This article is based on answering the question of netizens: Suppose a certain point in the universe emits a beam of light to the earth, and this beam of light reaches the earth after 1.3 billion years, how many kilometers is this point away from the earth?
It's a simple math problem, but to answer, you need to understand the definition of light years first.
<h1 class="pgc-h-arrow-right" data-track="42" > light-years</h1>
1 light-year is the scale of one year of light travel, and the exact value of the vacuum speed of light per second is 299792458m/s (meters/s), generally about 300,000 km/second (kilometers).
1 year in the cosmic measurements using the Julian year, 356.25 days a year, 24 hours a day, 3600 seconds per hour, each year is 31557600 seconds. In this way, 1 light-year is the scale of light walking 31557600 seconds, and the accurate value is 9460730472580800m, which is generally about 9.46 trillion km per light-year.
This is where light years come from. That light traveled 1.3 billion years to Earth, indicating that the light source was 1.3 billion light-years away from Earth. That is, the second it emits light, it is about 12,298 billion kilometers away from us.
But since this light has come to our earth for 1.3 billion years, the location of this light is also 1.3 billion years ago. And the universe has been expanding, distant galaxies are moving away from us at high speed, and this light source (or galaxy) has been moving away for 1.3 billion years and has long been out of that position.
So how far away is this light source from us now? This requires the use of Hubble's Law.
<h1 class="pgc-h-arrow-right" data-track="24" > Hubble's law</h1>
Hubble's law, a theory for calculating the rate at which different distances leave us, or the rate at which the universe expands, was discovered and created by the great astronomer Edwin Hubble of the last century.
After a long period of observation of the universe, Hubble discovered the law of the expansion of the universe: all distant objects are moving away from us, and they are all-directional, faster and faster, and linear. This means that no matter from which direction you look at it, all galaxies at the same distance in the distance leave us at the same speed, the farther away the faster the speed, and the increase in speed is proportional to the distance.
Thus he came up with a law of cosmic expansion, which people call Hubble's law, simply stated: V = HD. V here represents the rate at which distant galaxies leave us in km/s (km/s) and H represents the Hubble constant in (km/s)/Mpc (million parsecs, about 3.26 million light-years) ;D the distance of the observed galaxy, in Mpc.
From this formula, as long as we know how far this light source (galaxy) is from us, and then know the Hubble constant, we can calculate the speed of leaving us. In other words, the rate at which galaxies at a certain distance are leaving us is the rate at which the universe expands.
Regarding how to measure the distance between distant galaxies and us, there are many methods, such as spectral redshift, standard candlelight, Cepheid variable stars, trigonometric parallax, etc., which have been introduced in the past and will not be mentioned today. Under the premise of known celestial distances, in the Hubble Law formula, the Hubble constant is a key, as long as we know the Hubble constant, we can know how fast galaxies at different distances are leaving us.
<h1 class="pgc-h-arrow-right" data-track="30" > hubble constant</h1>
What is the Hubble constant? It's at a distance from us Mpc (million parsecs, about 3.26 million light-years) that galaxies are leaving us at a speed. We know that the speed at which distant galaxies leave us is isotropic, the farther away the faster, in a linear proportional relationship, so that with the hubble constant at this point speed, it is possible to calculate the expansion rate of the universe at different distances.
Here's a special explanation, why does the Hubble constant use a million-seconds gap of about 3.26 million light-years as large a unit? This is because the expansion of the universe is a large-scale expansion, and at smaller distance scales, the movement of celestial bodies is more constrained by gravity, and the expansion of the universe cannot be expressed.
For example, the Andromeda Galaxy is about 2.54 million light-years away from our Milky Way, and at present, the two galaxies are not separated by mutual gravity, but show a trend of convergence, with a rate of 300km/s, and it is expected that in 30 to 4 billion years, the two galaxies will collide and then fuse into a larger galaxy.
But farther beyond the Hubble constant, galaxies are generally moving away from us.
For decades, astronomers have been measuring hubble constants by various methods, such as the standard candlelight method for supernovae, gravitational lensing, and the Planck satellite and the Chandra X-ray Observatory, and the Hubble constant has also been measured in different ways, but they are roughly in the same range.
In 2013, the European Space Agency used the Planck satellite to measure the Hubble constant of 67.8, which is the smallest Hubble constant to date; in 2019, German scientists used the gravitational lensing effect to calculate the Hubble constant of 82.4, which is the largest Hubble constant to date.
These two data are the most cited data in the scientific community. We take an average of neither large nor small, compromise, and get the Hubble constant of 75.1.
<h1 class="pgc-h-arrow-right" data-track="33" > 1.3 billion light-years that light source is now at a distance from us</h1>
By applying the Hubble constant of 75.1 to the Hubble Law formula above, we can calculate that the rate at which the light source (or galaxy) leaves us at 1.3 billion light-years is about 30,000 km/s. If 1.3 billion years pass at this rate, this light source or galaxy is about 12,286 billion kilometers away from us on the basis of 1.3 billion light-years away, that is, about 130 million light-years.
In this way, when this light emitted from 1.3 billion light-years away from us reaches our earth, this light source or galaxy is no longer in its original position, but is already farther away than 1.43 billion light-years away.
Why is it going further? Because the distance between distant galaxies and us changes over time, it should be calculated according to the formula of co-progressive distance, that is, the speed of each far point is progressively increased, this formula is very complex, involving calculus and space-time degree gauges and other complex theories, as a popular science article, here is not so complicated, just simple calculations.
This simple calculation is that at 1.3 billion light-years, the rate at which cosmic expanding galaxies are leaving us is about 30,000 km/s, and at 1.43 billion light-years, the rate of cosmic expansion is about 33,000 km/s. With a compromise, the expansion rate is 31,500 km/s, and after 1.3 billion years of motion, the distance has increased by about 137 million light years, so the light source is now at a position of 1.437 billion light years.
<h1 class="pgc-h-arrow-right" data-track="36" gravitational waves transmitted > 1.3 billion light-years, and the location of the wave source can also be understood in this way</h1>
In 2015, the first gravitational wave was measured by a precision gravitational wave detector, which is a ripple of time and space from the collision of two black holes 1.3 billion light-years away, which has been transmitted to the earth in 1.3 billion years.
Science has proven that gravitational waves travel at the speed of light, so we can calculate that this larger black hole formed by the merger of two black holes is now actually 1.437 billion light-years away.
When I say this, everyone should be able to understand, right? Welcome to the discussion, thanks for reading.
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