Astronomy: Orbital Motion (Unit 3)

Question 1

Who was Aristotle?

Answer 1

Aristotle was a scientists and philosopher, who lived from 384 B.C. to 322 B.C.

Question 2

What is Aristotle credited for?

Answer 2

Aristotle is credited for using logical arguments to prove that Earth is round. Aristotle also used logical arguments to demonstrate, incorrectly, that the Earth is at the center of the solar system, with the sun and the planets revolving around it. This is a geocentric model of the solar system

Question 3

Why did no one question Aristotle’s geocentric model?

Answer 3

Because he was so respected

Question 4

Geocentric Definition

Answer 4

Centered on Earth

Question 5

According to Aristotle, where were the sun and planets located?

Answer 5

According to Aristotle, the Earth was at the center of the solar system, and the sun and planets were fixed to a crystalline sphere, each nested within another

Question 6

What was correct about Aristotle’s model? Where were the stars located in his model?

Answer 6

In Aristotle’s model, the order of the planets was correct, with the notable exception that Aristotle had placed the sun’s orbit between that of Venus and Mars. The model included an outermost sphere that held the stars in place

Question 7

What were Aristotle’s arguments for the validity of his model?

Answer 7

Aristotle’s arguments in favor of the geocentric model made sense at the time. He argued that if Earth were traveling around the sun, the change in location would affect the appearance of the stars. After moving to the other side of the sun, he argued, our angle for viewing the same stars would change. To prove this, Aristotle enlisted the help of assistants with sharp eyesight to observe stellar parallax, but no difference in the relative positions of the stars could be detected. Aristotle concluded Earth could not possibly be moving around the sun

Question 8

Stellar Parallax Definition

Answer 8

The appearance of movement of a star as a result of the Earth moving around the sun

Question 9

What is the true reason why Aristotle did not detect stellar parallax, that we now know today?

Answer 9

Today we understand that Aristotle did not detect Stellar Parallax because the stars were much farther away than he considered possible. It was impossible to observe the apparent motion of the stars with the aid of a telescope

Question 10

What other reasons, other than lack of stellar parallax, did Aristotle have to prove the accuracy of his model?

Answer 10

— If Earth moved, a wind would blow constantly over the planet’s surface

— If Earth moved, when he threw a ball straight up in the air, it would always land behind him on the surface

Question 11

What did Claudius Ptolemy do in 140 BCE? What was observed about the movement of the planets at the time?

Answer 11

Around 140 BCE, the Greek astronomer Claudius Ptolemy further developed Aristotle’s model. He built on the observations made by astronomers before him about the movements of the planets in the night sky. It had been noticed that the speed of the planets seemed to change. Against the backdrop of stars, at times planets appeared to slow down — and even go backwards — before moving forward again. Today, these motions are known to be a result of our perspective on a moving planet

Question 12

What did Ptolemy add in his model to explain the planets’ appearances of slowing down and then moving forward again?

Answer 12

Ptolemy’s model used circles upon circles to explain this uneven movement. He proposed that the planets orbit Earth on “epicycles”. As a planet travels around the Earth, it spins around as though on a bicycle wheel. To make this model more closely match the observations of the movements of planets, Ptolemy proposed the Earth was slightly off-center with respect to the orbits of the planets

Question 13

How did Ptolemy’s model, while incorrect, help astronomers?

Answer 13

Ptolemy’s model, while incorrect, helped astronomers for thousands of years by allowing them to predict the positions of the planets for any given hour or day

Question 14

Why was the Ptolemaic model the most accurate of its time?

Answer 14

No other model of the motion of the sun and planets was more accurate than the Ptolemaic model. This was because the accuracy of measurements made by astronomers of the time was limited by the technology that was available to them

Question 15

True or False: An Earth-centered model represents the Geocentric theory

Answer 15

True

Question 16

Why did Ptolemy’s model stay?

Answer 16

Ptolemy’s model stayed since it allowed astronomers to make accurate predictions given the limitations of technology of the time

Question 17

What simple instrument did Ptolemy use to observe the planets?

Answer 17

Ptolemy observed the planets using a simple instrument now known as Ptolemy’s ruler

Question 18

What did early astronomers use to predict planetary motion?

Answer 18

Early astronomers used “computers” to predict planetary motion. One tool was called an astrolabe. The user adjusted circles on the tool based on the time and position of the observer on the planet, and it would indicate where in the sky a plant could be observed

Question 19

What does the astrolabe consist of?

Answer 19

The astrolabe has two nested circles. The inner circle represents the position of a planet on its epicycle

Question 20

What was an early “computer” that Ptolemy used?

Answer 20

The astrolabe

Question 21

What was the armillary sphere?

Answer 21

Another tool early astronomers used was the armillary sphere, which was a set of seven nested rings. The outer rings were adjusted for the position of the viewer, and the inner rings gave the position of the planets

Question 22

What was the most complex of Ptolemy’s instruments?

Answer 22

The armillary sphere

Question 23

Why was Aristotle’s ideas appealing to the people of the time?

Answer 23

Aristotle’s idea of perfect circles, and his arguments for a stationary Earth, fit with religious beliefs at the time

Question 24

What happened to scientific progress in Europe after the development of the geocentric model?

Answer 24

Scientific progress slowed in Europe during the period when the geocentric model ruled. At the same time, Arabic scholars in the East made advances in science and math

Question 25

What are some ideas of why people used models in ancient times, and even now?

Answer 25

From modern day to ancient times, scientists used models, for it helped them visualize data and many people could not read back then

Question 26

How did Copernicus learn of the critiques of Ptolemy’s model of the solar system?

Answer 26

When Copernicus was a young student in Italy, he developed an interest in astronomy. At the time, people were beginning to translate Arabic books into European languages. This was likely how Copernicus learned about critiques of Ptolemy’s model of the solar system

Question 27

What did Copernicus believe was the problem with Ptolemy’s model?

Answer 27

Copernicus proposed that Ptolemy’s model was too complex. For much of the rest of his life, he made careful observations of the planets. In his final days, he published a book that would begin a new epoch in astronomy. Described in Copernicus’ book was a heliocentric model of the solar system, in which the planets travelled in perfect circles around the Sun and the stars were fixed to an outer sphere

Question 28

Heliocentric Definition

Answer 28

Centered on the sun

Question 29

How long did people follow the geocentric model?

Answer 29

More than 2,000 years

Question 30

Why was Copernicus troubled with the geocentric model?

Answer 30

In the early 1500s, Nicolaus Copernicus, from Poland, was troubled by the geocentric model, for it did not fit with the motion of the planets he observed

Question 31

Retrograde Motion Definition

Answer 31

The apparent backward motion of an object resulting from the circular motions of the viewer and the object

Question 32

What was Copernicus’ critique of Ptolemy’s explanation for retrograde motion in his model?

Answer 32

Copernicus believed Ptolemy’s explanation for retrograde motion in his model was too complicated to occur naturally

Question 33

Why did Copernicus believe a heliocentric model explained retrograde motion?

Answer 33

Copernicus believed if the sun was the center of the universe and Earth and all the other planets rotated around the sun, then the observed retrograde motion of the planets would make since

Question 34

What did Copernicus believe about Earth that explained retrograde motion and more?

Answer 34

Copernicus believed that Earth’s motion through space accounted for the retrograde motion of the other planets. Additionally, Earth’s own rotation on its axis explained the rising and setting of the sun as well as the movement of stars. Earth’s seasons were attributed to Earth’s rotation and orbit

Question 35

What was Copernicus’ process of making and publishing his book? Why did he wait so long?

Answer 35

In 1514, Copernicus compiled his ideas, shared them with some friends, and then began writing his book: “On the Revolutions of the Heavenly Spheres”., completed in 1532. He published the book 12 years after it had been completed, in 1544, waiting shortly before he died in the fear of backlash

Question 36

What did a Roman Catholic Church do with Copernicus’ book in 1616?

Answer 36

In 1616, A Roman Catholic Church banned Copernicus’ book

Question 37

What were some of the problems with Copernicus’ model?

Answer 37

The orbits of the planets are slightly more elliptical than circular, and the sun is not the center of the universe

Question 38

What did Copernicus notice about the relationship between a planet’s velocity and its distance from the sun? What did he conclude? What did he discover about the moon?

Answer 38

Copernicus noticed a relationship between the velocity of a planet and the distance of its orbits from the sun. He hypothesized that the planets move at a constant speed, and that planets closer to the sun orbit it more quickly. Copernicus also observed that the moon is the only body that revolves around Earth

Question 39

Why was Copernicus not able to prove his model was correct?

Answer 39

In spite of his years of observations and calculations, Copernicus was not able to prove that his model was correct. Although his model was much simpler than Ptolemy’s, his calculations for the movements of the planets were not more accurate. Copernicus’ heliocentric model would be dismissed for more than 50 years, until Italian astronomer Galileo Galilee built and used a telescope to observe the stars

Question 40

What did Copernicus’ model offend?

Answer 40

It offend both scientific and religious beliefs at the time

Question 41

How many planets were known at the time of Copernicus?

Answer 41

6; Mercury, Venus, Earth, Mars, Jupiter, and Saturn

Question 42

Where did Copernicus’ model state where the stars were?

Answer 42

Copernicus stated that the stars were fixed on an immobile sphere found beyond Saturn

Question 43

What did Copernicus do in 1543?

Answer 43

He published his model of the solar system in Latin

Question 44

Why do we have a leap year, and day, and what do they show?

Answer 44

It takes nearly 365 1/4 days for Earth to orbit the sun. After four years, the nearly 1/4 days add up to one day. Following certain rules, we add that day to the calendar as February 29, and call it leap day. This is one example of many ways in which the model of the solar system affects parts of everyday life

Question 45

What did the Ancient Greeks identify as planets? What did they know about the moon? How about the sun?

Answer 45

The ancient Greeks identified Mercury, Venus, Mars, Jupiter, and Saturn as planets. They also knew that Earth had a moon and that the sun was also part of the solar system

Question 46

What did the Ancient Greeks believe about the orbit of the planets?

Answer 46

The ancient Greeks believed that the planets had circular orbits

Question 47

What could the geocentric model not explain about Mercury and Venus?

Answer 47

The geocentric model could not explain why Mercury and Venus change in appearance throughout the year when viewed from Earth. When these planets are on the same side of the sun as Earth, they appear crescent-shaped. As Mercury and Venus move toward the opposite side of the sun in relation to Earth, they appear more circular. When these planets are correctly placed in their orbits between Earth and the sun, as they are in the heliocentric model, the observations are explained

Question 48

What have we added to the heliocentric model in modern times?

Answer 48

In modern times, we have added elliptical orbits, the planets of Uranus and Neptune, and Jupiter’s moons

Question 49

Which astronomers helped develop the heliocentric model?

Answer 49

Copernicus, Kepler, Galileo, and Newton developed the heliocentric model

Question 50

What did Copernicus observe about a planets speed when farther or closer to the Sun?

Answer 50

Copernicus made observations showing that a planet’s speed increased as it neared the sun and decreased as it moved farther away

Question 51

What does Kepler’s Second Law of Motion state?

Answer 51

Kepler’s second law of motion states that as a planet moves along it orbit, a line from the sun to the planet sweeps out equal areas in equal amounts of time. This law is known as the “Law of Areas”

Question 52

What is an example of Kepler’s Second Law of Motion (only for review)?

Answer 52

Suppose a planet moves between any 2 points on its orbit in time “t”. The line from the sun to the planet sweeps out an area “A”. If a planet moves between any two other points in the same amount of time “t”, according to Kepler’s second law, it again sweeps out an Area “A”. This is true for the motion of the planet all along its orbit

Question 53

How did Kepler learn of the planets? From who? What planet did he observe?

Answer 53

In 1600, Kepler was hired by Danish astronomer Tycho Brahe — who had generated an enormous collection of data by detailed tracking of planets along their orbits — to define the orbit of Mars, but Brahe passed away just a year later. Kepler continued the work using Brahe’s data. Most astronomers at the time assumed planetary orbits must be circular, but Brahe’s data did not support this conclusion. By comparing the positions of planets at different times along their orbits, he realized that a line between a planet and the sun sweeps out equal areas in equal times. Kepler had discovered his 2nd law of motion

Question 54

What did the discovery of Kepler’s Second Law of Motion lead to?

Answer 54

Despite the subsequent names given to the laws, the discovery of Kepler’s second law led to the determination of his first law, that planetary orbits are elliptical

Question 55

How long ago did Kepler develop his laws of motion? What tools did he use?

Answer 55

Kepler developed his laws of motion 400 years ago without telescopes

Question 56

Despite the fact that planets sweep out equal areas in equal times, what varies?

Answer 56

Even though planets sweep out equal areas in equal times in their orbits around the sun, the distance the planet moves varies

Question 57

According to Kepler’s Second Law of Motion, what proves that the closer a planet is to the sun, the faster it is?

Answer 57

When the planet is closer to the sun, it travels a longer distance as it sweeps out an equal area. This means the planet moves faster when it is closer to the sun. This is an important aspect of Kepler’s Second Law of Motion

Question 58

During which month does the Earth move the fastest? Why?

Answer 58

During the month of January, the Earth moves the fastest for it is when Earth is closet to the sun

Question 59

During which month does Earth move the slowest? Why?

Answer 59

During the month of July, the Earth moves the slowest for it is when Earth is farthest from the sun

Question 60

Although models make it seem like Earth’s orbit is highly elliptical, what is Earth’s true orbit like?

Answer 60

Earth’s actual orbit is almost circular

Question 61

What does a decreases or increase in the sun’s gravitational attraction change about a planet?

Answer 61

A decrease or increase in the sun’s gravitational atttarction changes only the shape of the orbit, not the speed of the planet

Question 62

What changes the speed of a planet along its orbit, according to Kepler’s Second Law of Motion?

Answer 62

Because of inertia, the planet always has a tendency to move along a straight line at a constant speed. As a planet moves toward the sun, the gravitational pull is generally forward, causing the planet to speed up. As a planet moves away from the sun, the gravitational pull is generally backward, causing the planet to slow down

Question 63

Inertia Definition

Answer 63

The tendency of an object to move along a straight path at a constant speed

Question 64

What relationship does Kepler’s Second Law of Motion describe?

Answer 64

Kepler’s Second Law of Motion describes the relationship between a planets’s distance from the sun and the planet’s velocity

Question 65

What is Kepler’s full name?

Answer 65

Johannes Kepler

Question 66

Between which two years did Kepler develop his series of laws? When was the first one made?

Answer 66

Between 1609 and 1618, Kepler developed a steric of laws describing the orbits of the planets. Kepler’s first law, developed in 1609, states that all planets in our solar system move around the sun in an elliptical orbit

Question 67

Elliptical Definition

Answer 67

Similar to an oval shape

Question 68

How did Kepler conclude that planets’ had an elliptical orbit, through his data on Mars?

Answer 68

If Mars had followed a circular orbit, the data Kepler studied would have shown that the sun was always at the center of orbit. The distance from Mars to the sun would always be the same. This was not what Kepler discovered. Instead, Kepler was able to determine that the shape of the orbit of Mars was not circular because the data showed that the orbit has a perihelion and an aphelion

Question 69

What is a perihelion?

Answer 69

A perihelion is the point on a planet’s orbit that is closest to the sun

Question 70

What is an aphelion?

Answer 70

An aphelion is the point on the orbit that is farthest from the sun

Question 71

What does Kepler’s First Law of Planetray Motion state?

Answer 71

Kepler’s first law of planetray Motion states that all planets move around the sun in elliptical orbits, where a planet’s path and speed are affected by the gravitational force of the sun. So as a planet travels in a parabolic path, it forms and elliptical orbit with the sun as one of the foci. So, the farther a planet is from the sun, the bigger the ellipse

Question 72

What are the major and minor axes? What are they divided into?

Answer 72

The line from the perihelion to the aphelion is the major axis, and the perpendicular line through the center is the minor axis. The major axis is divided into two semi-major axes, and the minor axis is divided into two semi-minor axes

Question 73

What are the foci on the major axis?

Answer 73

Along the major axis of an ellipse are two points, each called a focus (plural is foci), that are the same distance from the center. The sun of the distances from any point on the ellipse to the two foci is always the same. In planetary motion, the sun is always at one of the foci of the elliptical orbit

Question 74

For all of the planets, how would we describe their orbits, despite the un-proportional models?

Answer 74

For all the planets, however, the orbit is very close to circular

Question 75

Which planet has the most elliptical orbit?

Answer 75

Mercury

Question 76

How elliptical are the orbits of other objects that move around the sun, that are not planets?

Answer 76

Other objects moving around the sun, such as some asteroids and comets, have orbits that are highly elliptical

Question 77

How does the distance of Earth from the sun compare at its aphelion and its perihelion? How does the small difference of these amounts affect Earth’s climate?

Answer 77

The distance from Earth to the sun at aphelion is 152,100,000 km. The distance to the sun at perihelion is 147,095,000 km. This relatively small distance means Earth receives about the same amount of energy from the sun throughout the year. As a result, yearly climate variations are relatively minor on Earth

Question 78

What does an almost-circular orbit prevent on Earth?

Answer 78

An almost-circular orbits prevents huge temperature variations on Earth, for if our perihelion was closer, the summers and winters on Earth would be too hot for life to flourish

Question 79

What does Kepler’s Third Law of Planetary Motion state?

Answer 79

Kepler’s third law states that the square of a planet’s orbital period, “T”, is proportional to the cube of the semi-major axis, “a”, of the planet’s orbit

Question 80

What is the equation that represents Kepler’s Third Law of Planetary Motion?

Answer 80

T^2 ∝ a^3

Question 81

Orbital Period Definition

Answer 81

Time to complete one orbit

Question 82

How is the equation stated in Kepler’s Third Law of Planetary Motion modified for circular orbits?

Answer 82

For circular orbits, the semi-major axis equals the radius, “r”, of the orbit. This relationship can be written as an equation: T^2 = (4 π^2/Gm)r^3. In this equation, “G” is the universal gravitation constant equal to “6.673 x 10^-11 N. m^2/kg^2”. The variable “m” is the mass of the object being orbited. This equation is a good approximation in our solar system because the orbits are almost circular

Question 83

How does Kepler’ Third Law of Motion’s equation compare the motion of two objects orbiting the same object? What would be the equation simplified?

Answer 83

Kepler’s third law equation uses ratios to compare the motion of two objects orbiting the same object. The constant “4 π^2/Gm” cancels out in T1^2/T2^2 = r1^3/r2^3, which is simplified

Question 84

In what unit of measurement is the orbital period often expressed in? How about the radius?

Answer 84

The orbital period is often expressed in years, and the radius, or semi-major axis, is expressed in astronomical units (AU). Any units of time and distance, however, are acceptable

Question 85

Astronomical Unit Definition

Answer 85

The average distance from the sun to Earth

Question 86

How can Kepler’s Third Law of Planetary Motion be simplified for the planets in our solar system?

Answer 86

Kepler’s third law can be simplified for planets in our solar system. Information about the orbits of other planets can be determined using the orbit of Earth as a reference, with r1 = 1 astronomical unit and T1 = 1 year. Kepler’s third law equation relating the period and semi-major axis of other planets then becomes: T^2 = r^3. “T” must be expressed in years, and “a” must be expressed in AU in this relationship

Question 87

True or False: Kepler’s third law of planetary motion applies to all objects orbiting a central body

Answer 87

True

Question 88

What could a geocentric model not explain about Jupiter and Mars?

Answer 88

Additionally, the geocentric model could not explain why Mars and Jupiter both appear to move backward in the sky at some point during their orbits. Earth travels in its orbit faster than both Mars and Jupiter. Normally, Mars and Jupiter appear to move from west to east in the sky when viewed from Earth. Approximately once every two years, Earth passes Mars during its orbit. During these few months, Mars appears to move from east to west. The same thing happens when Earth passes Jupiter in its orbit. Once a year for a period of time, Jupiter appears to move from west to east when viewed from Earth. This phenomenon is called retrograde motion.

Question 89

What was Copernicus’s model of the solar system? What was the revolution time of each planet on the model?

Answer 89

Copernicus’s model demoted Earth from the center of the universe to just another planet, which was an idea contrary to both scientific and religious beliefs of the time.

I. Immobile sphere of the fixed stars.
II. Saturn completes one revolution every 30 years.
III. One revolution of Jupiter every
12 years.
IV. Biannual revolution
of Mars.
V. Annual revolution
of Earth and
sphere of Moon.
VI. Venus every 7 1/2
months.
VII. Mercury in
88 days.

In Copernicus’s model, the sun was in
the center of the solar system, and the
six known planets, including Earth,
revolved around the sun. He noted
that the outer planets revolve more Sun. slowly than the inner planets. He also
stated that the stars were fixed on an immobile sphere beyond Saturn.

Question 90

What is Gravity? On Earth, why do we perceive gravity as a downward force?

Answer 90

Gravity is a force of attraction between any two objects. On Earth, we perceive gravity as a downward force because of Earth’s very large mass

Question 91

What did Newton realize about gravity?

Answer 91

Newton realized that the force of gravity applied to everything — in other words, this force is universal

Question 92

What is gravity by Newton’s definition?

Answer 92

By Newton’s definition, gravity is not simply a force that pulls objects toward Earth, but a force of attraction between any two objects with mass. Newton published his theory of universal gravitation in 1687

Question 93

Universal Definition

Answer 93

Applying to all objects

Question 94

The works from which scientists helped Newton develop his theory of universal gravitation?

Answer 94

Newton would not have been able to develop his theory of universal gravitation without the important work of scientists that preceded him; Nicolaus Copernicus (1543), Tycho Brahe (1570s), and Johannes Kepler (1609) are some examples. Newton built on their ideas and could not have done it on his own

Question 95

What did Tycho Brahe do in the 1570s that supported Copernicus’ theory?

Answer 95

In the 1570s, the Danish astronomer Tycho Brahe carefully developed and calibrated instruments to collect data about the motion of planets. These data were ultimately used to support Copernicus’ theory

Question 96

What did Newton want to know about the planets?

Answer 96

Newton wanted to know why the planets orbit around the sun, which his theory of universal gravitation helps answer

Question 97

At what rate do objects accelerate toward Earth due to gravity?

Answer 97

Earth’s gravity causes all objects, all other factors being equal, to accelerate toward Earth at a rate of 9.8 m/s2

Question 98

Is there air resistance in a vacuum?

Answer 98

In a vacuum, there is no air resistance

Question 99

When Newton developed his theory of universal gravitation, what was he looking for specifically?

Answer 99

Newton was specifically looking for a simple explanation for why the solar system seems to follow Kepler’s 3 laws of planetary motion

Question 100

How did Hooke help Newton develop his theory of universal gravitation?

Answer 100

Hooke’s ideas about gravity helped Newton put together the full picture. He discovered that the force of gravity is proportional to the square of the distance between them. Simply stated, the more mass an object has, the more gravitational force it exerts on other objects. And the farther apart two objects are, the weaker the pull of gravity is between them

Question 101

What is the formula to solve for the gravitational force between two objects?

Answer 101

F = Gm1m2/r^2; here, “F” is the gravitational force, which is measured in Newtons. “G” is the gravitational constant. M1 and M2 are the masses of the objects. “R” is the distance between the objects. This is the Law of Universal Gravitation

Question 102

What does the gravitational force equal (verbal form of equation)?

Answer 102

Force equals the gravitational constant times the product of the masses of the two objects divided by the square of the distance between them

Question 103

True or False: all objects exert gravity on each other

Answer 103

True

Question 104

Who contributed the most to the development of Newton’s theory of universal gravitation?

Answer 104

Robert Hooke

Question 105

What was Robert Hooke’s contribution to the development of the law of universal gravitation?

Answer 105

Hooke lived at the same time of Newton, and made notable discoveries in nearly every area of science, from microbiology to physics. In 1670, Hooke had proposed the idea that gravity applied to all objects in space, such as planets and stars. He claimed that the strength of gravity increases as the distance between objects decreases, and that without gravity planets would move in straight lines. It is therefore likely that Hooke was the 1st scientists to described gravity as a universal force, but it was Newton who was able to build on his ideas and describe them mathematically

Question 106

What relationship did Newton develop? Why are the terms “m1” and “m2” included in the equation for gravity?

Answer 106

Newton developed the relationship between an object’s mass and the force needed to change the speed of its motion, or accelerate. He knew that the more mass an object has, the greater the force needed to accelerate it. At the same time, Newton was working on his 3rd law of motion, which states that for every action, there is an equal and opposite reaction (2 forces). This meant that when an apple falls, there is a force causing the apple to accelerate toward Earth, and also a force causing Earth to accelerate toward the apple. In other words, the force of gravity depends on the masses of both objects. This is why the equation for gravity includes “m1” and “m2”. As either of these masses increase, the force of gravity increases as well

Question 107

Why is the term “r” squared in the equation for gravity?

Answer 107

The other part of the equation accounts for the distance between objects. Newton observed that the force of attraction between two objects is greater when the objects are closer, but this relationship is a bit more complicated. Newton was able to use known quantities for the acceleration of the moon and its distance from Earth and compare them with objects closer to Earth. From his calculations, Newton saw that the effect of increasing distance was exponential. This is why the distance portion of the equation “r” is squared

Question 108

What is a constant in a scientific equation?

Answer 108

A constant is a set number that is always used to complete the equation

Question 109

How did Newton prove that gravity is universal through his calculation?

Answer 109

Not only did Newton apply mathematics to be able to measure the force of gravity — he showed that his calculations could apply to any two objects. Newton proved gravity’s universality

Question 110

How does gravitational force in Newtons compare to mass in kilograms?

Answer 110

Gravitational force in Newtons is roughly 10 (exactly 9.8) times the mass in kg

Question 111

What does Newton’s first law of motion state? How did it provide planetary clues?

Answer 111

Newton’s first law of motion states that objects in motion stay in motion unless acted upon by an outside force. This means that an object would continue to move in a straight line unless a force caused them to move in a circular pattern (planetary clues’

Question 112

True or False: Much of what we know about our solar system today stems from the discoveries made in the pursuit of understanding gravity

Answer 112

True

Question 113

What did the work of Kepler and Newton help scientists explain? What is eccentricity?

Answer 113

The work of Kepler and Newton enabled scientists to explain the irregular, or eccentric, motion of orbiting bodies. Orbital eccentricity, represented by “e”, is a measure of how much an orbit differs from a circle

Question 114

How does the eccentricity compare between a circular orbit and an elliptical orbit? What affects eccentricity?

Answer 114

A perfectly circular orbit has no eccentricity, or e = 0. An elliptical orbit has an eccentricity greater than 0 and less than 1, written as 0 < e < 1. The more stretched out, or elongated, the ellipse, the closer the value of “e” is to 1

Question 115

At what eccentricity does an object lose the ability to maintain a closed orbit?

Answer 115

Objects with an eccentricity equal to 1 (e = 1) or greater 1 (e > 1) cannot maintain a closed orbit. Objects like these, such as some comets, will enter the solar system, pass around the sun once, and then leave the solar system, never to return

Question 116

What does the eccentricity of an elliptical orbit depend on?

Answer 116

The eccentricity of an elliptical orbit depends on the distance “rp” from the sun to the perihelion point and the distance “ra” from the sun to the aphelion point. The formula, which uses simple algebra, is written as follows: e = ra — rp/ra + rp

Question 117

What is the eccentricity of the International Space Station (ISS)? What does this allow?

Answer 117

The ISS has an orbital eccentricity of 0, which means it has a circular orbit. It’s distance from Earth’s surface is nearly always the same

Question 118

What are the eccentricities of Mercury, Venus, Earth, and Mars?

Answer 118

Venus has the smallest eccentricity of 0.0068. Earth’s eccentricity measures 0.0167, but the eccentricity of Mars is larger at 0.0934. The smallest planet, Mercury, has the largest orbital eccentricity of 0.2056

Question 119

How have scientists measured the eccentricity of exoplanets?

Answer 119

Scientists have also been able to calculate the orbital eccentricities of exoplanets they have discovered. Studies show that solar systems with a smaller number of exoplanets tend to have orbits with larger eccentricities. On the other hand, in solar systems like ours, the orbits tend to have smaller eccentricities. Astronomers theorize that the gravitational attraction among a large number of planets and dwarf planets may help make orbits less eccentric

Question 120

Exoplanet Definition

Answer 120

Planet in a solar system other than ours

Question 121

What type of orbit does an eccentric measurement of 1 form? How about an eccentric measurement greater than 1?

Answer 121

An eccentric measurement of 1 forms a parabolic orbit. An eccentric measurement greater than 1 forms a hyperbolic orbit

Question 122

What causes Mars to experience dramatic seasonal changes?

Answer 122

Mars’ fairly high eccentric orbit combined with the tilt of its axis causes it to experience dramatic seasonal changes, greater than Earth’s

Question 123

What is the eccentricity of Jupiter?

Answer 123

0.049

Question 124

What is the eccentricity of Saturn?

Answer 124

0.057

Question 125

What is the eccentricity of Uranus? What makes Uranus different from other planets, in terms of rotation?

Answer 125

Uranus has an eccentricity of 0.046. Unlike most other planets, its axis lies almost parallel to its orbital plain, meaning it nearly spins on its side. Each pole takes turns pointing toward the sun as the planet orbits

Question 126

What is the eccentricity of Neptune?

Answer 126

0.0011

Question 127

What is the eccentricity of Pluto?

Answer 127

0.2488; higher than any planet in the solar system

Question 128

What is the eccentricity of the orbits of comets?

Answer 128

Comets tend to have extremely eccentric orbits. Halley’s Comet, for instance, has an eccentricity value of 0.97, a near perfect parabolic trajectory

Question 129

What is the eccentricity of the orbits of asteroids?

Answer 129

Asteroids have an average eccentricity of about 0.17, but some have highly elongated elliptical orbits

Question 130

Asteroid Definition

Answer 130

Small, rocky body orbiting the sun

Question 131

Which moon in the solar system has the highest eccentricity?

Answer 131

Earth’s moon has the largest eccentricity of 0.0549. Phobos, orbiting Mars, has a smaller eccentricity of 0.0151, while Neptune’s moon Triton has the smallest—a mere 0.000016

Question 132

What did Brahe do that was remarkable?

Answer 132

Brahe had complied the most accurate data of his day on the movements and positions of planets and stars over a span of 20 years

Question 133

Which astronomers helped Kepler develop his three laws of orbital motion?

Answer 133

Kepler was able to use the work of prior astronomers, such as Ptolemy, Copernicus, and Brahe

Question 134

How long, in Earth years, does it take for Mercury to complete an orbit?

Answer 134

1/5 of an Earth year

Question 135

How long, in Earth years, does it take Saturn to complete one orbit?

Answer 135

29 1/2 Earth years

Question 136

What is the difference of Earth’s distance at aphelion and perihelion?

Answer 136

3 million miles

Question 137

How are Newton’s and Kepler’s findings intertwined?

Answer 137

Patterns in Earth’s movements are identified in Kepler’s laws, and Newton discovered why these patterns occur

Question 138

Orbit Definition

Answer 138

Path of an object moving around a central attractive mass

Question 139

Gravitational Force Definition

Answer 139

Attractive force between 2 objects due to their mass

Question 140

How does distance and gravity affect speed?

Answer 140

As objects draw closer together, the force between them increases, increasing speed. As objects move apart, the force between them decreases, decreasing speed

Question 141

What does the solar system consist of?

Answer 141

The solar system consists of the sun and all the objects in orbit around it. These include the planets and their moons, asteroids, comets, and very thin gas called the interplanetary medium

Question 142

What does planet mean in Greek?

Answer 142

Wanderer

Question 143

Where must astronomer’s observations be made?

Answer 143

From Earth

Question 144

What is the difference between actual and apparent retrograde motion?

Answer 144

Actual retrograde motion is different from the expected direction of motion, such as the clockwise orbit of Halley’s Comet. Apparent retrograde motion appears backward at some points because of the speed of the observer on Earth

Question 145

What are the three pathways an object orbiting a massive central body can follow?

Answer 145

Spiral, hyperbola, and ellipse

Question 146

What happens in a spiral orbits?

Answer 146

In a spiral orbit, the object gradually moves inward until it falls into the central body, such as Comet Shoemaker-Levy spiraling into Jupiter

Question 147

What happens in a hyperbola orbit?

Answer 147

When an orbit is a hyperbola, the orbiting object swings around the central body once and the heads away in a u-shaped, one way trip. When spacecrafts perform this movement around a planet, it is called a gravitational slingshot

Question 148

What happens in a stable orbit? What type of orbit does it create?

Answer 148

In a stable orbit, the orbiting object’s momentum and the force of gravity are perfectly balanced, resulting in an ellipse

Question 149

True or False: a circle is a special case of an ellipse

Answer 149

True

Question 150

What does the orbital path an object follows depend on?

Answer 150

The orbital path an object follows depends on its mass, initial speed, and initial direction of motion

Question 151

What can acceleration do to an object? What causes this?

Answer 151

Acceleration can speed an object, slow it, or turn it — in the case of orbital mechanics, all 3 occur, and it is caused by gravitational force

Question 152

What does the amount of acceleration depend on? What is its formula?

Answer 152

The amount of acceleration decreases as the mass of the object increases; a relationship expressed by the formula “ a = F/m” where “a” represents acceleration, “F” represents force, and “m” represents the mass of the object

Question 153

Acceleration Definition

Answer 153

Change in an object’s motion

Question 154

What are the components of the equation: “F = Gm1m2/r^2”?

Answer 154

“F” is the force, “G” is the gravitational constant, “m1”is the mass of a central body, “m2” is the mass of an orbiting body, and “r” is the distance between the centers of the objects

Question 155

What are the components of the equation: “a = F/m2”?

Answer 155

“a” is the acceleration, “F” is the force, and “m2” is the mass of the orbiting body

Question 156

What does the speed of an object in orbit depend on?

Answer 156

The speed of an object in orbit depends on its distance from the central body and the mass of the central body

Question 157

Combined with Newton’s laws of motion, how can one find the acceleration of an object in orbit?

Answer 157

Combined with Newton’s laws of motion, one can find the acceleration of an object in orbit: Combine “F = Gm1m2/r2” and “a = F/m2” to get “a = G m2/r2”

Question 158

What is the center of a circular orbit?

Answer 158

The center of a circular orbit is not the exact center of the central body. Instead, the central body and the orbiting object both rotate around the center of mass of the system

Question 159

In the Earth-moon system, the point around which both objects orbit is located where?

Answer 159

Within Earth’s mantle, not at its exact center

Question 160

For two identical objects, where is the center of mass?

Answer 160

The center of mass is halfway between them

Question 161

For one very massive object and one object with a much smaller mass, where is the center of mass?

Answer 161

The center of mass for the system may lie within the central body

Question 162

How do stars help astronomers detect extrasolar planets?

Answer 162

When a star is orbited by a planet, each moves around their center of mass. This leads to a slight wobble in the star, pulled back and forth as the planet moves around it. The wobble can be detected by astronomers and used to detect extrasolar planets. The larger the planet and the closer it is to the star, the larger force it exerts. The 1st planets detected in this manner were very large and close. As astronomers have refined their techniques, smaller and more distant planets have been detected

Question 163

How did astronomers identify Neptune?

Answer 163

Scientists observing the orbit of Uranus noticed that it did not follow the smooth elliptical path they expected, but seemed to be tugged on by some more distant body. Using this evidence, they predicted and then confirmed the existence of another giant planet in the solar system, Neptune

Question 164

How can the motion of a satellite be described?

Answer 164

The motion of a satellite can be described by equating the universal gravitational force and the centripetal force that act on the satellite and solving for the velocity: V = sqrt(Gmp/r); “G” is the universal gravitation constant equal to “6.673 x 10^-11 N.m^2” and “mp”is the mass of the planet. The orbital radius, “r” is the sun of the altitude, “h”, of the satellite and the radius, “rp”, of the planet

Question 165

What does the equation for the velocity of a satellite depend on?

Answer 165

The equation for the velocity of a satellite depends on the mass of the planet and the radical height, but it does not depend on the mass of the satellite

Question 166

What can the acceleration of a satellite be derived from?

Answer 166

The acceleration of a satellite can also be derived by equating the universal gravitational force and the centripetal force. It can then be written in terms of the gravitational constant, “G”, and the mass of the planet, or in terms of the satellites velocity, “v”, and its orbital radius, “rp”: a = Gmp/r^2 or a = V^2/r

Question 167

What are the three main regions the orbit of a satellite can be classified into?

Answer 167

A low Earth orbit, A medium Earth orbit, and a high Earth orbit

Question 168

What position is a satellite in at a low Earth orbit?

Answer 168

A low Earth orbit has an orbital radius from about 6,500 to 8,400 km

Question 169

What position is a satellite in at a medium Earth orbit?

Answer 169

A medium Earth orbit has an orbital radius from about 8,400 km to about 42,000 km

Question 170

What position is a satellite in at a high Earth orbit?

Answer 170

A high Earth orbit has an orbital radius of about 42,000 km or higher

Question 171

What position is a satellite in at a polar orbit?

Answer 171

Some satellite orbits are also named according to their orientation. Polar orbits, for example, are oriented perpendicular to the equator so that a satellite on this orbit crosses over polar regions

Question 172

What position is a geosynchronous satellite placed in?

Answer 172

A geosynchronous satellite is placed into orbit so that its orbital speed is the same as the rotational speed of Earth. It circles Earth every 24 hrs. In order to maintain this speed, the orbital radius of the geosynchronous satellite must be 42,164 km

Question 173

What position is a communication satellite placed in?

Answer 173

Communication satellites are often put into geostationary orbits so that ground-based antennas can be direct toward the satellite without having to track its motion

Question 174

What is a comet? Why does it form a “tail”? What are their orbits like?

Answer 174

A comet is made up of an icy core surrounded by a cloud of dust and gases. As the comet approaches the sun’s heat, some of its ice begins to melt and evaporate, creating a long, wispy tail. For early astronomers, comets were a source of wonder and fear whenever they mysteriously appeared in the night sky. We know now that comets orbit the sun like the planets, but their orbits are far more eccentric. Some comets approach the sun every few years, while others have much longer orbital periods. Like other orbiting bodies within our solar system, comets have a wide range of eccentricities

Question 175

From Earth, what is the normal movement of the planets in the sky?

Answer 175

East to West

Question 176

What happens in retrograde, as seen from Earth?

Answer 176

Some of the wanderers—Mars, Jupiter, and Saturn—would occasionally slow down and move westward for a few months. This is called retrograde. Then they would slow again and revert back to their eastward progression across the sky.

Question 177

True or False: Different orbital motions can offer a clue to the different early history of orbiting objects.

Answer 177

True

Question 178

In what direction do moons orbit their planets?

Answer 178

On a smaller scale, most moons move in the direction of their planet’s rotation, but a few moons move in retrograde orbits around their planets.

Question 179

How does the Hubble Space Telescope produce clearer images than telescopes on Earth?

Answer 179

Images of distant galaxies and other astronomical objects produced by telescopes on Earth are limited. Light from the objects used to form the images is slightly scattered as it passes through the atmosphere. The Hubble Space Telescope avoids this problem because it is in orbit above Earth’s atmosphere. It is able to produce clear images of much more distant objects

Question 180

What is the position of the Hubble Space Telescope?

Answer 180

The telescope was placed in a low Earth orbit so that it would be easier to service and make equipment upgrades with space shuttle missions. Its altitude has sometimes been altered, but it is now orbiting at about 547 km (339 mi). Its orbital radius is about 6,925 km (4,302 mi) and its speed is about 27,300 km per hour (about 7.6 m per second)

Question 181

What is the relationship between velocity and orbital radius, when viewing a satellite?

Answer 181

The velocity is inversely proportional to the square root of the orbital radius, not proportional to it.