How can knowing parallax of a farther object help with finding a nearer object?

[NanaToru]

my professor kind of off-handedly said something along the lines of "Parallex can help you find the distance to a nearby object if you have a farther one as a reference." I think he means general, so I've been assuming that our farther object is so far that parallex shifts are ignored.

I mean, I know this means we can figure out that our baseline isn't big enough to help in determining the distance, but I kind of fail to see how having just a "reference" and not a distance to a farther object can help with finding the nearer object...

Thanks in advance.

 

[Drakkith]

I think he means that the further object is what you are comparing the nearer object to. At large distances you can just say the object is stationary and get a direct reading of parallax on the nearer object. Even though you don't know the distance to the further object it just doesn't matter if you can't even measure the parallax because it's so small.

 

[NanaToru]

See, this is why I was confused by what he said. I wrote down what he said as "explain how parallex can help find the distance to a nearby object if you have a farther object as a reference."

 

[cepheid]

By "farther object" he meant a background object that is far enough away that it doesn't have a perceptible parallax of its own.

Parallax is a shift in the apparent position of a foreground object relative to the background, due to the changing vantage point of the observer.

Say if you're a surveyor and you want to find the distance to a tree that is a few miles away. Observe where it appears relative to some background mountains that are tens or hundreds of miles away. Now strike off 100 paces in some direction perpendicular to your line of sight to the tree (or an even longer baseline if you need to be really accurate) and record where the tree appears relative to the background mountains again. Find the angle between these two apparent positions. Using trig, you can now calculate the distance to the tree.

In astronomy, the foreground object (tree) is a nearby star, at most a few kpc away (or farther if you can measure really small angles). The background objects are the background stars, so far away that they appear "fixed". The baseline is the diameter of Earth's orbit.

 

[pmacias]

Knowing the parallax of a farther object can indeed help with finding the distance to a nearer object. Parallax is the apparent shift in the position of an object when viewed from different locations. This shift is due to the change in the observer's perspective. The farther an object is, the smaller the parallax shift will be. This is because the angle of the parallax shift is inversely proportional to the distance of the object.

Therefore, if we have a reference object that is very far away and its parallax shift is negligible, we can use it as a baseline to compare the parallax shift of a nearer object. By measuring the difference in the parallax shift between the two objects, we can calculate the distance of the nearer object.

For example, let's say we have a star that is very far away and a planet that is relatively closer. When we observe the star from two different locations, its parallax shift is negligible. However, when we observe the planet from the same two locations, its parallax shift is more significant. By comparing the two parallax shifts, we can calculate the distance of the planet from us.

In summary, knowing the parallax of a farther object can act as a reference point to determine the distance of a nearer object. This method is commonly used in astronomy to measure the distances of celestial objects.