<p>This is impossible to answer without clearly defining the geometry of your setup. VLBI delay <em>and delay rate</em> are calculated assuming the source is a long way away. This essentially means the incoming signal can be assumed to be planar waves arriving at each receiver. This significantly simplifies the maths and allows astronomers to assume the sources they are observing are projected onto a 2D celestial sphere which is a long way away.</p>
<p>In your specific case, if the objects is within the <a href="https://en.wikipedia.org/wiki/Near_and_far_field" rel="nofollow noreferrer">near field</a> of the baseline, then the maths changes significantly and you have to consider the 3D volume the source is in. Note for the near field calculation, you need to consider the separation of the receivers, not the size of the individual receivers.</p>
<p>The VLBI case gets complex pretty quickly, even assuming far field. You have to consider the rotation of the earth wrt the source you are observing, as well as the full 3D spherical geometry. Add into this relativistic effects, compensation for the ionosphere and troposphere, <a href="https://en.wikipedia.org/wiki/Earth_tide" rel="nofollow noreferrer">earth tide</a>, tectonic plate movement, you may find the VLBI case is a long way removed from what you really want.</p>
<p>If you really want to find some software which does the VLBI delay calculation, you could look at <a href="http://astrogeo.org/vtd/" rel="nofollow noreferrer">VTD</a> (and links therein):</p>
<blockquote>
<p>Library VTD computes a priori VLBI time delay and delay rate with precision needed for geodetic applications. Terms which contributes to delay at the level 10<sup>-13</sup> sec for delay and 10<sup>-15</sup> for delay rate are kept. The accuracy of VTD is determined by the accuracy of a priori values. If the <em>a priori</em> site positions, source coordinates, EOP, tropospheric path in zenith direction were perfect, the theoretical time delay and delay rate would be accurate to that level. Library VTD also computes the Doppler frequency shift for the Solar system objects.</p>
</blockquote>

CC BY-SA 4.0
2021-07-07T03:08:59.447Z
Great answer! For more about VLBI within our solar system see [How are precision trajectory measurements made of trans-Neptunian spacecraft?](https://space.stackexchange.com/q/14681/12102) and other questions there [mentioning VLBI](https://space.stackexchange.com/search?q=+vlbi) You may also be interested in answering or commenting on [How to attract real-world radio telescopists to radio astronomy observational techniques questions?](https://astronomy.meta.stackexchange.com/q/685/7982) or the questions linked within it.
uhoh
CC BY-SA 4.0
2021-06-07T01:15:29.407Z
2021-07-13T04:39:44.660Z
2021-07-13T04:39:44.660Z
Chris
<p>I’m working on a research project wherein we are trying to solve a problem very similar to VLBI delay. We have two radio receivers, and we know their locations. We also know at what time one receiver detected a signal, and the coordinates of it’s beam-pointing center. We want to determine at what time the second receiver should’ve seen the signal.</p>
<p>I understand <em>in principle</em> how VLBI delay is calculated; I’ve seen a few different formulas, such as <a href="https://astronomy.stackexchange.com/a/36763/7982">the dot product of a vector between the receivers, and between the receiver and the source</a> but practically speaking, how would I actually go about producing numbers?</p>

CC BY-SA 4.0
2020-07-14T09:51:54.473Z
Yes this task needs a more definitive solution than what I gave before. Can you use Python? Or are you planning to use a spread sheet or pencil and paper, or do you need a website? I am not sure I can post a complete answer but probably someone can. But it will be helpful to them if you can mention which resources or calculation techniques you have available.
uhoh
<radio-astronomy><interferometry>
How is VLBI delay calculated?
PerplexedDimension
# How is VLBI delay calculated?

(Asked by: username_0 on 2020-07-14)

I’m working on a research project wherein we are trying to solve a problem very similar to VLBI delay. We have two radio receivers, and we know their locations. We also know at what time one receiver detected a signal, and the coordinates of it’s beam-pointing center. We want to determine at what time the second receiver should’ve seen the signal.

I understand *in principle* how VLBI delay is calculated; I’ve seen a few different formulas, such as [the dot product of a vector between the receivers, and between the receiver and the source](https://astronomy.stackexchange.com/a/36763/7982) but practically speaking, how would I actually go about producing numbers?

**Tags:** radio-astronomy, interferometry
> **Comments:**
> **username_1**: Yes this task needs a more definitive solution than what I gave before. Can you use Python? Or are you planning to use a spread sheet or pencil and paper, or do you need a website? I am not sure I can post a complete answer but probably someone can. But it will be helpful to them if you can mention which resources or calculation techniques you have available.  

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## 1 answers

### Answer by username_2 on 2021-06-07. Score: 2

This is impossible to answer without clearly defining the geometry of your setup. VLBI delay *and delay rate* are calculated assuming the source is a long way away. This essentially means the incoming signal can be assumed to be planar waves arriving at each receiver. This significantly simplifies the maths and allows astronomers to assume the sources they are observing are projected onto a 2D celestial sphere which is a long way away.

In your specific case, if the objects is within the [near field](https://en.wikipedia.org/wiki/Near_and_far_field) of the baseline, then the maths changes significantly and you have to consider the 3D volume the source is in. Note for the near field calculation, you need to consider the separation of the receivers, not the size of the individual receivers.

The VLBI case gets complex pretty quickly, even assuming far field. You have to consider the rotation of the earth wrt the source you are observing, as well as the full 3D spherical geometry. Add into this relativistic effects, compensation for the ionosphere and troposphere, [earth tide](https://en.wikipedia.org/wiki/Earth_tide), tectonic plate movement, you may find the VLBI case is a long way removed from what you really want.

If you really want to find some software which does the VLBI delay calculation, you could look at [VTD](http://astrogeo.org/vtd/) (and links therein):

> Library VTD computes a priori VLBI time delay and delay rate with precision needed for geodetic applications. Terms which contributes to delay at the level 10-13 sec for delay and 10-15 for delay rate are kept. The accuracy of VTD is determined by the accuracy of a priori values. If the *a priori* site positions, source coordinates, EOP, tropospheric path in zenith direction were perfect, the theoretical time delay and delay rate would be accurate to that level. Library VTD also computes the Doppler frequency shift for the Solar system objects.

> **Comments:**
> **username_1**: Great answer! For more about VLBI within our solar system see [How are precision trajectory measurements made of trans-Neptunian spacecraft?](https://space.stackexchange.com/q/14681/12102) and other questions there [mentioning VLBI](https://space.stackexchange.com/search?q=+vlbi) You may also be interested in answering or commenting on [How to attract real-world radio telescopists to radio astronomy observational techniques questions?](https://astronomy.meta.stackexchange.com/q/685/7982) or the questions linked within it.  

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