Need an algorithm for satellite passing through non-penumbral earth shadow

[TheFerruccio]

I have a simulation with a satellite that orbits Earth in 3d.

Earth's shadow, for simplification purposes (the satellite is pretty close to earth) is either on or off. There's no light diffraction here. It can be represented as a cylinder with radius ~6378km, and an axis which aligns with the sun's relative position to earth.

This shadow changes position, as I calculated, by 1 degree approximately every 87660 seconds (slightly more than 1 day). I need a function that takes the satellite's position with respect to an earth-centered inertial coordinate system, and time (t=0 has Earth's shadow being perfectly horizontal with vector i), and outputs a 1 or a 0, depending on whether this satellite is in the shadow or not.

Both the satellite's position vector and the vector representing the axis of Earth's shadow change with respect to time.


I have the beginnings of a solution here, but it's really short.

Basically:

if dot(satellite position vector, cylindrical shadow axis vector) > certain value
output value = 1
else
output value = 0
end

if any are curious, I am programming this in Simulink. I have a clock and the satellite R vector as inputs. I'm doing it for a thermal simulation.

 

[Future Bruno]

Thanks to anyone who can help.The solution you are looking for is to find the angle between the satellite position and the axis of the Earth's shadow, and then compare that angle to some threshold value. If the angle is less than or equal to the threshold, then the satellite is in the shadow and you should output a value of 1. Otherwise, the satellite is not in the shadow and you should output a value of 0.To do this, you need to find the unit vectors pointing in the direction of the satellite and the axis of the Earth's shadow. Then, calculate the angle between them using the dot product:angle = acos(dot(satellite_unit_vector, shadow_axis_unit_vector))Then, compare the resulting angle to your threshold to determine whether the satellite is in the shadow or not.

 

[quicknote]

I would recommend using a combination of mathematical equations and computer simulations to create an algorithm for the satellite passing through non-penumbral earth shadow. Here are some possible steps to consider:

1. Define the Earth's shadow as a cylindrical shape with a radius of ~6378km and an axis aligned with the sun's relative position to Earth. This will help in visualizing and understanding the shadow's position and movement.

2. Use mathematical equations to determine the position and orientation of the Earth's shadow at any given time. This can be done by taking into account the Earth's rotation and the satellite's orbit.

3. Determine the position of the satellite with respect to an Earth-centered inertial coordinate system. This can be done using the satellite's orbital parameters and the current time.

4. Use the dot product formula to calculate the angle between the satellite's position vector and the cylindrical shadow axis vector. This will help in determining if the satellite is within the shadow or not.

5. Set a threshold value for the angle calculated in step 4. This value will determine the boundary between the satellite being in the shadow or not.

6. Use a conditional statement to compare the calculated angle with the threshold value. If the angle is greater than the threshold, the satellite is considered to be in the shadow and a value of 1 is output. If the angle is less than the threshold, the satellite is considered to be outside the shadow and a value of 0 is output.

7. Test the algorithm using different satellite positions and times to ensure its accuracy and effectiveness.

8. Implement the algorithm in Simulink or any other programming language to create a simulation of the satellite passing through the Earth's shadow.

9. Continuously monitor and update the algorithm to account for any changes in the satellite's orbit or the Earth's rotation.

Overall, creating an algorithm for the satellite passing through non-penumbral earth shadow will require a combination of mathematical calculations and computer simulations. It is important to thoroughly test and update the algorithm to ensure its accuracy and reliability.