Astronomy: Orbital Motion (Unit 3) Flashcards
1
Q
Who was Aristotle?
A
Aristotle was a scientists and philosopher, who lived from 384 B.C. to 322 B.C.
2
Q
What is Aristotle credited for?
A
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
3
Q
Why did no one question Aristotle’s geocentric model?
A
Because he was so respected
4
Q
Geocentric Definition
A
Centered on Earth
5
Q
According to Aristotle, where were the sun and planets located?
A
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
6
Q
What was correct about Aristotle’s model? Where were the stars located in his model?
A
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
7
Q
What were Aristotle’s arguments for the validity of his model?
A
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
8
Q
Stellar Parallax Definition
A
The appearance of movement of a star as a result of the Earth moving around the sun
9
Q
What is the true reason why Aristotle did not detect stellar parallax, that we now know today?
A
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
10
Q
What other reasons, other than lack of stellar parallax, did Aristotle have to prove the accuracy of his model?
A
— 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
11
Q
What did Claudius Ptolemy do in 140 BCE? What was observed about the movement of the planets at the time?
A
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
12
Q
What did Ptolemy add in his model to explain the planets’ appearances of slowing down and then moving forward again?
A
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
13
Q
How did Ptolemy’s model, while incorrect, help astronomers?
A
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
14
Q
Why was the Ptolemaic model the most accurate of its time?
A
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
15
Q
True or False: An Earth-centered model represents the Geocentric theory
A
True
16
Q
Why did Ptolemy’s model stay?
A
Ptolemy’s model stayed since it allowed astronomers to make accurate predictions given the limitations of technology of the time
17
Q
What simple instrument did Ptolemy use to observe the planets?
A
Ptolemy observed the planets using a simple instrument now known as Ptolemy’s ruler
18
Q
What did early astronomers use to predict planetary motion?
A
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
19
Q
What does the astrolabe consist of?
A
The astrolabe has two nested circles. The inner circle represents the position of a planet on its epicycle
20
Q
What was an early “computer” that Ptolemy used?
A
The astrolabe
21
Q
What was the armillary sphere?
A
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
22
Q
What was the most complex of Ptolemy’s instruments?
A
The armillary sphere
23
Q
Why was Aristotle’s ideas appealing to the people of the time?
A
Aristotle’s idea of perfect circles, and his arguments for a stationary Earth, fit with religious beliefs at the time
24
Q
What happened to scientific progress in Europe after the development of the geocentric model?
A
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
25
What are some ideas of why people used models in ancient times, and even now?
From modern day to ancient times, scientists used models, for it helped them visualize data and many people could not read back then
26
How did Copernicus learn of the critiques of Ptolemy’s model of the solar system?
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
27
What did Copernicus believe was the problem with Ptolemy’s model?
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
28
Heliocentric Definition
Centered on the sun
29
How long did people follow the geocentric model?
More than 2,000 years
30
Why was Copernicus troubled with the geocentric model?
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
31
Retrograde Motion Definition
The apparent backward motion of an object resulting from the circular motions of the viewer and the object
32
What was Copernicus’ critique of Ptolemy’s explanation for retrograde motion in his model?
Copernicus believed Ptolemy’s explanation for retrograde motion in his model was too complicated to occur naturally
33
Why did Copernicus believe a heliocentric model explained retrograde motion?
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
34
What did Copernicus believe about Earth that explained retrograde motion and more?
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
35
What was Copernicus’ process of making and publishing his book? Why did he wait so long?
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
36
What did a Roman Catholic Church do with Copernicus’ book in 1616?
In 1616, A Roman Catholic Church banned Copernicus’ book
37
What were some of the problems with Copernicus’ model?
The orbits of the planets are slightly more elliptical than circular, and the sun is not the center of the universe
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?
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
39
Why was Copernicus not able to prove his model was correct?
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
40
What did Copernicus’ model offend?
It offend both scientific and religious beliefs at the time
41
How many planets were known at the time of Copernicus?
6; Mercury, Venus, Earth, Mars, Jupiter, and Saturn
42
Where did Copernicus’ model state where the stars were?
Copernicus stated that the stars were fixed on an immobile sphere found beyond Saturn
43
What did Copernicus do in 1543?
He published his model of the solar system in Latin
44
Why do we have a leap year, and day, and what do they show?
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
45
What did the Ancient Greeks identify as planets? What did they know about the moon? How about the sun?
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
46
What did the Ancient Greeks believe about the orbit of the planets?
The ancient Greeks believed that the planets had circular orbits
47
What could the geocentric model not explain about Mercury and Venus?
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
48
What have we added to the heliocentric model in modern times?
In modern times, we have added elliptical orbits, the planets of Uranus and Neptune, and Jupiter’s moons
49
Which astronomers helped develop the heliocentric model?
Copernicus, Kepler, Galileo, and Newton developed the heliocentric model
50
What did Copernicus observe about a planets speed when farther or closer to the Sun?
Copernicus made observations showing that a planet’s speed increased as it neared the sun and decreased as it moved farther away
51
What does Kepler’s Second Law of Motion state?
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”
52
What is an example of Kepler’s Second Law of Motion (only for review)?
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
53
How did Kepler learn of the planets? From who? What planet did he observe?
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
54
What did the discovery of Kepler’s Second Law of Motion lead to?
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
55
How long ago did Kepler develop his laws of motion? What tools did he use?
Kepler developed his laws of motion 400 years ago without telescopes
56
Despite the fact that planets sweep out equal areas in equal times, what varies?
Even though planets sweep out equal areas in equal times in their orbits around the sun, the distance the planet moves varies
57
According to Kepler’s Second Law of Motion, what proves that the closer a planet is to the sun, the faster it is?
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
58
During which month does the Earth move the fastest? Why?
During the month of January, the Earth moves the fastest for it is when Earth is closet to the sun
59
During which month does Earth move the slowest? Why?
During the month of July, the Earth moves the slowest for it is when Earth is farthest from the sun
60
Although models make it seem like Earth’s orbit is highly elliptical, what is Earth’s true orbit like?
Earth’s actual orbit is almost circular
61
What does a decreases or increase in the sun’s gravitational attraction change about a planet?
A decrease or increase in the sun’s gravitational atttarction changes only the shape of the orbit, not the speed of the planet
62
What changes the speed of a planet along its orbit, according to Kepler’s Second Law of Motion?
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
63
Inertia Definition
The tendency of an object to move along a straight path at a constant speed
64
What relationship does Kepler’s Second Law of Motion describe?
Kepler’s Second Law of Motion describes the relationship between a planets’s distance from the sun and the planet’s velocity
65
What is Kepler’s full name?
Johannes Kepler
66
Between which two years did Kepler develop his series of laws? When was the first one made?
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
67
Elliptical Definition
Similar to an oval shape
68
How did Kepler conclude that planets’ had an elliptical orbit, through his data on Mars?
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
69
What is a perihelion?
A perihelion is the point on a planet’s orbit that is closest to the sun
70
What is an aphelion?
An aphelion is the point on the orbit that is farthest from the sun
71
What does Kepler’s First Law of Planetray Motion state?
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
72
What are the major and minor axes? What are they divided into?
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
73
What are the foci on the major axis?
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
74
For all of the planets, how would we describe their orbits, despite the un-proportional models?
For all the planets, however, the orbit is very close to circular
75
Which planet has the most elliptical orbit?
Mercury
76
How elliptical are the orbits of other objects that move around the sun, that are not planets?
Other objects moving around the sun, such as some asteroids and comets, have orbits that are highly elliptical
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?
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
78
What does an almost-circular orbit prevent on Earth?
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
79
What does Kepler’s Third Law of Planetary Motion state?
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
80
What is the equation that represents Kepler’s Third Law of Planetary Motion?
T^2 ∝ a^3
81
Orbital Period Definition
Time to complete one orbit
82
How is the equation stated in Kepler’s Third Law of Planetary Motion modified for circular orbits?
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
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?
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
84
In what unit of measurement is the orbital period often expressed in? How about the radius?
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
85
Astronomical Unit Definition
The average distance from the sun to Earth
86
How can Kepler’s Third Law of Planetary Motion be simplified for the planets in our solar system?
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
87
True or False: Kepler’s third law of planetary motion applies to all objects orbiting a central body
True
88
What could a geocentric model not explain about Jupiter and Mars?
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.
89
What was Copernicus’s model of the solar system? What was the revolution time of each planet on the model?
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.
90
What is Gravity? On Earth, why do we perceive gravity as a downward force?
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
91
What did Newton realize about gravity?
Newton realized that the force of gravity applied to everything — in other words, this force is universal
92
What is gravity by Newton’s definition?
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
93
Universal Definition
Applying to all objects
94
The works from which scientists helped Newton develop his theory of universal gravitation?
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
95
What did Tycho Brahe do in the 1570s that supported Copernicus’ theory?
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
96
What did Newton want to know about the planets?
Newton wanted to know why the planets orbit around the sun, which his theory of universal gravitation helps answer
97
At what rate do objects accelerate toward Earth due to gravity?
Earth’s gravity causes all objects, all other factors being equal, to accelerate toward Earth at a rate of 9.8 m/s2
98
Is there air resistance in a vacuum?
In a vacuum, there is no air resistance
99
When Newton developed his theory of universal gravitation, what was he looking for specifically?
Newton was specifically looking for a simple explanation for why the solar system seems to follow Kepler’s 3 laws of planetary motion
100
How did Hooke help Newton develop his theory of universal gravitation?
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
101
What is the formula to solve for the gravitational force between two objects?
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
102
What does the gravitational force equal (verbal form of equation)?
Force equals the gravitational constant times the product of the masses of the two objects divided by the square of the distance between them
103
True or False: all objects exert gravity on each other
True
104
Who contributed the most to the development of Newton’s theory of universal gravitation?
Robert Hooke
105
What was Robert Hooke’s contribution to the development of the law of universal gravitation?
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
106
What relationship did Newton develop? Why are the terms “m1” and “m2” included in the equation for gravity?
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
107
Why is the term “r” squared in the equation for gravity?
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
108
What is a constant in a scientific equation?
A constant is a set number that is always used to complete the equation
109
How did Newton prove that gravity is universal through his calculation?
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
110
How does gravitational force in Newtons compare to mass in kilograms?
Gravitational force in Newtons is roughly 10 (exactly 9.8) times the mass in kg
111
What does Newton’s first law of motion state? How did it provide planetary clues?
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’
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
True
113
What did the work of Kepler and Newton help scientists explain? What is eccentricity?
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
114
How does the eccentricity compare between a circular orbit and an elliptical orbit? What affects eccentricity?
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
115
At what eccentricity does an object lose the ability to maintain a closed orbit?
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
116
What does the eccentricity of an elliptical orbit depend on?
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
117
What is the eccentricity of the International Space Station (ISS)? What does this allow?
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
118
What are the eccentricities of Mercury, Venus, Earth, and Mars?
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
119
How have scientists measured the eccentricity of exoplanets?
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
120
Exoplanet Definition
Planet in a solar system other than ours
121
What type of orbit does an eccentric measurement of 1 form? How about an eccentric measurement greater than 1?
An eccentric measurement of 1 forms a parabolic orbit. An eccentric measurement greater than 1 forms a hyperbolic orbit
122
What causes Mars to experience dramatic seasonal changes?
Mars’ fairly high eccentric orbit combined with the tilt of its axis causes it to experience dramatic seasonal changes, greater than Earth’s
123
What is the eccentricity of Jupiter?
0.049
124
What is the eccentricity of Saturn?
0.057
125
What is the eccentricity of Uranus? What makes Uranus different from other planets, in terms of rotation?
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
126
What is the eccentricity of Neptune?
0.0011
127
What is the eccentricity of Pluto?
0.2488; higher than any planet in the solar system
128
What is the eccentricity of the orbits of comets?
Comets tend to have extremely eccentric orbits. Halley’s Comet, for instance, has an eccentricity value of 0.97, a near perfect parabolic trajectory
129
What is the eccentricity of the orbits of asteroids?
Asteroids have an average eccentricity of about 0.17, but some have highly elongated elliptical orbits
130
Asteroid Definition
Small, rocky body orbiting the sun
131
Which moon in the solar system has the highest eccentricity?
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
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What did Brahe do that was remarkable?
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
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Which astronomers helped Kepler develop his three laws of orbital motion?
Kepler was able to use the work of prior astronomers, such as Ptolemy, Copernicus, and Brahe
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How long, in Earth years, does it take for Mercury to complete an orbit?
1/5 of an Earth year
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How long, in Earth years, does it take Saturn to complete one orbit?
29 1/2 Earth years
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What is the difference of Earth’s distance at aphelion and perihelion?
3 million miles
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How are Newton’s and Kepler’s findings intertwined?
Patterns in Earth’s movements are identified in Kepler’s laws, and Newton discovered why these patterns occur
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Orbit Definition
Path of an object moving around a central attractive mass
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Gravitational Force Definition
Attractive force between 2 objects due to their mass
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How does distance and gravity affect speed?
As objects draw closer together, the force between them increases, increasing speed. As objects move apart, the force between them decreases, decreasing speed
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What does the solar system consist of?
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
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What does planet mean in Greek?
Wanderer
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Where must astronomer’s observations be made?
From Earth
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What is the difference between actual and apparent retrograde motion?
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
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What are the three pathways an object orbiting a massive central body can follow?
Spiral, hyperbola, and ellipse
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What happens in a spiral orbits?
In a spiral orbit, the object gradually moves inward until it falls into the central body, such as Comet Shoemaker-Levy spiraling into Jupiter
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What happens in a hyperbola orbit?
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
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What happens in a stable orbit? What type of orbit does it create?
In a stable orbit, the orbiting object’s momentum and the force of gravity are perfectly balanced, resulting in an ellipse
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True or False: a circle is a special case of an ellipse
True
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What does the orbital path an object follows depend on?
The orbital path an object follows depends on its mass, initial speed, and initial direction of motion
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What can acceleration do to an object? What causes this?
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
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What does the amount of acceleration depend on? What is its formula?
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
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Acceleration Definition
Change in an object’s motion
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What are the components of the equation: “F = Gm1m2/r^2”?
“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
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What are the components of the equation: “a = F/m2”?
“a” is the acceleration, “F” is the force, and “m2” is the mass of the orbiting body
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What does the speed of an object in orbit depend on?
The speed of an object in orbit depends on its distance from the central body and the mass of the central body
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Combined with Newton’s laws of motion, how can one find the acceleration of an object in orbit?
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”
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What is the center of a circular orbit?
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
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In the Earth-moon system, the point around which both objects orbit is located where?
Within Earth’s mantle, not at its exact center
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For two identical objects, where is the center of mass?
The center of mass is halfway between them
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For one very massive object and one object with a much smaller mass, where is the center of mass?
The center of mass for the system may lie within the central body
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How do stars help astronomers detect extrasolar planets?
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
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How did astronomers identify Neptune?
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
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How can the motion of a satellite be described?
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
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What does the equation for the velocity of a satellite depend on?
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
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What can the acceleration of a satellite be derived from?
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
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What are the three main regions the orbit of a satellite can be classified into?
A low Earth orbit, A medium Earth orbit, and a high Earth orbit
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What position is a satellite in at a low Earth orbit?
A low Earth orbit has an orbital radius from about 6,500 to 8,400 km
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What position is a satellite in at a medium Earth orbit?
A medium Earth orbit has an orbital radius from about 8,400 km to about 42,000 km
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What position is a satellite in at a high Earth orbit?
A high Earth orbit has an orbital radius of about 42,000 km or higher
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What position is a satellite in at a polar orbit?
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
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What position is a geosynchronous satellite placed in?
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
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What position is a communication satellite placed in?
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
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What is a comet? Why does it form a “tail”? What are their orbits like?
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
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From Earth, what is the normal movement of the planets in the sky?
East to West
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What happens in retrograde, as seen from Earth?
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.
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True or False: Different orbital motions can offer a clue to the different early history of orbiting objects.
True
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In what direction do moons orbit their planets?
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.
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How does the Hubble Space Telescope produce clearer images than telescopes on Earth?
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
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What is the position of the Hubble Space Telescope?
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)
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What is the relationship between velocity and orbital radius, when viewing a satellite?
The velocity is inversely proportional to the square root of the orbital radius, not proportional to it.
