Finding the distance of two points from observer

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Discussion Overview

The discussion revolves around the measurement of distances from an observer to two closely positioned points, A and B. Participants explore the precision of these measurements, the implications of distance and angle, and the potential challenges in determining these distances accurately.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the clarity of the initial scenario, suggesting that the independence of observations may complicate the measurement of distances DA and DB.
  • There are mentions of aberration affecting measurements, indicating potential complications in determining distances accurately.
  • One participant requests a sketch to better illustrate the situation, indicating a need for visual clarification.
  • Concerns are raised about the feasibility of measuring distances when the objects are very far away, with some noting that parallax becomes ineffective beyond certain distances.
  • Participants discuss using basic geometry and trigonometry to determine the distance between points A and B based on known angles and distances.
  • One participant introduces the small angle approximation as a potential method for simplifying calculations when distances are large.
  • Another participant suggests that if measurement errors exceed the separation between points A and B, it complicates the ability to determine their actual separation.
  • There is a suggestion to find a range of values for DA and DB to understand the limits of their separation based on measurement uncertainties.

Areas of Agreement / Disagreement

Participants express varying levels of clarity regarding the scenario, with some agreeing on the use of geometry for calculations while others highlight the complexities introduced by measurement errors and distance. The discussion remains unresolved with multiple competing views on the best approach to measuring the distances.

Contextual Notes

Limitations include the dependence on the definitions of points A and B, the assumptions about their distances, and the unresolved nature of measurement errors affecting the precision of the distances.

Tahmeed
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Lets suppose that two points A and B are very close together compared to their distance from an observer who is very far. Suppose the distance from observer to point A is DA and to point B is DB. How precisely we can find the distances separately.
 
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Tahmeed said:
How precisely we can find the distances separately
Your question isn't clear to me: Aren't the two observations independent ?
 
BvU said:
Your question isn't clear to me: Aren't the two observations independent ?
There can be aberration.
 
Can you illustrate what you mean with a sketch ?
 
BvU said:
Can you illustrate what you mean with a sketch ?
Yes, i will.
 
Tahmeed said:
Lets suppose that two points A and B are very close together compared to their distance from an observer who is very far. Suppose the distance from observer to point A is DA and to point B is DB. How precisely we can find the distances separately.
I'm sorry, but as written, the scenario seems like a non-sequitur: There isn't anything described that enables determining distance at all and even if there was, it wouldn't make any difference if the two objects were near to each other or not.

Is this question about Halton Arp?
 
1487182559566-1056983779.jpg
 
how precisely can we measure the DA and DB here?
 
Tahmeed, your situation is still unclear. What do points A and B represent? What are the approximate distances you're asking about? The precision and error of our measurements greatly depend on how far away the objects are. Nearby stars are relatively easy to measure, but beyond a few hundred or thousand light years things begin to change since parallax cannot be used. And if you're asking about cosmological distances (greater than a few million light years) then that's a very different scenario indeed...
 
  • #10
Are you trying to simply determine the distance between A and B based on known angle of separation between them and known distances? You can know that exactly using pretty basic geometry.

IMG_0220.JPG


I would set DB to be your x axis, then use trig to figure out (XA, YA).
The orange vertical is YA.
The orange horizontal is then XA - DB.
The pink line is found using the Pythagorean theorem.
 
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  • #11
if they are a long way away wouldn't you use the small angle approximation?
 
  • #12
newjerseyrunner said:
Are you trying to simply determine the distance between A and B based on known angle of separation between them and known distances? You can know that exactly using pretty basic geometry.

View attachment 113274

I would set DB to be your x axis, then use trig to figure out (XA, YA).
The orange vertical is YA.
The orange horizontal is then XA - DB.
The pink line is found using the Pythagorean theorem.
Yes, its kinda like this, but if the error in measurement of DA and DB is higher than their separation, then will we be able to find outt their actual separation? so i wanted to know how precisely we can measure DA and DB
 
  • #13
No, if you turn those values into variables, then the equation can only be made to provide a range.

Find the values for DB and DA that place them closest together and those that place them furthest apart. That's your range.
 
  • #14
newjerseyrunner said:
Are you trying to simply determine the distance between A and B based on known angle of separation between them and known distances? You can know that exactly using pretty basic geometry.

View attachment 113274

I would set DB to be your x axis, then use trig to figure out (XA, YA).
The orange vertical is YA.
The orange horizontal is then XA - DB.
The pink line is found using the Pythagorean theorem.
I got my answer here. thanks
 
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Likes   Reactions: newjerseyrunner

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