Orbital Motion – Kepler’s Laws Answer Key
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...
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.)
[Note: The purpose of these questions is to activate prior knowledge and get students
thinking. Students are not expected to know the answers to the Prior Knowledge Questions.]
1. The orbit of Halley’s Comet, shown at right, oval
has an shape. In which part of its orbit do you
think Halley’s Comet travels fastest? Slowest?n
Mark these points o the diagram at right.
Slowest
2. How might a collision between Neptune and
Halley’s Comet affect Neptune’s orbit?
Answers will vary. [A collision would probably causea Fastest
small change in Neptune’s orbit, but would not havea
drastic effect on Neptune’s orbit because Neptune
is much more massive than Halley’s Comet.]
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 oval
2. Watch the orbit over time. Does the orbit ever change, or is it stable? The orbit is
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 orbit becomes smaller and more flattened.
, Get the Gizmo ready:
Activity A:
• 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?
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 = –3.00i 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.
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 (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?
The Sun is located at one of the foci of the ellipse.
3. Experiment: Try several other combinations of initial position and velocity.
A. What do you notice about the orbits?
Sample answer: The orbits all have an elliptical shape.
B. What do you notice about the position of the Sun?
The Sun is always located at one focus of the ellipse.
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
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