# Distance Measurement

Discussion in 'Physics & Math' started by The God, Jul 26, 2017.

1. ### The GodValued Senior Member

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3,546
We are able to measure the distance of remote cosmic objects based on cosmological redshifts.

We can measure the distance of a receding sound source by recording it's frequency, if we know the original wave character, medium etc (Doppler).

What is necessary in both the cases is movement of the object, without which we cannot measure the distance even if we record the emitted light/sound.

I am opening this thread for a discussion to find out if it is possible to ascertain the distances of objects (sound sources and light sources) by any other means. (Leaving aside geometrical two position based measurement of a light source). I am just trying to ascertain if cosmological redshift is a nature's sole gift to us to ascertain such vast distances.

Last edited: Jul 26, 2017

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5. ### LaurieAGRegistered Senior Member

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320
It depends on what distance you are looking at and how you measure shift.

Have you ever thought about a situation where the distance stayed the same while the shifts changed depending on the angle of the observer to the centre of the plane of rotation of the sources? It's like taking a photo of one complete circle of a sparkler and looking at that basic process on galactic time and distance scales. Lets start simple and look at how we can receive different shifts even though the distance between the rotating sources centre of mass and the observer stays the same before we start moving the observer or the centre of mass anywhere else.

Consider a basic model of two rotating sources and an observer who is stationary with respect to the centre of mass of the plane of rotation of the 2 sources shown in the image below. In this model the distance between the sources at the time of emission (1,0 and 3, 0) and the observer will always equal 2 * Pi * c/v where v is the angular velocity of the sources around their centre of mass and r = 1. If the sources are rotating at 0.5c the distance travelled by a photon during one complete revolution will equal 4 * Pi . The colours of the photon paths reflect the movement of the source with respect to the observer at the time and point of the photon emission, regardless of the angle of the observer to the plane of rotation of the sources.

The following image shows a quarter by quarter walk through on how the photon paths for one complete rotation of 2 rotating sources are constructed in the images below.

After one quarter of rotation the photons emitted at the start point 1,0 have travelled to 1, 1 with the photons emitted at the end of the quarter coming from 4, 0 along with all other emitted photons lying at locations on a line connecting these 2 points.
After two quarters of rotation the photons at 1, 1 have travelled to 1, 2, the photons at 4, 0 have travelled to 4, 1, with the photons emitted at the end at 3, 0 along with all other emitted photons lying at locations on a line connecting these 3 points.
After three quarters of rotation the photons at 1, 2 have travelled to 1, 3, the photons at 4, 1 have travelled to 4, 2, the photons emitted at 3,0 have travelled to 3, 1 with the photons emitted at the end at 2, 0 along with all other emitted photons lying at locations on a line connecting these 4 points.
After one complete rotation the photons at 1, 3 have travelled to 1, 4 (the observer), the photons at 4, 2 have travelled to 4, 3, the photons emitted at 3,1 have travelled to 3, 2, the photons emitted at 2,0 have travelled to 2, 1 with the photons emitted at the end back at 1, 0 along with all other emitted photons lying at locations on a line connecting these 5 points.