### The Size of the Cosmos

Henrietta Leavitt,

Much of astronomy is tied up in attempts to determine the distance to various objects, such as planets, stars, and galaxies. This seemingly simple task is actually shockingly difficult when astronomical distances are involved. The easiest way to measure a distance is to actually travel the distance, effectively counting your steps. This is impractical even on Earth when the destination is too far away or too inaccessible (e.g. when measuring the height of Mt. Everest). In these cases, geometry can be used. If you start with two points that are a known distance apart, you can measure the direction from these two points to a third point and work out the distances. Effectively, you measure one side and two angles of a triangle, which provides enough information to work out the lengths of the other two sides.

This method only works if the known side's length is large enough when compared to the unknown lengths. Otherwise there will be no measureable difference between the two angles. In 1672, the distances to the planets were measured in this way, with the two known points on opposite sides of the planet (Paris, France, and Cayenne Island, French Guyana). By 1838, the distances to some stars were measured, with the two known points on opposite sides of the solar system: one measurement is taken in summer, and the other in winter, when the planet is on the opposite side of the sun!

Unfortunately, only the nearest stars can have their distances measured in this way. Out of literally

Enter Henrietta Leavitt. She was a "computer" at Harvard College Observatory, literally a person who was hired to compute numbers. She computed, and studied, the brightnesses of stars. There is a simple relationship between the amount of light a star produces, its distance, and how bright it appears to us. To understand this, imagine all the light produced by a star at a particular instant in time. As time passes, it heads away from the star in all directions at the same speed. The light appears, in other words, to be spread evenly across the surface of an expanding sphere. As the distance grows, the surface area of the sphere grows, and the light is spread more and more thinly. Because the surface area of a sphere grows with the square of its radius, the light reaching an observer decreases in intensity with the square of the distance to the source of light. In other words, if you know how much light a star is putting out, and you can see how bright it is, you can work out how far away it must be.

Isacc Newton guestimated some stellar distances by assuming that all stars are identical to the sun. He correctly concluded that stars are very, very far away. Unfortunately, once nearby stars had their distances measured by geometry, it was shown that stars vary a

Anyway, back to Miss Leavitt. One of the tasks she accomplished was to assign known brightnesses to sets of stars. The ideal way to do this is to take many pictures of a star of known brightness at carefully varied exposure times. This produces a set of pictures that vary in brightness in exactly the same way that the exposure times were varied. Then you can compare these to pictures of other stars taken with the same equipment and determine their brightness. Keep in mind that you're doing this by comparing the size of spots of light on photographic negatives using a magnifying glass.

Miss Leavitt was given 277 photographs from 13 telescopes, with varying apertures and exposure times, and asked to calculate the brightnesses of 96 stars in the pictures, so that they could be used as a standard by which other astronomers could measure brightnesses. She succeeded. From this, you can infer that she was an expert at measuring the brightnesses of stars.

At about the same time as this project, she started studying stars whose brightness varied noticeably over time. In her landmark paper, she looked at 25 variables of a particular type, called Cepheid variable stars, all in the Small Magellanic Cloud, a group of stars thought to be at roughly the same distance from us. Because of this, she knew that their apparent brightnesses were not being significantly distorted by distance: if one of them appeared to be twice as bright as another, it had to be because it was putting out twice as much light, not because of a difference in distance between the two stars.

Each Cepheid variable varies in brightness over a particular period: e.g. the brightness of star #7 in her paper peaked every 45 days, while the brightness of star #2 peaked every 20 days. Much to everyone's surprise, Miss Leavitt discovered that the period of each star was related to its apparent brightness, and therefore to the amount of light it was putting out. In other words, if you can find a Cepheid variable star

Although the Cepheids Miss Leavitt studied were not at a known distance, within a year someone found a Cepheid close enough to measure its distance by simple geometry. With this discovery, the measurement of distances expanded from around 500 light years to over 20

*Periods of 25 Variable Stars in the Small Magellanic Cloud*, 1912Much of astronomy is tied up in attempts to determine the distance to various objects, such as planets, stars, and galaxies. This seemingly simple task is actually shockingly difficult when astronomical distances are involved. The easiest way to measure a distance is to actually travel the distance, effectively counting your steps. This is impractical even on Earth when the destination is too far away or too inaccessible (e.g. when measuring the height of Mt. Everest). In these cases, geometry can be used. If you start with two points that are a known distance apart, you can measure the direction from these two points to a third point and work out the distances. Effectively, you measure one side and two angles of a triangle, which provides enough information to work out the lengths of the other two sides.

This method only works if the known side's length is large enough when compared to the unknown lengths. Otherwise there will be no measureable difference between the two angles. In 1672, the distances to the planets were measured in this way, with the two known points on opposite sides of the planet (Paris, France, and Cayenne Island, French Guyana). By 1838, the distances to some stars were measured, with the two known points on opposite sides of the solar system: one measurement is taken in summer, and the other in winter, when the planet is on the opposite side of the sun!

Unfortunately, only the nearest stars can have their distances measured in this way. Out of literally

*millions*of stars visible in telescopes, only those closer than about 500 light years can have their distances measured with any accuracy using geometry alone.Enter Henrietta Leavitt. She was a "computer" at Harvard College Observatory, literally a person who was hired to compute numbers. She computed, and studied, the brightnesses of stars. There is a simple relationship between the amount of light a star produces, its distance, and how bright it appears to us. To understand this, imagine all the light produced by a star at a particular instant in time. As time passes, it heads away from the star in all directions at the same speed. The light appears, in other words, to be spread evenly across the surface of an expanding sphere. As the distance grows, the surface area of the sphere grows, and the light is spread more and more thinly. Because the surface area of a sphere grows with the square of its radius, the light reaching an observer decreases in intensity with the square of the distance to the source of light. In other words, if you know how much light a star is putting out, and you can see how bright it is, you can work out how far away it must be.

Isacc Newton guestimated some stellar distances by assuming that all stars are identical to the sun. He correctly concluded that stars are very, very far away. Unfortunately, once nearby stars had their distances measured by geometry, it was shown that stars vary a

**lot**in the amount of light they put out: they aren't all identical to the sun.Anyway, back to Miss Leavitt. One of the tasks she accomplished was to assign known brightnesses to sets of stars. The ideal way to do this is to take many pictures of a star of known brightness at carefully varied exposure times. This produces a set of pictures that vary in brightness in exactly the same way that the exposure times were varied. Then you can compare these to pictures of other stars taken with the same equipment and determine their brightness. Keep in mind that you're doing this by comparing the size of spots of light on photographic negatives using a magnifying glass.

Miss Leavitt was given 277 photographs from 13 telescopes, with varying apertures and exposure times, and asked to calculate the brightnesses of 96 stars in the pictures, so that they could be used as a standard by which other astronomers could measure brightnesses. She succeeded. From this, you can infer that she was an expert at measuring the brightnesses of stars.

At about the same time as this project, she started studying stars whose brightness varied noticeably over time. In her landmark paper, she looked at 25 variables of a particular type, called Cepheid variable stars, all in the Small Magellanic Cloud, a group of stars thought to be at roughly the same distance from us. Because of this, she knew that their apparent brightnesses were not being significantly distorted by distance: if one of them appeared to be twice as bright as another, it had to be because it was putting out twice as much light, not because of a difference in distance between the two stars.

Each Cepheid variable varies in brightness over a particular period: e.g. the brightness of star #7 in her paper peaked every 45 days, while the brightness of star #2 peaked every 20 days. Much to everyone's surprise, Miss Leavitt discovered that the period of each star was related to its apparent brightness, and therefore to the amount of light it was putting out. In other words, if you can find a Cepheid variable star

*anywhere*, you can measure its period, use that to work out the amount of light it puts out, measure its apparent brightness, and combine those to work out how far away it is. With this, you can estimate the distance to any*group*of stars that happens to contain a Cepheid.Although the Cepheids Miss Leavitt studied were not at a known distance, within a year someone found a Cepheid close enough to measure its distance by simple geometry. With this discovery, the measurement of distances expanded from around 500 light years to over 20

*million*light years. Within a decade, studies of globular clusters had mapped out the shape of the Milky Way, our home galaxy, and Hubble soon discovered the existence of stars well outside the Milky Way, in other galaxies entirely.
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