Satellite Position: Calculating ECI from ECEF

In summary, the poster is seeking help in calculating the matrix of a satellite's site vectors in ECI form. They have provided data in the ECEF form and are unsure of how to transform it to ECI. They have also mentioned using equations for ECEF to ECI transformation and are seeking guidance on how to perform the operation.
  • #1
Imagin_e
60
0

Homework Statement


Hi!

I just found this forum after trying to calculate something regarding a satellite's orbit. Hope that you can help me here. So, I need to calculate the matrix of a satellite's site vectors. I have found it in the ECEF form, but since the satellite is doing observations in different times, I need it in ECI for this particular problem.

Homework Equations


See below.

The Attempt at a Solution


I searched and for the ECEF position, we have the following equations to use: (see the attached file)

I have, from my values and by using these equation, the site position in ECEF:

r = [-7166.056 -6364.272 -3210.412
-1309.400 -186.778 824.20
669.27 -3545.190 -6467.48 ]

How do I get the ECI position now? I guess that I need to consider the rotation of the Earth and the time between the observations. Is a matrix multiplication necessary?

Thanks in advance!
 

Attachments

  • EFEC position.png
    EFEC position.png
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  • #2
Welcome to PF! Your problem is very special. Yes, change of coordinate system involves matrix multiplication. You can ask about ECI and ECEF in general in the Forum "Classical Physics". If you want to ask about a homework problem, write the question in detail, and post it to Homework/Advanced Physics.
 
  • #3
ehild said:
Welcome to PF! Your problem is very special. Yes, change of coordinate system involves matrix multiplication. You can ask about ECI and ECEF in general in the Forum "Classical Physics". If you want to ask about a homework problem, write the question in detail, and post it to Homework/Advanced Physics.
Thanks!
The thing is, I cannot find it here. Let be show what I've done so far. I have the data below, and I'm only going to look at the nr 3, 5 and 6 data (See data).

I calculated the Julian date (easy), which is:

JD1= 2,456,159.986 435
JD2= 2,456,159.991 991
JD3= 2,456,159.994

Next, the change in times between the observations : tau1= 2,456,159.986 435− 2,456,159.991 991 = -8 min and
tau2=2,456,159.994 769 − 2,456,159.991 991 = 4 min

The I used the equations I posted above and got (see EFEC)

NOW I'm stuck, how should I rotate/transform it to get the ECI position?
 

Attachments

  • data.png
    data.png
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  • ECEF.png
    ECEF.png
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  • #4
Also, I know how the formula for ECEF to ECI looks like (rather a matrix), but how should I perform the operation?
 

Attachments

  • Screen Shot 2015-10-19 at 12.07.29.png
    Screen Shot 2015-10-19 at 12.07.29.png
    2.3 KB · Views: 442
  • #5
Soory, I am not familiar with the topic. I ask the Mentors to move your thread to Advanced Physics.
 

1. What is ECI and ECEF?

ECI stands for Earth-Centered Inertial and ECEF stands for Earth-Centered Earth-Fixed. ECI is a coordinate system that is fixed to the Earth's axis of rotation and does not rotate with the Earth. ECEF is a coordinate system that is fixed to the Earth's surface and rotates with the Earth.

2. Why is it important to calculate ECI from ECEF?

Calculating ECI from ECEF is important because it allows us to accurately determine the position of a satellite relative to the Earth. This information is crucial for satellite tracking and navigation.

3. How is ECI calculated from ECEF?

ECI is calculated from ECEF using a mathematical transformation known as a rotation matrix. This matrix takes into account the Earth's rotation and the position of the satellite in the ECEF system to determine its position in the ECI system.

4. What factors affect the accuracy of ECI calculations?

There are several factors that can affect the accuracy of ECI calculations, including errors in the satellite's orbit data, atmospheric drag, and gravitational pull from other celestial bodies. These must be taken into account when calculating ECI from ECEF to ensure accurate results.

5. Are there any tools or software available for calculating ECI from ECEF?

Yes, there are various tools and software available for calculating ECI from ECEF. Some popular options include the Satellite Tool Kit (STK), MATLAB, and Python libraries such as PyEphem and Skyfield. These tools use advanced algorithms and data to accurately calculate the position of a satellite in the ECI system.

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