|
|
|
|
Ellipses
and Orbits
Materials needed for this lab: string,
cardboard, two stick pins, paper, and metric ruler
Procedure: One of Kepler’s
laws states that each planet has an elliptical orbit.
Kepler came up with this theory by plotting the orbit of Mars, his
assignment when he was invited to become one of Tycho Brahe’s assistants at
his new observatory in Prague. 1.
Place a sheet of paper over the cardboard
and tape it down. 2.
Press 2 stick pins, exactly 5.00 cm apart, through the paper into the
cardboard. 3.
Cut a piece of string (dental floss works great) a length about 3 times
the distance between the pins, plus enough for a knot. 4.
Tie a knot to form a loop and
lay the loop on the paper so that is encloses the two pins. 5.
Place a sharp pencil inside the loop and stretch the loop taut against
the pins (keeping the string flat on the paper surface).
Draw an ellipse around the two pins by keeping the pencil point as far
from the pins as the string will allow. 6.
Remove the string and pins. 7. Draw
the major axis through the two pinholes.
This will be the longest distance across the ellipse. 8.
Draw the minor axis through the shortest distance across the ellipse.
It will be perpendicular to the major axis at its midpoint. 9.
Label the two foci. These
are the holes left by the pins. 10. Label the perihelion
on your drawing. This is the
point on the orbit closest to the sun (one of the foci).
It is at one end of the major axis. 11. Label the aphelion
on your drawing. This is the
point farthest from the sun in the orbit of the planet.
It also is at one end of the major axis.
Kepler discovered that the orbit of Mars is elliptical and that the sun
is at one focus, with the other empty. He
plotted the orbits of the other planets and determined that they are also
elliptical. Kepler then
formulated his Law of Elliptical Orbits:
Each planet moves in an orbit around the sun, called an ellipse.
The sun is located at one focus of the elliptical orbit.
Questions: 1.
In cm and to the correct number of significant figures, record the: length of major axis:
__________cm length
of minor axis: _____________cm 2.
The semimajor axis is measured from the midpoint of the major axis to
the aphelion. length of semimajor
axis: __________cm 3.
Eccentricity equals the distance between the foci divided by the length
of the major axis. eccentricity = distance
between foci =
___________ (no units
here)
length of major axis 4.
If you increase the distance between the two foci will the eccentricity
become greater or less? Explain your answer. 5.
The eccentricity of a circle is zero.
Look up the eccentricity of the orbit of the earth around the sun.
List it: ____________________
Part 2 From any point on this
curve, the sum of the distances from that point to the two foci is constant in
length. In each planet-sun
system, the sun is at one foci. The
other foci is a point in space, not occupied by any astronomical body. 1.
Indicate the sun’s position on your drawing by Q.
Label the other foci, F. 2.
Draw and label the major axis as AB.
Label the center of the ellipse as C. 3.
Draw and label the minor axis as GH. 4.
Indicate the position of a planet in its orbit at two different times
(any two places on the ellipse). Label
one position P1 and the other P2.
Draw in the lines: P1Q,
P1F, P2Q,
and P2F 5.
Measure the following lengths: length of P1Q
= __________cm length of P1F
= __________cm length of P2Q
= __________cm length of P2F
= __________cm
length of P1Q
+ P1F =
________cm length of P2Q
+ P2F =
________cm
are the sums
P1Q
+ P1F and
P2Q
+ P2F equal or unequal?
Explain
Part 3 – Construction Construct the ellipse
whose major axis is 16 000 000 km and whose eccentricity is 0.5
(hint: let 1 cm = 1 000 000 km) a) If this ellipse were
the orbit of a planet, what would be the aphelion distance of the planet? b) What is the length of
the minor axis of this ellipse? |
|
Page Last Updated: Friday March 02, 2007 Webmaster: Larry Jones Pickens County School District |