1976, NASA’s two Viking landers sent back the first pictures of Mars. Following this success, many more rovers were planned, but most of these projects never reached their destination, succumbing to what the press dubbed the “Martian Curse.”

NASA eventually had a success with its 1997 Mars Pathfinder mission. In July of that year, the Pathfinder spacecraft entered the Martian atmosphere. Slowed first by the friction of a heat shield and then by a large parachute, the spacecraft jettisoned its outer shielding, and the lander inside was lowered on a 65-ft (20-m) tether. As it neared the surface, huge protective airbags inflated around the lander, and retrorockets on the spacecraft holding the tether fired to slow the speed of descent. The tether was then cut, and the lander bounced across the Martian surface until it rolled to a stop. Fortunately, once the airbags had deflated, the lander was the right side up. The three upper sides or “petals” of the tetrahedral lander folded outward, revealing the 24-lb (11-kg) rover.

During development, the rover was called MFEX, short for Microrover Flight Experiment. However, it was known to the public as Sojourner, meaning “traveler” and chosen for its link to Sojourner Truth, a 19th-century US abolitionist and rights activist.

“We landed in a nice flat spot. Beautiful, really beautiful.” Adam Steltzner

## Rolling on Mars

Sojourner was the first rover to take a tour of the Martian surface. However, the Pathfinder mission was really a test for the innovative landing system and the technology that would power larger rovers in the future. The minuscule vehicle traveled just 300 ft (100 m) during its 83-day mission, and never ventured farther than 40 ft (12 m) from the lander. Now named the Carl Sagan Memorial Station, the lander was used to relay data from the rover back to Earth. Most of the rover’s power came from small solar panels on the top. One of the goals of the mission was to see how these panels stood up to extreme temperatures and what power could be generated in the faint Martian sunlight.

The rover’s activities were run from NASA’s Jet Propulsion Laboratory (JPL) in California, and JPL has remained the lead agency in developing Martian rovers. With the time delays inherent in communicating with Mars, it is not possible to drive a rover in real time, so every leg of a journey must be preprogrammed. To achieve this, cameras on the lander were used to create a virtual model of the surface around Sojourner. Human controllers could view the area in 3-D from any angle before mapping a route for the rover.

## Spirit and Opportunity

Despite its limitations in terms of size and power, Sojourner’s mission was a great success, and NASA pressed ahead with two Mars Exploration Rovers (MERs). In June 2003, MER A, named Spirit, and MER B, Opportunity, were ready for launch. They were about the same size as a Lunokhod rover, but were much lighter, at around 400 lb (180 kg). By the end of January the following year, both were traveling across the Martian deserts, hills, and plains, photographing surface features and chemically analyzing rock samples and atmosphere. They sent back the most glorious vistas of the Martian landscape ever seen, enabling geologists to examine the large-scale structures of the planet.

Spirit and Opportunity had landed using the same airbag-and-tether system as Sojourner. Like Sojourner, both relied on solar panels, but the new rovers were built as self-contained units, able to wander far from their landers. Each vehicle’s six wheels were attached to a rocking mechanism, which made it possible for the rovers to keep at least two wheels on the ground as they crossed rugged terrain. The software offered a degree of autonomy so that the rovers could respond to unpredictable events, such as a sudden dust storm, without needing to wait for instructions from Earth.

“Whatever the reason you’re on Mars is, I’m glad you’re there. And I wish I was with you.” Carl Sagan

## Low expectations

Nevertheless, expectations for these rovers were low. JPL expected that they would cover about 2,000 ft (600 m) and last for 90 Martian sols (equivalent to about 90 Earth days). During the Martian winter, however, the team did not know whether the solar-powered rovers would retain adequate power to keep working. Of all the solar system’s rocky planets, the seasons of Mars are the most Earth-like, due to the similar tilts of the planets’ rotational axes. Martin winters are dark and bitterly cold, with surface temperatures falling to as low as –225°F (–143°C) near the polar ice caps.

As predicted, Martian winds blew fine dust onto the solar arrays, cutting their generating power; but the wind also blew the panels clean from time to time. As winter drew nearer, the JPL team searched for suitable locations in which the rovers could safely hibernate. To do this, they used a 3-D viewer built from the images taken from the rover’s stereoscopic cameras. They chose steep slopes that faced the rising sun in order to maximize electricity generation and to top off the batteries. All nonessential equipment was shut down so that power could be diverted to heaters that kept the rovers’ internal temperature above –40°F (–40°C).

## Continuing mission

The hibernation worked, and incredibly, JPL has managed to extend the rover missions from a few days to several years. More than five years into its mission, however, Spirit became bogged down in soft soil; all attempts to free it by remote control from Earth failed, and unable to move to a winter refuge, Spirit finally lost power 10 months later. It had traveled 4.8 miles (7.73 km). Opportunity, meanwhile, has avoided mishap and continues to operate. In 2014, it beat Lunokhod 2’s distance record, and by August 2015 it had completed the marathon distance of 26.4 miles (42.45 km). This was no mean feat on a planet located some hundreds of millions of miles from Earth.

## Curiosity needed

Spirit and Opportunity were equipped with the latest detectors; including a microscope for imaging mineral structures and a grinding tool for accessing samples from the interiors of rocks.

However, Curiosity, the next rover to arrive on the planet in August 2012, carried instruments that not only studied the geology of Mars but also looked for biosignatures—the organic substances that would indicate whether Mars once harbored life. These included the SAM or Sample Analysis at Mars device, which vaporized samples of ground rock to reveal their chemicals. In addition, the rover monitored radiation levels to see whether the planet would be safe for future human colonization.

Considerably larger than previous rovers, Curiosity was delivered to Mars in an unusual way. During the landing phase of the mission, the radio delay (caused by the sheer distance from Earth) was 14 minutes, and the journey through the atmosphere to the surface would take just seven—all on autopilot (not remotely controlled from Earth). This created “seven minutes of terror”: the engineers on Earth knew that by the time a signal arrived informing them that Curiosity had entered the Martian atmosphere, the rover would already have been on the ground for seven minutes—and would be operational or smashed to pieces.

“The Seven Minutes of Terror has turned into the Seven Minutes of Triumph.” John Grunsfeld

## Safe landing

As Curiosity’s landing craft moved through the upper atmosphere, its heat shield glowed with heat, while rockets adjusted the descent speed to reach the Gale Crater, an ancient crater caused by a massive meteorite impact. A parachute slowed the craft to about 200 mph (320 km/h), but this was still too fast for a landing. It continued to slow its descent over a flat region of the crater, avoiding the 20,000-ft (6,000-m) mountain at its center. The craft reached about 60 ft (20 m) above the surface and then had to hover, since going too low would create a dust cloud that might wreck its instruments. The rover was finally delivered to the surface via a rocket-powered hovering platform called a sky crane. The sky crane then had to be detached and blasted clear of the area so that its eventual impact did not upset any future exploration.

Having survived the landing, Curiosity signaled to Earth that it had arrived safely. Curiosity’s power supply is expected to last at least 14 years, and the initial two-year mission has now been extended indefinitely. So far, it has measured radiation levels, revealing that it may be possible for humans to survive on Mars; discovered an ancient stream bed, suggesting a past presence of water and perhaps even life; and found many of the key elements for life, including nitrogen, oxygen, hydrogen, and carbon.

## EXOMAR

In 2020, the European Space Agency, in collaboration with the Russian space agency, Roscosmos, will launch its first Mars rover, ExoMars (Exobiology on Mars), with the goal of landing on Mars the following year. In addition to looking for signs of alien life, the solar-powered rover will carry a ground-penetrating radar that will look deep into Martian rocks to find groundwater. The ExoMars rover will communicate with Earth via the ExoMars Trace Gas Orbiter, which was launched in 2016. This system will limit data transfer to twice a day. The rover is designed to drive by itself; its control software will build a virtual model of the terrain and navigate through that. The rover software was taught how to drive in Stevenage, England, at a mockup of the Martian surface called the Mars Yard (above).

The ExoMars rover is expected to operate for at least seven months and to travel 2.5 miles (4 km) across the Martian surface. It will be delivered to the surface by a robotic platform that will then remain in place to study the area around the landing site.

# WE CHOOSE TO GO TO THE MOON

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In the early 1960s, the US lagged behind the Soviet Union in the “Space Race.” The Soviets had launched the first satellite in 1957, and on April 16, 1961, Yuri Gagarin became the first human in space. In response, in 1961 US President John F. Kennedy publicly committed to landing a man on the moon before the end of the decade. The project was carefully chosen—landing on the moon was so far beyond the capabilities of either protagonist that the Soviets’ early lead might not seem so significant.

Despite the reservations of many at the time regarding a moon landing’s scientific value, especially given the dangers and technical complexities involved, human spaceflight was now the focus of the US space program. NASA managers felt that with enough funding they could put a man on the moon by 1967. NASA administrator James E. Webb suggested another two years be added as a contingency.

In those six years from 1961 to 1967, NASA tripled its workforce, even though most of the planning, designing, and building of the hardware was undertaken by private industry, research institutes, and universities. NASA claimed that only the construction of the Panama Canal and the Manhattan Project to develop the nuclear bomb rivaled the effort and expense of the Apollo program.

“I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the moon and returning him safely to the Earth.” John F. Kennedy

## Which way to the moon?

At the time of Kennedy’s historic announcement, the US boasted a grand total of 15 minutes of human spaceflight. To move from here to a moon landing, many technological hurdles needed to be overcome. One of the first was the method of getting to the moon. Three options, known as mission architectures, were on the table. The direct ascent (DA) profile, or “all-theway,” required an enormous multistage rocket with enough fuel on board to transport the crew back to Earth. This was initially the favored approach. However, it was also the most expensive, and doubts were raised over the feasibility of building such a monster rocket before the 1969 deadline.

In the Earth-orbit rendezvous (EOR) profile, a moon-bound rocket ship would be assembled in space and dock with modules that had already been placed in orbit. Lifting things into space is the most energy-consuming part of any off-Earth mission, but multiple rocket launches would sidestep the need for a single spaceship. This was the safest option, but it would be slow. The real weight-savings came with the lunar-orbit rendezvous (LOR) profile.

Here, a smaller rocket would put a three-part spaceship on course to the moon. At the moon, a command module would remain in orbit with the fuel for the journey home, while a lightweight two-stage lunar lander would be sent to the surface. This quick and comparatively cheap option carried with it the very real risk of leaving a crew stranded in space should anything go wrong. After much debate and lobbying, influential figures, such as Wernher von Braun, director of NASA’s Marshall Space Flight Center, threw their backing behind LOR, and in 1962, LOR was chosen. This was the first of many leaps of faith for Apollo.

## Technological hurdles

On February 20, 1962, John Glenn became the first American to orbit Earth, looping three times around the planet in Friendship 7, as part of the US’s first spaceflight program, Project Mercury, which ran from 1958 to 1963. Three more successful Mercury flights followed, but there was a big difference between operations in low Earth orbit and landing on the moon. An entire new fleet of launch vehicles was required. Unlike Mercury spacecraft, which carried a single astronaut, Apollo missions would need a crew of three. In addition, a more reliable power source was needed and much more experience in space. The world’s first fuel cells were built to provide the power.

Project Gemini, NASA’s second human spaceflight program, provided the skills, with endurance spaceflights, orbital maneuvers, and space walks. Scientists also needed to know more about the moon’s surface. A deep layer of dust could swallow up a spacecraft and prevent it from leaving, clog up the thrusters, or cause the electronics to malfunction.

Unmanned fact-finding missions were mounted in parallel with Apollo, but the first wave of robotic explorers dispatched to the moon was an unmitigated failure. Six Ranger landers failed on launch, missed the moon, or crashed on impact, causing the program to be nicknamed “shoot and hope.” Luckily, the final three Rangers were more successful.

Between 1966 and 1967, five Lunar Orbiter satellites were placed in orbit around the moon. They mapped 99 percent of the surface and helped to identify potential Apollo landing sites. NASA’s seven Surveyor spacecraft also demonstrated the feasibility of a soft landing on the lunar soil.

“From this day forward, Flight Control will be known by two words: “Tough and Competent.”” Gene Kranz

## A gamble and a disaster

At 363 ft (110.5 m), Saturn V—the heavy-lift booster that carried the Apollo astronauts out of Earth’s atmosphere—is still the tallest, heaviest, and most powerful rocket ever built. “Man-rating” the rocket (certifying it to carry a human crew) proved particularly troublesome. The mammoth engines generated vibrations that threatened to break the rocket apart. Knowing that the project was behind schedule, NASA’s associate administrator for manned spaceflight, George Mueller, pioneered a daring “all-up” testing regime. Rather than the cautious stage-by-stage approach favored by von Braun, Mueller had the entire Apollo–Saturn systems tested together.

While striving for perfection, the NASA engineers developed a new engineering concept: that of redundancy. Key or critical components were duplicated in order to increase overall reliability. The Mercury and Gemini projects had taught engineers to expect unforeseen risks. A fully assembled Apollo vehicle had 5.6 million parts, and 1.5 million systems, subsystems, and assemblies. Even with 99.9 percent reliability, the engineers could anticipate 5,600 defects. Nevertheless, over its 17 unmanned and 15 manned flights, the Saturn boosters had shown 100 percent reliability. With two partially successful test flights under its belt, Mueller declared that the next launch would carry astronauts.

Until 1967, progress had been smooth, despite the breakneck pace. Then disaster struck. An electrical short-circuit during a launch rehearsal started a fire that incinerated the Apollo 1 crew inside the Command Module. The toxic smoke and intensity of the fire in a pressurized, pure-oxygen atmosphere killed Virgil “Gus” Grissom, Ed White, and Roger Chaffee in less than five minutes. In the wake of this tragedy, the next five Apollo missions were unmanned tests. Modifications were made, resulting in a safer spacecraft with a new gas-operated hatch, a 60–40 oxygen–nitrogen mix in the cockpit, and fireproof wiring throughout.

“Apollo riding his chariot across the sun was appropriate to the grand scale of the proposed program.” Abe Silverstein

## Earth’s place in space

Apollo 8 was the first manned spacecraft to leave Earth’s orbit. On Christmas Eve 1968, Frank Borman, James Lovell, and Bill Anders looped around the far side of the moon and witnessed the astounding sight of Earth rising from behind the moon’s surface. For the first time, humans could see their home from space—a startlingly blue world lost in the immensity of the void. As Anders put it: “We came all this way to explore the moon, and the most important thing is that we discovered the Earth.”

The crew was also the first to pass through the Van Allen radiation belts. This zone of charged particles extends up to 15,000 miles (24,000 km) from Earth, and was initially thought to be a serious barrier to human space travel. As it turned out, it resulted in a dosage of radiation only equivalent to a chest X-ray.

Finally, the program was ready for the last step—to take real steps on the moon itself. On July 21, 1969, an estimated global audience of 500 million tuned in to watch Neil Armstrong land the Lunar Module and step out onto the surface of the moon, closely followed by Buzz Aldrin. It was the culmination of nearly a decade of collaborative effort and effectively ended the Space Race.

There were six more missions to the moon following Apollo 11, including the near-disaster of Apollo 13, whose lunar landing in 1970 was aborted after an oxygen tank exploded on board. The crew was returned safely to Earth on the crippled spacecraft in a real-life drama that played out in front of a worldwide television audience.

Before Apollo, much of what was known about the physical nature of Earth’s only natural satellite was speculation but, with the political goals achieved, here was an opportunity to find out about an alien world firsthand. Each of the six landing missions carried a kit of scientific tools—the Apollo Lunar Surface Experiments Package (ASLEP). Apollo’s instruments tested the internal structure of the moon, detecting seismic vibrations that would indicate a “moonquake.” Other experiments measured the moon’s gravitational and magnetic fields, heat flow from its surface, and the composition and pressure of the lunar atmosphere.

Thanks to Apollo, scientists have compelling evidence from analysis of moon rock that the moon was once a part of Earth. Like Earth, the moon also has internal layers and was most likely molten at some point in its early history. Unlike Earth, however, the moon has no liquid water. Since it has no moving geological plates, its surface is not continually repaved, and so the youngest moon rocks are the same age as Earth’s oldest. The moon is not entirely geologically inactive, however, and occasionally has moonquakes that last for hours.

One Apollo 11 experiment remains active and has been returning data since 1969. Reflectors planted on the lunar surface bounce back laser beams fired from Earth, enabling scientists to calculate the distance to the moon to within an accuracy of a couple of millimeters. This gives precise measurements of the moon’s orbit, and the rate at which it is drifting away from Earth (about 1½ in [3.8 cm] per year).

## Apollo’s legacy

On December 19, 1972, the sonic boom over the South Pacific, as the Apollo 17 capsule thumped into Earth’s atmosphere, sounded the end of the Apollo program. In total, 12 men had walked on the moon. At the time, it was widely assumed that routine flights to Mars would soon be a reality, but in the intervening 40 years, scientific priorities changed, politicians worried about costs, and human space travel has not ventured farther than Earth’s orbit.

For many, the decision to end manned moon missions was a wasted opportunity, caused by a lack of imagination and leadership. However, the end of the acute Cold War competition that gave rise to the Apollo program heralded a new era of international cooperation for NASA, with Skylab, Mir, and the International Space Station.

Gene Cernan, the last man on the moon, predicted that it could be another 100 years before humankind appreciates the true significance of the Apollo missions. One result could be that it may have made the US smarter—the intake for doctoral degrees at American universities tripled during the 1960s, particularly in the field of physics. Apollo contracts also nurtured nascent industries, such as computing and semiconductors. Several employees of the California-based Fairchild Semiconductors went on to found new companies, including Intel, a technology giant. The Santa Clara area where these firms were based has become today’s Silicon Valley. But perhaps Apollo’s real legacy is the idea of Earth as a fragile oasis of life in space. Photos taken from orbit, such as the “Blue Marble” and “Earthrise”, fed into a growing awareness of planet Earth as a single entity, and the need for careful stewardship.

“Houston. Tranquility Base here. The Eagle has landed.” Neil Armstrong

## GENE KRANZ

Perhaps the embodiment of the NASA spirit is not the heroic astronauts but the legendary Apollo flight director Gene Kranz. Born in 1933, Kranz was fascinated by space from an early age. He served as a pilot with the US Air Force before leaving to pursue rocket research with the McDonnell Aircraft Corporation and then NASA.

Prominent and colorful, with a brutally close-cut flattop hairstyle, Kranz was unmistakable in Mission Control, dressed in his dapper white “mission” vests made by his wife.

Although he never actually spoke the words “Failure is not an option”— they were written for his character in the movie Apollo 13—they sum up his attitude. Kranz’s address to his Flight Control staff after the Apollo 1 disaster has gone down in history as a masterpiece of motivational speaking. In it, he stated the Kranz Dictum—“tough and competent”—that would guide Mission Control. Kranz was awarded the Presidential Medal of Freedom in 1970 for successfully returning Apollo 13 to Earth.

# THE MOST TREU PATH OF THE PLANER IS AN ELLIPSE

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Before the 17th century, all astronomers were also astrologers. For many, including German astronomer Johannes Kepler, casting horoscopes was the main source of their income and influence. Knowing where the planets had been in the sky was important, but of greater significance for constructing astrological charts was the ability to predict where the planets would be over the next few decades.

To make predictions, astrologers assumed that the planets moved on specific paths around a central object. Before Copernicus, in the 16th century, this central body was thought by most to be Earth. Copernicus showed how the mathematics of planetary prediction could be simplified by assuming that the central body was the sun. However, Copernicus assumed that orbits were circular, and to provide any reasonable predictive accuracy, his system still required the planets to move around a small circle, the center of which moved around a larger circle. These circular velocities were always assumed to be constant.

Kepler supported the Copernican system, but the planetary tables it produced could still easily be out by a day or two. The planets, the sun, and the moon always appeared in a certain band of the sky, known as the ecliptic, but actual paths of individual planets around the sun were still a mystery, as was the mechanism that made them move.

“Kepler was never satisfied by a moderate agreement between theory and observation. The theory had to fit exactly otherwise some new possibility had to be tried.” Fred Hoyle

## Finding the paths

To improve the predictive tables, Danish astronomer Tycho Brahe spent more than 20 years observing the planets. He next tried to ascertain a path of each planet through space that would fit the observational data. This is where the mathematical abilities of Kepler, Brahe’s assistant, came into play. He considered specific models for the solar system and the paths of the individual planets in turn, including circular and ovoid (egg-shaped) orbits. After many calculations, Kepler determined whether or not the model led to predictions of planetary positions that fit into Tycho’s precise observations. If there was not exact agreement, he would discard the idea and start the process again.

## Abandoning circles

In 1608, after 10 years of work, Kepler found the solution, which involved abandoning both circles and constant velocity. The planets made an ellipse— a kind of stretched-out circle for which the amount of stretching is measured by a quantity called an eccentricity. Ellipses have two foci. The distance of a point on an ellipse from one focus plus the distance from the other focus is always constant. Kepler found that the sun was at one of these two foci.

These two facts made up his first law of planetary motion: the motion of the planets is an ellipse with the sun as one of the two foci. Kepler also noticed that the speed of a planet on its ellipse was always changing, and that this change followed a fixed law (his second): a line between the planet and the sun sweeps out equal areas in equal times. These two laws were published in his 1609 book Astronomia Nova.

Kepler had chosen to investigate Mars, which had strong astrological significance, thought to influence human desire and action. Mars took variable retrograde loops—periods during which it would reverse its direction of movement—and large variations in brightness. It also had an orbital period of only 1.88 Earth years, meaning that Mars went around the sun about 11 times in Tycho’s data set. Kepler was lucky to have chosen Mars, since its orbit has a high eccentricity, or stretch: 0.093 (where 0 is a circle and 1 is a parabola). This is 14 times the eccentricity of Venus. It took him another 12 years to show that the other planets also had elliptical orbits.

Studying Brahe’s observations, Kepler was also able to work out the planets’ orbital periods. Earth goes around the sun in one year, Mars in 1.88 Earth years, Jupiter in 11.86, and Saturn in 29.45. Kepler realized that the square of the orbital period was proportional to the cube of the planet’s average distance from the sun. This became his third law and he published it in 1619 in his book Harmonices Mundi, alongside lengthy tracts on astrology, planetary music, and platonic figures. The book had taken him 20 years to produce.

## Searching for meaning

Kepler was fascinated by patterns he found in the orbits of the planets. He noted that, once you accepted the Copernican system for the cosmos, the size of the orbits of the six planets—Mercury, Venus, Earth, Mars, Jupiter, and Saturn—appeared in the ratios 8 : 15 : 20 : 30 : 115 : 195.

Today, astronomers might look at a list of planetary orbital sizes and eccentricities and regard them as the result of the planetary formation process coupled with a few billion years of change. To Kepler, however, the numbers needed explanation. A deeply religious man, Kepler searched for a divine purpose within his scientific work. Since he saw six planets, he presumed that the number six must have a profound significance. He produced an ordered geometric model of the solar system in which the sun-centered spheres that contained each planetary orbit were inscribed and circumscribed by a specific regular “platonic” solid (the five possible solids whose faces and internal angles are all equal). The sphere containing the orbit of Mercury was placed inside an octahedron. The sphere that just touched the points of this regular solid contained the orbit of Venus. This in its turn was placed inside an icosahedron. Then followed the orbit of Earth, a dodecahedron, Mars, a tetrahedron, Jupiter, a cube, and finally Saturn. The system was beautifully ordered, but inaccurate.

Kepler’s great breakthrough was his calculation of the actual form of the planetary orbits, but the physics behind his three laws did not seem to concern him. Rather, he suggested that Mars was carried on its orbit by an angel in a chariot, or swept along by some magnetic influence emanating from the sun. The idea that the movements were due to a gravitational force only arrived with the ideas of Isaac Newton some 70 years later.

## Wider contributions

Kepler also made important advances in the study of optics, and his 1604 book Astronomiae Pars Optica is regarded as the pioneer tome in the subject. Galileo’s telescope interested him greatly and he even suggested an improved design using convex lenses for both the objective and the magnifying eyepiece. He wrote, too, about the supernova that was first seen in October 1604, today commonly called Kepler’s supernova. Following Tycho, Kepler realized that the heavens could change, contradicting Aristotle’s idea of a “fixed cosmos.” A recent planetary conjunction coupled with this new star led him to speculate about the Biblical “Star of Bethlehem.” Kepler’s fervent imagination also produced the book Somnium, in which he discusses space travel to the moon and the lunar geography a visitor might expect on arrival. Many regard this as the first work of science fiction.

Kepler’s most influential publication, however, was a textbook on astronomy called Epitome Astronomiae Copernicanae, and this became the most widely used astronomical work between 1630 and 1650. He ensured that the Rudolphine Tables (named after Emperor Rudolf, his patron in Prague) were eventually published, and these tables of predicted planetary positions helped him greatly with the well-paid calendars that he published between 1617 and 1624. The accuracy of his tables, proven over a few decades, also did much to encourage the acceptance of both the Copernican sun-centered solar system and Kepler’s own three laws.

“Kepler was convinced that God created the world in accordance with the principle of perfect numbers, so that the underlying mathematical harmony … is the real and discoverable cause of the planetary motion. “ William Dampier

## JOHANNES KEPLER

Born prematurely in 1571, Kepler spent his childhood in Leonberg, Swabia, in his grandfather’s inn. Smallpox affected his coordination and vision. A scholarship enabled him to attend the Lutheran University of Tübingen in 1589, where he was taught by Michael Maestlin, Germany’s top astronomer at the time. In 1600, Tycho Brahe invited Kepler to work with him at Castle Benátky near Prague. On Tycho’s death in 1601, Kepler succeeded him as Imperial Mathematician.

In 1611, Kepler’s wife died, and he became a teacher in Linz. He remarried and had seven more children, five of whom died young. His work was then disrupted between 1615 and 1621 while he defended his mother from charges of witchcraft. The Catholic Counter-Reformation in 1625 caused him further problems, and prevented his return to Tübingen. Kepler died of a fever in 1630.