OrbitalMotionSE+(1)
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2019
Name: Ashlee Garcia Date: 1/22/2023
Student Exploration: Orbital Motion – Kepler’s Laws
Vocabulary:
astronomical unit, eccentricity, ellipse, force, gravity, Kepler’s first law, Kepler’s second law, Kepler’s third law, orbit, orbital radius, period, vector, velocity
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
1.
The orbit
of Halley’s Comet, shown at right, has an oval
shape. In which part of its orbit do you think Halley’s Comet travels fastest? Slowest? Mark these points on the diagram at right.
2.
How might a collision between Neptune and Halley’s Comet affect Neptune’s orbit?
It would not affect Neptune’s orbit
Gizmo Warm-up
The path of each planet around the Sun is determined by two factors: its current velocity
(speed and direction) and the force
of gravity
on the planet. You can manipulate both
of these factors as you investigate planetary orbits in the Orbital Motion – Kepler’s Laws Gizmo.
On the CONTROLS pane of the Gizmo, turn on Show trails
and check that Show vectors is on. Click Play
(
).
1.
What is the shape of the planet’s orbit? An eplise
2.
Watch the orbit over time. Does the orbit ever change, or is it stable? Stable 3.
Click Reset (
). Drag the tip of the purple arrow to shorten it and reduce the planet’s initial velocity. Click Play
. How does this affect the shape of the orbit? The eclipse becomes more elongated /flatter
Activity A: Shape of orbits
Get the Gizmo ready
:
Click Reset
.
Turn on Show grid
. Introduction:
The velocity of a planet is represented by an arrow called a vector
. The vector is described by two components: the i
component represents east-west speed and the j
component represents north-south speed. The unit of speed is kilometers per second (km/s).
2019
Question: How do we describe the shape of an orbit?
1.
Sketch
: The distance unit used here is the astronomical
unit
(AU), equal to the average Earth-Sun distance. Place the planet on the i
axis at r
= –3.00
i
AU. Move the velocity vector so that v
= -8.0
j
km/s (|
v
| = 8.00 km/s). The resulting vectors should look like the vectors in the image at right. (Vectors do not have to be exact.)
Click Play
, and then click Pause (
) after one revolution. Sketch the resulting orbit on the grid.
2.
Identify
: The shape of the orbit is an ellipse
, a type of
flattened circle. An ellipse has a center (C) and two points called foci
(F
1
and F
2
). If you picked any point on the ellipse, the sum of the distances to the foci is constant. For example, in the ellipse at left: a
1
+ a
2
= b
1
+ b
2
Turn on Show foci and center
. The center is represented by a red dot, and the foci are shown by two blue dots. What do you notice about the position of the Sun?
The sun is located at one of the foci.
3.
Experiment
: Try several other combinations of initial position and velocity. A.
What do you notice about the orbits? The orbits are either circular or elliptical shape.
B.
What do you notice about the position of the Sun? The sun remains at the center as one of the foci.
You have just demonstrated Kepler’s first law
, one of three laws discovered by the German astronomer Johannes Kepler (1571–1630). Kepler’s first law states that planets travel around the Sun in elliptical orbits with the Sun at one focus of the ellipse.
(Activity A continued on next page)
2019
Activity A (continued from previous page)
4.
Observe
: Use the Gizmo to create an orbit that is nearly circular. Then create an orbit that is
flattened. Observe the foci in each ellipse.
A.
What do you notice about the spacing of the foci when the ellipse is very round?
The closer the foci are, the more round the ellipse is.
B.
What do you notice about the spacing of the foci when the ellipse is very flat?
The foci are further apart.
5.
Calculate
: The eccentricity
of an ellipse is a number that describes the flatness of the ellipse. Eccentricity is equal to the distance between foci divided by the total width of the ellipse. There are no units for eccentricity. Click Reset
. Move the planet to r
= –5.00
i
AU (does not have to be exact) and drag the velocity vector to set the velocity close to –8.0
j
km/s. Click Play
, and then click Pause after one full revolution.
A.
What is the distance between the foci? 2
B.
What is the approximate width of the ellipse? 8
C.
What is the eccentricity of the ellipse? 0.25
D. Click Reset
, and change the initial velocity to –4.0
j
km/s. Click Play
. What is the eccentricity of this ellipse?
Distance between foci: 4.5 Width: 5.5 Eccentricity: 0.81
6.
Draw conclusions
: Think about the eccentricity and shape of each ellipse.
A.
What is the relationship between the eccentricity of an ellipse and its shape?
The lower the eccentricity the smaller the ellipse. The larger the eccentricity the larger the ellipse.
B.
What is the eccentricity of a circle? Explain. The eccentricity of a circle is zero because the distance between foci and the center are zero.
C.
What is the eccentricity of a completely flat ellipse? Explain. A completely flat ellipse would have an eccentricity closer to one because the foci and the center are further apart.
D.
The eccentricity of Earth’s orbit is 0.017. What can you infer about the shape of Earth’s orbit? Earth’s orbit is more circular in shape.
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Related Questions
1. using Newton’s Law of Universal Gravitation and some kinematics calculation we can calculate the mass of the planet. For this, use this equation in the image:
Given:
- vmax = 1.5 m/s
- Pstar = 3.5 days
- Mstar = 1.148 Msun, where Msun = 1.98847×1030 kg. This calculation is not shown.
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Astronomy help please
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10. Match Kepler Laws with the correct description.
Kepler's First Law
Kepler's Second Law Kepler's Third Lav
A planet sweeps out
equal areas in equal
time frames as it
orbits the Sun.
Orbits are ellipses
with the Sun at a
focus.
The orbital period is
related to the average
distance from the
Sun.
20 points
arrow_forward
2. The generalized Kepler orbit is given in polar coordinates r($)=c/(1+e cos()), where c is a constant and
& is the eccentricity of the orbit. Rewrite this in Cartesian coordinates for -1 and show that the orbit is a
parabola, y² = A + B x, where A and B are constants. Define constants A and B via constant c.
arrow_forward
please don't reject, this is not about astronomy*
How was it possible for the Copernican model of the universe to account for the complicated motion of the planets?
PLEASE DO A CLEAR AND UNDERSTANDABLE ANSWER.
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3
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7
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Astronomy help please
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I hope you answer this:)
1. Ancient civilizations observed and kept track of daily movement of heavenly bodies. Which one is NOT the reason for this?
a. navigation purposes
b. time keeping
c. annual cultural cycles
d. agricultural cycles
2. What Kepler's Law of Planetary Motion is related to the Newton's Law of Motion based from the statement below:
The statement:
"Since the planets move on ellipses they are continually accelerating."
a. Law of Ellipses and Law of Acceleration
b. Law of Ellipses and Law of Inertia
c. Law of Equal Areas and Law of Interaction
d. Law of Period and Law of Inertia
e. Law of Period and Law of Acceleration
3. Edwi Hubble proposed a way to organize galaxies in 1920. How are galaxies classified?
a. color of stars
b. shape of galaxy
c. age of stars
d. composition of stars
e. diameter of galaxy
4. Find the magnifying power (M) and the length (L) of a simple telescope with 30-inches focal length of the objective and 2 inches focal length of the eyepiece.…
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Question 1 (Total: 30 points)
a. What is a repeat ground-track orbit?
b. Explain why repeat ground-track and Sun-synchronous orbits are typically used for Earth observation missions.
c. The constraint for a Sun-synchronous and repeat ground-track orbit is given by T = 286, 400, where I is the orbital period in seconds, m the number of days and k
the number of revolutions. Explain why this is, in fact, a constraint on the semi-major axis of the orbit.
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number 4 please
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41. Suppose the orbit of a planet is an ellipse of eccentricity e = c/a
and period T (Figure 2). Use Kepler's Second Law to show that the
time required to travel from A' to B' is equal to
T
B
b
Sun
A'
a
(c, 0)
B'
FIGURE 2
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This is a practice questions for my class. What would this sketch look like? Help me figure it out
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Kepler's laws of planetary motion
6. Halley's Comet has an orbital eccentricity of 0.967 and a perihelion distance of 89,000,000 km.
(a) Find the orbital period.
(b) Find the comet's speed at perihelion and aphelion.
7. Show that the orbital period of a satellite close to the surface of a spherical object depends on the
mean density of the object, but not on its size. Find this period for the Earth (density 5.51 g cm-3).
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Ma
years, what is
2. Saturn has an orbital period of 29.46 years, and its average distance to
the sun is 9.54 A.U. If Venus has an orbital period of 0.62
its average distance to the sun in astronomical units (A.U.)?
M
stance
A.U.,
Conceptual Physics Reading and Study Workbook Chapter 14
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The planet Mercury takes 0.24 sidereal years to go around the sun. What is
the distance from the center of Mercury to the center of the sun?
(Remember 1 sidereal year = 1 revolution) *
Your answer
The Planet Jupiter's mean orbital radius is 5.2025 AU's. What is the period
of Jupiter in Earth years?
Your answer
There is belt of asteroids between Mars and Jupiter which circles the
"inside" of our solar system. This "Asteroid Belt" has a mean radius from
the Sun of 2.6 AU's. How long does it take for one asteroid in the belt to
travel around the Sun once? *
Your answer
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1)If the Moon were twice the distance from Earth than it currently is, the amount of time it would take to go around Earth would be roughly (the current orbital period of the Moon is four weeks)
Group of answer choices
A.eight weeks.
B.11 weeks.
C.six weeks.
D.88 weeks.
2)A satellite is in orbit around a planet. The orbital radius is 46 km and the gravitational acceleration at that height is 7.09 ms-2 . What is the satellite's orbital speed in m/s? (with step)
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The Universal Law of Gravitation
a. How does halving the distance between two objects affect the gravitational force between them?
b. Suppose the Sun was somehow replaced by a star with five times as much mass. What would happen to the gravitational force between the Earth and the Sun?
c. How long would the Earth year last in this last case? (hint: Newton’s version of Kepler’s 3rd Law)
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1) Calculate the tidal force (the difference in gravitational force from right to left side or G(R) - G(L) ) from a person sitting next to you (approximately 1 meter away). You will need to make some estimations on mass and size of a normal person.
2) Compare the tidal force on a person from the Moon and a person standing nearby (the answers to the previous two questions). Which is greater and by how much?
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please don't reject, this is not about astronomy*
How was it possible for the Copernican model of the universe to account for the complicated motion of the planets?
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Predict the time for Mars to orbit around the Sun if the orbital distance of Mars is1.52 times of Earth`s orbital distance. Note: Earth`s orbital distance (T1) = 1, and Earth`s orbital period (a1) = 1 year. Express your answer in the unit year.
pls help me thankyou
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8) The figure shows a planet traveling in a clockwise
direction on an elliptical path around a star located at
one focus of the ellipse. When the planet is at point A,
describe what is happening to the speed of the planet.
(Speeding up, remaining the same, slowing down).
Explain what principle you use to make answer this
question.
travels
clockwise
STAR
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1. Which planetary model allows a scientist to predict the exact positions of the planets in the night sky over many years?
2. Which object orbits Earth in both the Earth – centered (geocentric) and Sun – centered (heliocentric) models of our solar system?
3. What is the actual shape of the Earth’s orbit around the Sun?
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Johannes Kepler worked as an assistant to the observatory of Brahe at the age of 27.
Brahe collected astronomical observations, which were passed into Kepler, on his death.
Among the significant contributions of Brahe:
1. His observations on the planetary motion of Mars were used by later astronomers, including
Kepler to construct the present model of the solar system.
2. In 1572, he observed supernova as a star that appeared suddenly, became visible for 18
months before it faded from view. Nowadays, supernova is called an exploding star.
3. In 1577, he observed a comet by measuring its parallax. His claim contradicted the idea of
Aristotle that comets are "gases burning in the atmosphere." By measuring the parallax for
the comet, he was able to show that the comet was further away than the Moon.
4. His findings that stars do not have parallax, he concluded that either: (a). the earth was
motionless at the center of the universe; or (b). the stars were so far away that their parallax…
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Sun midway between the orbits of Mars and Jupiter.
Determine, to three significant digits,
(a) the period of the asteroid's orbit in Earth
(b) the asteroid's speed
years
35. Scientists want to place a satellite in a circular orbit
around Neptune with an orbital period of 24.0 h.
(a) Determine Kepler's third-law constant for
Neptune using Neptune's mass.
(b) What distance from Neptune's centre must the
satellite be to maintain its circular orbit?
(c) What is the altitude of this orbit in kilometres?
1:1
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20) Planet Dwovy circles its star at a distance of 8.75 × 109 km once every 325 Earth years. The planet Spitnik circles the same star at a distance of 76.1 × 109 km. What is the orbital period of Spitnik in Earth years?
a) 65,800 years
b) 2570 years
c) 0.004 years
d) 8336 years
e) 257 years
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1. How does the speed of revolution depend on its distance from the sun?
2. How were tycho brahe's observaions used by kepler to produce his laws of planetary motion?
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4
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Find time period only
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Directions: Choose the letter that corresponds to the best answer.
1. He is the scientist or philosopher responsible for the theory that proposed that planets, as well as the sun and the moon, moved in a circular motion around the earth.A. Claudius Ptolemy B. Copernicus C. Galileo D. Kepler
2. The following statements are reasons why the geocentric theory was believed or remained unquestioned for more than one (1) millennium, EXCEPT:A. This belief was aligned with the teachings of the church; thus cannot be questioned.B. Majority of the famous philosophers during that period in history supported the idea.C. There was no evidence to prove otherwise due to lack of astronomical instruments.D. People were busy with politics and economics hence it is the least of their concern.
3. Why were most intellectual ideas controversial?A. They challenge the long-held belief and the established institutions.B. They resulted to revolutions and public outcry against governments.C. Many of these ideas…
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Related Questions
- 1. using Newton’s Law of Universal Gravitation and some kinematics calculation we can calculate the mass of the planet. For this, use this equation in the image: Given: - vmax = 1.5 m/s - Pstar = 3.5 days - Mstar = 1.148 Msun, where Msun = 1.98847×1030 kg. This calculation is not shown.arrow_forwardAstronomy help pleasearrow_forward10. Match Kepler Laws with the correct description. Kepler's First Law Kepler's Second Law Kepler's Third Lav A planet sweeps out equal areas in equal time frames as it orbits the Sun. Orbits are ellipses with the Sun at a focus. The orbital period is related to the average distance from the Sun. 20 pointsarrow_forward
- 2. The generalized Kepler orbit is given in polar coordinates r($)=c/(1+e cos()), where c is a constant and & is the eccentricity of the orbit. Rewrite this in Cartesian coordinates for -1 and show that the orbit is a parabola, y² = A + B x, where A and B are constants. Define constants A and B via constant c.arrow_forwardplease don't reject, this is not about astronomy* How was it possible for the Copernican model of the universe to account for the complicated motion of the planets? PLEASE DO A CLEAR AND UNDERSTANDABLE ANSWER.arrow_forward3arrow_forward
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- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning