Research Ideas and Outcomes :
Methods

Corresponding author: Yuanchuan Zou (zouyc@hust.edu.cn)
Received: 12 Nov 2020  Published: 16 Nov 2020
© 2020 Yuanchuan Zou
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Zou Y (2020) Distance measurement using the spherical wave fact of astronomical objects. Research Ideas and Outcomes 6: e60713. https://doi.org/10.3897/rio.6.e60713

Distance measurement is very important for astrophysics, and it is also an arduous task. Here we propose an independent method to measure the distances directly. Considering that electromagnetic waves are actually spherical waves from the source, people can get the distance of the source by accurately measuring the curvature of the spherical surface. The farthest measurable distance is roughly b^{2}/b, where d is the separation of telescopes, and b is the position accuracy of the telescopes.
methods: observational, distance measurement, astrometry
The trigonometric parallax is now the most powerful modelindependent method for measuring astronomical distances. Astronomical research still needs more independent methods of distance measurements, such as using the phase information of the sources (
A schematic plot is shown in Fig.
A schematic figure shows the spherical wave observed with 3 telescopes located at positions A, O, and B. The 3 telescopes are settled at the spherical wavefront. The source S is the center of the circle. With the measuring of distance \(b\)=OO', one is able to get the distance \(D = {d^2 \over 2b}\), where \(d\) is the distance between B and O'.
The schematic configuration is designed for clear expression. An actual observing system does not require the 3 telescopes to be located in the circle. Only the precise positions and accurate time sequences are required. The existing VLBI system might be directly used with this method to measure the distances of nearby objects.
Gravitational waves can also be used to measure the distance of the source in a similar way if the time and the position of the receiver are obtained accurately.
The accuracy is basically restricted by the working wavelength. With THz telescopes, one is able to measure the small distance of \(b \sim {\rm mm}\). Notice that with the increase of the baseline \(d\), the measurable distance \(D\) increases quickly. This might be a potentially powerful tool to measure extragalactic cosmological distances directly. Considering 3 spaceborne telescopes in the Earth's orbit with \(d \sim 10^{13}cm\) , with the position accuracy of 1 mm, the measurable distance can reach up to 1 Gpc.
The threetelescope system is sensitive to the sources located on the same plane of the system. A more general system could consist of four telescopes, by putting the fourth telescope noncoplanarly.
Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. This work was supported by the National Natural Science Foundation of China (Grant No. U1738132 and 11773010).