Student Exploration: Orbital Motion – Kepler’s
Laws (ANSWER KEY)
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Student Exploration: Orbital Motion – Kepler’s Laws
Vocabulary: astronomical unit, A unit of measurement that is equal to 149.6 million km.
eccentricity, Measurement of how flat an orbit is.
ellipse, Flattened circle
force, action that causes an object to shift
gravity, force that acts on other bodies to pull them in.
Kepler’s first law, Planets travel around the sun in elliptical orbits.
Kepler’s second law, Planets accelerate when they near the sun, and decelerate when the move
away from it.
Kepler’s third law, Cube of planets orbital radius is proportional to its period.
orbit, curved revolution of object around a planet, moon, or star.
orbital radius, the average orbit distance from the sun
period, Length of time
vector, A quantity.
velocity, speed and direction
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
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.
How might a collision between Neptune and Halley’s Comet 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 ().
What is the shape of the planet’s orbit?
This study source was downloaded by 100000835361505 from CourseHero.com on 01-28-2022 06:44:32 GMT -06:00
https://www.coursehero.com/file/42331621/Student-Exploration-Orbital-Motion-Keplers-Laws-ANSWER-KEYdocx/
, Watch the orbit over time. Does the orbit ever change, or is it stable?
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?
Activity A:
Get the Gizmo ready:
Click Reset.
Shape of orbits 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).
Question: How do we describe the shape of an orbit?
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 = –3.00i AU. Move the velocity vector so that v =
-8.0j 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.
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 (F1 and F2). 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:
a1 + a2 = b1 + b2
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?
Experiment: Try several other combinations of initial position and velocity.
What do you notice about the orbits
What do you notice about the position of the Sun?
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)
Activity A (continued from previous page)
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.
This study source was downloaded by 100000835361505 from CourseHero.com on 01-28-2022 06:44:32 GMT -06:00
https://www.coursehero.com/file/42331621/Student-Exploration-Orbital-Motion-Keplers-Laws-ANSWER-KEYdocx/
Laws (ANSWER KEY)
Download
Student Exploration: Orbital Motion – Kepler’s Laws
Vocabulary: astronomical unit, A unit of measurement that is equal to 149.6 million km.
eccentricity, Measurement of how flat an orbit is.
ellipse, Flattened circle
force, action that causes an object to shift
gravity, force that acts on other bodies to pull them in.
Kepler’s first law, Planets travel around the sun in elliptical orbits.
Kepler’s second law, Planets accelerate when they near the sun, and decelerate when the move
away from it.
Kepler’s third law, Cube of planets orbital radius is proportional to its period.
orbit, curved revolution of object around a planet, moon, or star.
orbital radius, the average orbit distance from the sun
period, Length of time
vector, A quantity.
velocity, speed and direction
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
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.
How might a collision between Neptune and Halley’s Comet 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 ().
What is the shape of the planet’s orbit?
This study source was downloaded by 100000835361505 from CourseHero.com on 01-28-2022 06:44:32 GMT -06:00
https://www.coursehero.com/file/42331621/Student-Exploration-Orbital-Motion-Keplers-Laws-ANSWER-KEYdocx/
, Watch the orbit over time. Does the orbit ever change, or is it stable?
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?
Activity A:
Get the Gizmo ready:
Click Reset.
Shape of orbits 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).
Question: How do we describe the shape of an orbit?
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 = –3.00i AU. Move the velocity vector so that v =
-8.0j 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.
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 (F1 and F2). 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:
a1 + a2 = b1 + b2
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?
Experiment: Try several other combinations of initial position and velocity.
What do you notice about the orbits
What do you notice about the position of the Sun?
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)
Activity A (continued from previous page)
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.
This study source was downloaded by 100000835361505 from CourseHero.com on 01-28-2022 06:44:32 GMT -06:00
https://www.coursehero.com/file/42331621/Student-Exploration-Orbital-Motion-Keplers-Laws-ANSWER-KEYdocx/
