planetary-orbits-report (1)
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Florida International University *
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Course
1002L
Subject
Astronomy
Date
Jan 9, 2024
Type
docx
Pages
4
Uploaded by ChiefPigeon3890
Name: Sachintha Peiris
AST1002L RVC RVF RVD RVE 1238
Planetary Orbits
Kepler’s 1
st
Law
If you have not already done so, launch the NAAP Planetary Orbit Simulator.
Open the Kepler’s 1st Law tab if it is not already (it’s open by default).
Enable all 5 check boxes.
The white dot is the “simulated planet”. One can click on it and drag it around.
Change the size of the orbit with the semimajor axis slider. Note how the background grid
indicates change in scale while the displayed orbit size remains the same.
Change the eccentricity and note how it affects the shape of the orbit.
Tip:
You can change the value of a slider by
clicking
on
the slider
bar
or
by entering a
number in the value box.
Be aware that the ranges of several parameters are limited by practical issues that occur when
creating a simulator rather than any true physical limitations.
We have limited the semi-major
axis to 50 AU since that covers most of the objects in which we are interested in our solar system
and have limited eccentricity to 0.7 since the ellipses would be hard to fit on the screen for larger
values. Note that the semi-major axis is aligned horizontally for all elliptical orbits created in this
simulator, where they are randomly aligned in our solar system.
Animate the simulated planet. You may need to increase the animation rate for very large
orbits or decrease it for small ones.
The planetary presets set the simulated planet’s parameters to those like our solar
system’s planets. Explore these options.
1.
For what eccentricity is the secondary focus (which is usually empty) located at the sun?
What is the shape of this orbit?
ANS: 0, circlular
2.
Create an orbit with
a
=
1.00
AU and
e
=
0
.5 Drag the planet first to the far left of the
ellipse and then to the far right. Complete the table below.
r
1
(AU
)
r
2
(AU
)
r
1
+
r
2
(AU)
2a
(AU
)
Far Left
.5
1.5
.5+1.5
2
Far
Right
1.5
.5
1.5+.5
2
What can you conclude after completing the table?
ANS:
Credit ~ NAAP
Name: Sachintha Peiris
AST1002L RVC RVF RVD RVE 1238
The left and the right are opposite order of r1 and r2 but have the same AU.
3.
Set parameters to Uranus, press ok, then change the eccentricity to 0.6 Drag the planet first
to the far left of the ellipse and then to the far right. Complete the table below.
r
1
(AU
)
r
2
(AU
)
r
1
+
r
2
(AU)
2a
(AU
)
Far Left
18.3
20.1
18.3+20.
1
38.4
Far
Right
20.1
18.3
20.1+18.
3
38.4
4.
Create an orbit with
a
=
1.5
AU and
e
=
0.7
, can you find a point in the orbit where
r
1
and
r
2
are equal?
Sketch or crop a picture of the ellipse with all relevant
information below, and the value of
r
1
and
r
2
.
ANS: yes, the planet at the bottom center, 3.00AU.
5.
What is the value of the sum of
r
1
and
r
2
and how does it relate to the ellipse
properties? Is this true for all ellipses?
Be specific.
ANS: The sum of r_1 and r_2 in an ellipse refers to the length of its major axis, and it varies for
different ellipses. This sum is equal to twice the semi-major axis (2 * r_1) and relates to the
ellipse's eccentricity, representing how stretched or elongated it is. For a circle, a special case of
an ellipse, r_1 + r_2 equals the diameter of the circle.
Kepler’s 2
nd
Law
Use the “clear optional features” button to remove the 1st Law features.
Open the Kepler's 2nd Law tab.
Press the “start sweeping” button. Adjust the semimajor axis and animation rate so that the planet
moves at a reasonable speed.
Adjust the size of the sweep using the “adjust size” slider.
Click and drag the sweep segment around. Note how the shape of the sweep segment changes, but
the area does not.
Add more sweeps. Erase all sweeps with the “erase sweeps” button.
The “sweep continuously” check box will cause sweeps to be created continuously when
sweeping. Test this option.
Credit ~ NAAP
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