Where is my CubeSat?
You have been provided with a box of data with a date and time and this Activity
sheet.
The box of data is in fact the Orbital Elements from a CubeSat satellite. A
10cmx10cmx10cm cube which is transmitting these orbital elements every time it
passes within detection range of a grounding station. From these numbers, it is
possible to calculate, predict, and extrapolate the satellites orbital path. That’s what
will be done today.
It’s only the second line that we are interested in, the first line describes the timings
from Launch and when it will tumble back to the Earth.
On your spreadsheet you have 7 columns. That is for 7 pieces of information. Now
imagine the characters in the second line, that’s all the individual letters AND SPACES
are all in separate columns. Fill in your spreadsheet following this guide for
identifying which number is what:
Line 2
Column Characters Description
----- ---------- ----------1
1
Line No. Identification
3
5
Catalog No.
9
8
Inclination
18
8
Right Ascension of Ascending Node
27
7
Eccentricity with assumed leading decimal
35
8
Argument of the Perigee
44
8
Mean Anomaly
53
11
Revolutions per Day (Mean Motion)
64
5
Revolution Number at Epoch
69
1
Check Sum Modulo 10
Inclination
(Degrees)
RA of
Ascending
Node
(degrees)
Eccentricity
Arg.
Perigree
Mean
Anomaly
Mean
Motion
Fill in the table above following the column and character description, and then
proceed with the rest of the activity.
INCLINATION
When were the measurements taken at (Time and Date)? In Astronomy terms, this is
the Epoch.
Inclination is the angle at which the orbital path is ‘leaning’ compared to the
horizontal.
What is the inclination of the satellite? Draw a line on the diagram and label the
angle it is at. (HINT: you will need a protractor. Line the 0˚ to 180˚ line along the ‘zero
degrees’ line and plot it)
0◦
180 ◦
If an orbit is near to 90 degrees it’s called a Polar Orbit. Close to zero degrees it’s
called an equatorial orbit. Which type would yours be?
RIGHT ASCENSION OF THE ASCENDING NODE
The Right Ascension of the Ascending node, is a fantastic name, it was named purely
to confuse everyone. Do you know where the equator is? The ‘Ascending node’ part
means where the satellite crosses the equator going from North to South (like
someone from London going to Australia). The Right Ascension part is also tricky.
Lines of longitude run down the Earth from North to South and all the way back
round again. Now if you imagine yourself standing on the Earth, you are standing on
a line of longitude, if you project that line to the sky, and imagine you are in a bubble
with the same lines running on the bubble, that’s what Right Ascension is. In simple
orbiting terms anyway!
What is the Right Ascension of the Ascending mode?
Then follow these instructions:
Using this Site: http://www.csgnetwork.com/siderealjuliantimecalc.html and the
latitude and longitude of Geneva (where the ground station for SwissCube is located)
to find out: Local Side Real Time:
 LST in decimal hours:
 Greenwich mean time:
 GST in decimal hours:
 What is your RAAN in decimal hours?
 Do the equation: LST (decimal) – RAAN (decimal) = longitude (If negative add
24, this means it is WEST of the Greenwich Meridian)
 Mark the location on this map. What countries (if any) are near it?
(HINTS: 1 degree = 4mins, for the decimal hours, take the part after the decimal,
divide it by 60, then add it again to the part divided by 60 again. SO = hour.
((decimal/60)+((decimal/60)/60)) write it out in full if you don’t understand it.)
Remember drawing your line of inclination? Ie what angle the orbit is at? Draw it on
the World map. But make sure it crosses the equator when it’s supposed to!
What direction is it going in? Add an arrow.
THE ARGUMENT OF PERIGEE
Although we like to draw it that way, orbits of satellites are not perfectly circular.
They are in fact an ellipse (an elongated circle). To add a bit more confusion, one of
its elongated ends passes closer to the body it’s orbiting than the other. The closest
point the satellite comes to a body is called the Perigee, the furthest point is called
the Apogee. Joining these two points together is called the major axis. The semi
major axis is half the distance of the major axis.
To help you understand it better, here is a planet. Draw an elliptical orbit and label
the axis, and the closest and furthest point.
In simple terms, The Argument of Perigee is the angle between the point of Perigee
and the Right Ascension of the Ascending node. So if the angle is 180 degrees, we
then know it will be at the point of Apogee, the furthest distance it orbits at.
Which point is yours closest too? Using the following diagram mark where it is (Hint:
assume 90◦ is up!):
ECCENTRICITY
Now how do we know what type of ellipse we have? Is it going to be long and
skinny? Or is it going to be closer to a circular shape? The eccentricity tells up this.
The closer it is to 1, the longer and thin it is. The closer to 0 it is the more like a circle
it appears.
What’s your value of eccentricity and which shape is it closer too?
USING KEPLER’S LAWS
What is the mean altitude of the satellite? (ie, what’s the average distance from the
Earth):
How many times does the satellite orbit the Earth a day? (Revs per day).
How long is each revolution?
From this, and the following relationship (Kepler’s law of motion), calculate the semimajor axis distance. (Look back at your diagram to see which distance that is)
P 2 = a3
Where ‘P’ is the period of one orbit (in seconds) and ‘a’ is the length of the semimajor axis (in meters). Use the space below to calculate the semi-major axis
Where is the Satellite? Using the value for Mean Anomaly, and the Epoch time, we
can show where on the ellipse you have defined, the satellite was at the time of
Epoch. Then, since you have the orbital speed, inclination, Right Ascension of the
Ascending node, and eccentricity as well as perigee and apogee positions, you can
accurately predict where the satellite will be!
In Astronomy, Anomaly is another word for angle. It is just equal angular increments
for the time taken for 1 orbit (like a clock face, 60 minutes = 360 degrees). Where
zero degrees is a perigee and 180 degrees is at apogee.
Where was your Epoch taken?
Make a Poster by drawing your own diagram with a scaled down image or your orbit.
Try and include smaller diagrams showing Inclination and Right Ascension of the
Ascending node. Include any information you believe is needed or interesting.