Download 46. Elliptical Orbits

Name ___________________________________
Date _______________
Class Period _____
Instructor _____________
Lab Period ______
5 points
Elliptical Orbits
Data Table 2 points each
c (focal distance) a (major axis)
e (eccentricity)
f0
f1
f2
f3
Questions: 3 points each Answer questions # 1 – 4 in complete sentences.
1.
2.
3.
4.
5.
A
B
C
D
6.
A
B
C
D
7.
A
B
C
D
8.
A
B
C
D
9.
A
B
C
D
10.
A
B
C
D
f2
f1
f0
f1
f2
Plot ellipses on this sheet. 10 points each
Lab #46 Elliptical Orbits
Introduction:
Even after the heliocentric (sun centered) model of the solar system was
accepted, people continued to believe that the orbits of the planets were perfect circles. In
1609, Johann Kepler announced that the planets’ orbits, including earth’s, were ellipses.
These slightly flattened circles were all of slightly different shapes. The planets orbited
around two focal points, or centers. The sun was located at one of the foci. In this lab, the
relationship between an ellipse and a circle will be explored.
Procedure:
Remove the data sheet and fasten the drawing page to cardboard using map or dissecting
pins.
Place one pin in f0 and place a string loop around the pin. Place a pencil inside the string
loop and pull the loop tight with one hand, while securing the pin with the other hand. Tilt
the pencil slightly and move the pencil around 360o, keeping the string tight. This will draw
a circle. Label the circle F0.
Remove the pin and insert two pins, one into each point marked f1. Place the string loop
around the pins. Place a pencil inside the string loop and pull the loop tight with one hand,
while securing the pins with the other hand. Tilt the pencil slightly and move the pencil
around 360o, keeping the string tight. This will draw an ellipse. Label the ellipse F1.
Repeat using the foci labeled f2. Label the ellipse F2.
Finally, pull the string loop tight using two pins, until the loop is stretched to the limit.
Center the loop along the line that has all of the other foci. When centered, push the pins into
the paper and label the holes f3. Drawing will yield a straight line, or totally flattened circle.
For each circle, line and ellipse; measure the focal distance, c, or distance between foci, and
place this in the chart. Next measure the major axis, a , which is the largest possible
diameter (this will be a line that passes through both foci). Calculate the eccentricity, e ,
using the equation below. Calculators are allowed. For f3, the major axis and focal distance
will be equal to each other.
c
e = -------a
Complete the data table on the lab sheet.
focal distance
eccentricity = ---------------------------major axis
Questions: 3 points each
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
What effect does increasing the focal distance, c, have on the shape (not the size) of
the ellipse?
What is the minimum eccentricity that an ellipse can have? Give a number. (Look at
the range of eccentricities obtained in the lab)
What is the maximum eccentricity that an ellipse can have? Give a number.
What shapes do the ellipses have for the minimum and maximum eccentricity?
What is the apparent shape of the Earth’s orbit as seen from space?
A)
a perfect circle
B)
slightly elliptical
C)
very elliptical
D)
a flat line
Where would the sun be located on a diagram of the earth’s orbit?
A)
at the center of the earth’s circular orbit
B)
3 parsecs from the planet Remulak, orbiting a black hole
C)
at the center of the earth’s slightly elliptical orbit
D)
at one of the foci of the earth’s slightly elliptical orbit
Which planets have the most eccentric orbits?
A)
Venus and Neptune
B)
Mercury and Pluto
C)
Mars and Saturn
D)
Pluto and Uranus
Which planets have the least eccentric orbits?
A)
Venus and Neptune
B)
Mercury and Pluto
C)
Mars and Saturn
D)
Pluto and Uranus
Which statement is true about a planet if its orbit is an ellipse?
A)
The planet travels in a perfect circle around its sun.
B)
Its sun travels around the planet in a slightly flattened circle.
C)
The distance between the planet and its sun varies.
D)
The planet is always the same distance from its sun.
Which statement about elliptical orbits is true?
A)
As the focal distance increases, the eccentricity decreases, making the planet’s
orbit more circular.
B)
As the focal distance increases, the eccentricity decreases, making the planet’s
orbit less circular.
C)
As the focal distance increases, the eccentricity increases, making the planet’s
orbit more circular.
D)
As the focal distance increases, the eccentricity increases, making the planet’s
orbit less circular.