## Friday, February 19, 2021

### How do we measure the distances in space?

8:16 PM | ,

Estimating the distances to celestial bodies can be a challenging endeavor, given their vast distances from Earth. It's not as if we can simply stretch out a tape measure from here to there! For such measurements, we resort to a tool known as the "cosmic distance ladder". This term refers to the various methods employed by astronomers to gauge the distances of celestial bodies, the technique of which hinges on the object's remoteness.

## Understanding the Cosmic Distance Ladder

The cosmic distance ladder, also known as the extragalactic distance scale, is a sequence of techniques used by astronomers to ascertain distances to celestial objects. Direct distance measurement of astronomical objects is only feasible for objects that are relatively close to Earth, within about a thousand parsecs. Techniques for determining distances to more remote objects are based on various observed correlations between methods suitable for close distances and those for larger distances. Many of these methods depend on a standard candle - an astronomical object with a known luminosity.

The "ladder" metaphor is employed because no single technique can measure distances across all ranges encountered in astronomy. Instead, one method measures close distances, another measures intermediate distances, and so forth. Each step on this ladder provides data that can be used to ascertain distances on the following step.

## Understanding the Astronomical Unit (AU)

The astronomical unit (AU) is a measure of distance now defined as precisely 149,597,870,700m (92,955,807.3 mi) or approximately the average distance from Earth to the Sun. Historical observations of Venus's transit were pivotal in determining the AU; observations of asteroids also played a significant role in the first half of the 20th Century. The AU is currently calculated with high precision using radar measurements of Venus and other nearby planets and asteroids, as well as tracking interplanetary spacecraft in their orbits around the Sun. While Kepler’s Laws offer precise ratios of the sizes of the orbits of objects revolving around the Sun, they do not provide an actual measurement of the orbits. Radar offers a value in kilometers for the variance in two orbits’ sizes, and from this and the ratio of the two orbit sizes, the size of Earth’s orbit is directly derived. Venus's transits across the Sun's face, despite the challenges and rarity of observations, were for a long time the best method of measuring the AU.

## Understanding Parallax

Trigonometric parallax is the cornerstone of fundamental distance measurements. As Earth orbits the Sun, the location of nearby stars seems to shift slightly against the more distant backdrop. These shifts are angles in a right triangle, with 2 AU constituting the short leg of the triangle and the star's distance forming the long leg. The shift is minute, measuring 1 arcsecond for a celestial object at a distance of 1 parsec (3.26 light-years), and decreases in angular amount as the reciprocal of the distance. Astronomers typically express distances in parsecs; light-years are commonly used in popular media, but usually, these values are converted from numbers originally calculated in parsecs.

As parallax shrinks with increasing stellar distance, useful distances can only be measured for stars with a parallax larger than the precision of the measurement. Parallax measurements usually have an accuracy measured in milliarcseconds. For instance, in the 1990s, the Hipparcos mission recorded parallaxes for over a hundred thousand stars with a precision of about a milliarcsecond, providing useful distances for stars up to a few hundred parsecs away.

Using Parallax to measure a star as seen from earth 6 months aparts. Credit: ESA Science & Technology:

## Standard Candle

A standard candle is an astronomical object that has a known absolute magnitude. They are extremely important to astronomers since by measuring the apparent magnitude of the object we can determine its distance using the formula:

m-M = 5 log d – 5

where m is the apparent magnitude of the object, M is the absolute magnitude of the object, and d is the distance to the object in parsecs.

The most commonly used standard candles in astronomy are Cepheid Variable stars and RR Lyrae stars. In both cases, the absolute magnitude of the star can be determined from its variability period.

The Standard Candle approach to measuring distance. Credit: Univ. of California

## Intergalactic Measurements

Distances from the Earth to nearby stars can conveniently be expressed in parsecs; for example, the nearest star, Proxima Centauri, is 1.295 parsecs distant. Because a parsec equals 3.27 light years, that's 4.225 light years. Even parsecs, however, prove inadequate for measuring distances within the galaxy or intergalactic distances. Astrophysicists frequently express these in kiloparsecs and megaparsecs, which equal 1,000 and 1 million parsecs, respectively. For example, the center of the galaxy is about 8 kiloparsecs distant, which equals 8,000 parsecs, or 26,160 light years. You’d need 16 digits to express that number with kilometers or miles.

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