Calculating Satellite Velocity from taken photos

[Moon_1975]

Hi All,


I'm having difficultly with some data i have.

I have captured a passing satellite using my nikon DSLR, and using a timed exposure the satellite travelled 430x10-6m (from the pixels) in 5 seconds.

The satellite was at a rough height of 800km
and at an altitude of 20 degrees.

i've used all the trigonometry i know of but i cannot get a value of the velocity


thanks
David

 

[BrianJ]

Hi David, welcome to the forum :hello:

First thing I'd do is find the angular field of view of the image (you might know it already, or you could take a photo of the full-moon which is about 0.5degrees diameter)

Then you can figure out how many pixels per degree, then count the pixels in the satellite trail. From this you can find how fast the satellite is travelling across your field of vision (in degrees per second).

Next you need to find out how far away the satellite is from you - that's some fairly simple trig using the Sine and Cosine Rules, I think.

Probably easier to draw a diagram, so - you have a triangle of
point A (you)
point B (centre of the Earth)
point C (satellite)

you know length side A-B is the diameter of Earth (about 6371km)
you know length side C-B is diameter of Earth + 800km(altitude of sat)
you know angle B-A-C is 90+20 degrees

That's enough info to find the length of A-C.

After that, you could approximate with
velocity = cos(degrees per sec)*(length A-C)

NB! Having written all that, I realise it only works if the satellite is moving tangentially to you - it doesn't account for any velocity towards, or away from, the camera :facepalm: :lol:

To really calculate the velocity, I guess you'd need to do a proper orbit determination using as many data points over as long a time as possible.

All the best,
Brian

 

[Krikkit]

around 7.5 km/s in circular orbit, just using orbital mechanics.

If it is in a highly elliptical orbit the this can vary greatly depending on where it is in its orbit.

 

[tblaxland]

Orbit determination on an unknown object would normally be done using radar so you know range and range-rate as well as angular rate.

For me, I normally just make a note of the observation time and approximate altitude/azimuth angles and/or bright stars it passed nearby and do an elimination search of known objects on Heavens-Above.com.

 

[Urwumpe]

You could use the Gauss method, if you have enough photographs, it requires at least 4 measurements for calculating a good estimate of the orbit.

It is described over MANY pages in "Fundamentals of Astrodynamics".

 

[Moon_1975]

Hi all,

thanks for the information.

BrianJ - you suggested the angle of view which if i'm right, using the equation on [ame]http://en.wikipedia.org/wiki/Angle_of_view[/ame] and my known sensor size and f length i have calculated the satellite distance in degrees per second.

I'm struggling however to calculate the distance from A-C as you pointed out. With the cosine law i have used, i have the wrong angle to work out the distance. I've draw it out but I can't get distance A-C out of it. I'm sure its something simple but I don't know what!!

thanks
David

 

[BrianJ]

Hi,
actually I think you need the Sine Rule. Take a look at example(ii) further down on this page: http://www.ict-teacher.com/Mathstutor/Trigonometry(ii).html

You need to find one more angle (using the sine rule) - then you know the remaining angle (total of angles in triangle = 180). Then use the sine rule again to find the length of the remaining side.

Let us know how you get on

Cheers,
Brian

 

[Moon_1975]

Thanks,

I was thinking, would it not just be possible to use normal trig

taking the opp angle as that of 800km and the angle of 20 degrees to calculate the distance from observer to the satellite?

so sin20 (opp/hyp)
and find for hyp

David

 

[BrianJ]

Hi,
well, I think I'd call the Sine and Cosine rules "normal trig" ;-)

But anyway.....if "the Earth is flat" is a good enough approximation for you, you could do it that way. The result is about 25% different to the result using the Sine rule method.

atb,
Brian