Mr. Gord
Astronomy
Kepler’s 3 Planetary Laws
Total Possible Points = 20
PURPOSE: To demonstrate Kepler's 3 Laws of Planetary Motion.
BACKGROUND
One of the greatest scientific achievements of all time was Kepler's 1609 discovery of the true shape of the planets' paths
around the sun, stated as Kepler's first law: A planet orbits the sun in the an ellipse, with the sun located at one focus.
Kepler's second law , also called the "law of equal areas", states that A line drawn from the Sun to a planet sweeps out
equal areas of space in equal amounts of time.
Kepler's third law of planetary motion states: A planet’s orbital period is proportional to its average distance from the
sun. For example, Mercury, the closest planet to the sun at an average distance of 0.4 AUs, takes only 88 earth days to
travel once around the sun. Pluto, previously the farthest (former) planet from the sun at an average distance of 40 AUs,
takes 248 earth years to travel once around the sun!
Kepler's laws are obeyed throughout the universe. They are obeyed by each of the planets, comets, and asteroids that
revolve around the Sun. Kepler's laws are also obeyed by the moon and man-made satellites orbiting the Earth. By
discovering that orbiting bodies move in an ellipse, and further discovering the ideas represented by his 2nd and 3rd laws,
Kepler, in the early 1600s, both built on Copernicus' radical introduction of a sun-centered solar system and laid the
foundation on which Isaac Newton formed his historic laws of gravitation. Kepler was, in a scientific historical sense,
“Da Man!”
MATERIALS: ruler, calculator, string???
PROCEDURE
1. The accompanying diagram (last page) shows the path of an asteroid (irregular shaped rock, less than 600 miles
across) in its orbit around the sun. The numbers, increasing counter-clockwise show the asteroid's position in
one-year time intervals. The asteroid, therefore, completes one orbit around the sun every 12 Earth years.
2. Measure the distance between the sun and the asteroid at each numbered position, accurately, to the nearest 0.1
cm. Record these sun-to-asteroid distances in Table 1 in the DATA section.
3. To convert the distance on paper in centimeters to actual distances in space in astronomical units (AU’s),
multiply the sun-to-asteroid distances in centimeters by 0.7. Record these values in Table 1.
4. The Sun-to-asteroid distance is the line drawn from the Sun to the asteroid. This line sweeps out a certain area
of space in a given amount of time. Look on the orbit diagram. The shaded area represents the area swept out
during the first earth-year (Year 0 to Year 1). A simple way of estimating this area is to simply count the number
of squares that are covered by one year's sweep. If the square is 1/2 or more, then count it, if it is less than 1/2
then do not include it your count total. To ease this burden and share the counting, the class will be divided into
six groups, each being responsible for two sections. Record the results in Table 2.
5. Using a curved object – such as a piece of paper, piece of string, etc. – measure as accurately as possible the
distance on paper that the asteroid travels during each one-year interval. Record these distances, to the nearest
0.1 cm, in Table 2.
6. Convert your lengths from cm on paper to miles in space, by multiplying your length in cm by 65,100,000.
This Answer is the number of miles the asteroid actually travels in space in a one-year period. Record these
values in Table 2.
7. To find the average speed of the asteroid during each 1-year period, divide the distance (results from step 6) by
the number of hours in a year. Record these average speeds, in miles/hour, in Table 2.
PART A
Astrophysicist: _____________________
DATA & CALCULATIONS
Table 1
Year Number
or Asteroid
Position
Sun-to-Asteroid
Distance
(cm on paper)
Sun-to-Asteroid Distance
(AU’s in space)
0
1
2
3
4
5
6
7
8
9
10
11
Table 2
Asteroid
Moved
From...
Area Swept out
(# squares)
Distance Asteroid
Travels
(cm on paper)
Distance Asteroid
Travels in 1 year
(miles in space)
Average Speed
of Asteroid
(miles per hour)
0–1
1–2
2–3
3–4
4–5
5–6
6–7
7–8
8–9
9 – 10
10 – 11
11 – 0 (12)
1
GRAPHS
1. On Graph 1, plot the Asteroid-to-Sun distances (from Table 1 – in AUs) vs. the Year Number or Asteroid
Position (0, 1, 2, 3, ...). Make sure you draw the dots dark enough to be easily visible. Smoothly connect the
dots with a line or curve.
Graph 1: Sun-to-Asteroid Distance
Sun-Asteroid Distance (AU's)
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
Year Number
8
9
10
11
12
2. On Graph 2, plot the area swept out by the line connecting the Sun and asteroid (in squares) vs. the Year
Number (0-1, 1-2, 2-3, ...). Smoothly connect the dots with a line or curve. Note how the value of area changes
(or better yet, doesn't change) throughout each one-year time intervals.
600
Graph 2: Area Swept
Area Swept ( # of Squares)
500
400
300
200
100
0
0-1
1- 2
2-3
3-4
4-5
5-6
6-7
7-8
Year Number
8-9
9-10 10-11 11-12
2
Astronomer: _______________________
3. On Graph 3, plot the average speed of the asteroid (in miles/hour) vs. the Year (0-1, 1-2, 2-3, ...). For this final
graph you need to label the y-axis appropriately. Smoothly connect the dots with a line or curve. Note at what
position the asteroid is at perihelion and where it is at aphelion. Identify perihelion and aphelion on graph!!
Graph 3: Average Speed
0-1
1- 2
2-3
3-4
4-5
5-6
6-7
7-8
Year Number
8-9
9-10 10-11 11-12
Get Mr. Gord’s Signature: _____________________ Do not go any further until you have it checked by Mr. Gord (this
is worth 10 POINTS!)
3
PART B
Astrophysicist: _____________________
QUESTIONS – Worth 10 More POINTS!!
1. What is the asteroid's maximum distance from the sun, in AU's? _________________
2. At this point, the asteroid is said to be at _____________________ . (this is the term that defines the
farthest point an orbiting body is from the sun)
3. What is the asteroid's minimum distance from the sun, in AU's? _________________
4. At this point, the asteroid is said to be at _____________________ . (this is the term that describes
defines the closest point an orbiting body is to the sun)
5. Calculate the asteroid's average distance from the sun, by averaging the aphelion and perihelion values.
Show work (equation you used):
6. Observe the graphs. State the relationship between the asteroid's distance from the sun and its speed (in
other words, how does distance from sun affect the asteroid's speed)?
______________________________________________________________________________
______________________________________________________________________________
7. Observe the graphs. State the relationship that exists between the distance from the sun and the area
swept by the sun-to-asteroid line?
______________________________________________________________________________
______________________________________________________________________________
8. Using Kepler's 3rd Law [ p2 = d3 ] calculate the orbit period of a planet whose average distance from the
sun is the same as for this asteroid (your answer to question 5).
4
Astronomer: __________________________
Asteroid’s Path Orbiting the Sun
5