Chapter 24. The Distance Ladder

24.1 Introduction

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Hubble Space Telescope image thumbnail

Author: Scott Miller, Pennsylvania State University

Editor: Grace L. Deming, University of Maryland

Hubble Space Telescope image
A Hubble Space Telescope image reveals galaxies in the constellation of Hercules (the ones shown in boxes are roughly 11 billions light years away from us).

The goals of this module: After completing this exercise, you should be able to:

  1. Explain how various techniques are used to measure distances to galaxies.
  2. Describe what makes an object a good standard candle.
  3. Explain how the uncertainty of distance measurements increases with distance.

In this module you will explore:

  1. How the luminosities of a variety of objects are determined.
  2. How luminosity is used to calculate distance with the inverse square law of light.
  3. How astronomers use the distances to nearby objects to determine distances to farther objects.

Why you are doing it: When we look out into the heavens, one of the questions that always fills us with awe is "Just how big is the universe?" To determine the answer to this question, a number of techniques are used to measure distances to farther and farther galaxies. Ultimately we would like to determine the size of the universe itself.

24.2 Background

Stellar Parallax
Stellar parallax can be used to measure distances to the nearest stars.

When astronomers first observed other galaxies, there was a debate as to whether they were "spiral nebulae" located within the Milky Way or if they were "island universes" outside the bounds of our Galaxy. To help resolve this, astronomers developed a number of distance measurement techniques to objects farther and farther away.

Within our local neighborhood of stars, we can use stellar parallax to measure distances to nearby objects. Stellar parallax, as you may recall, is an apparent shift in the position of a nearby objects relative to background objects due to a change in perspective of the observer. The farther away an object is, the smaller its parallax. As the Earth moves around the Sun, nearby objects appear to shift back and forth over the span of a year. By measuring this apparent shift, we can determine distances to nearby stars. With the Hipparcos satellite, we measured accurate distances using stellar parallax out to about 500 pc away.

Question 24.1

bYQyyLWb+Ne++fS1t5emiQIfASInu1BxF/LmxAXnKC8G1h/3UqmWTuZeHkXQwjRCsoXtfuXORrUNO0IK7YBp5SPWR9FYfvgYa6mtPZ4YsaWU7ahTkIGWSuBugoIffVow46fMXnaqfPzp91tT6VhFwRwkKQ1ym/ubMbfZUa+1NZ1yaJzR/9VKfK9my+x6G8wJiLn3nxK8kM+AjZv0jq9/Im4DNcYHo7sS0SLN6h4oGMo4h31niJiWv0CqnV9ntRYYY0TdJA3qGcK1QIOi7ekLogAB7Jw=
3
Try again. If 500 pc corresponds to the maximum distance Hipparcos can accurately measure, then what is the smallest angle it can observe? Use the formula that relates parallax and distance. If the distance is inversely proportional to the parallax, then we can write their relationship as p = 1/d.
Correct. The formula for parallax is d = 1/p, or p = 1/d. A maximum distance of 500 pc, the farthest Hipparcos can observe, corresponds to an angle of 1/500 = 0.002 arcsec, the smallest angle Hipparcos can accurately measure.
Incorrect. The formula for parallax is d = 1/p, or p = 1/d. A maximum distance of 500 pc, the farthest Hipparcos can observe, corresponds to an angle of 1/500 = 0.002 arcsec, the smallest angle Hipparcos can accurately measure.

Once astronomers displayed stellar properties on an H-R diagram, they found that it could be used as a distance indicator as well, through a process known as Spectroscopic Parallax. Given a well-defined H-R diagram, if you observe a star of known spectral type and luminosity class (like main sequence or red giant, which can be determined by examination of the width of the spectral lines), you can determine its position on the H-R diagram. Determining its luminosity is then as simple as reading it off of the axis. Once you know the star's luminosity, you can observe its apparent brightness, and then use the inverse square law of light to determine its distance. This method is useful out to a distance of about 10 kpc (10,000 parsecs).

Question 24.2

kuVUZ+jRFRzxuWtdF/yfjUnDlyruL8G/3EKfglJCAEdKcMOC5rUrJRtr+GYFC0LAf95GmKfWldnD+pdz6VKG3odQRc1aFkHJWV/dn8HzCJeJ6s7TIuv6oVC7gMV/NhFyFfQofoPmmGuaTT3b0zTph4WBrG6tkV4TuJKfPfzBWZWGX8Dk4L1d7LwdRugyWZQgbxhYUe3+VN+R9itEZBAEs1L0kY3TZKADEscoTt1zAJ8ew+HVLQSQlg==
3
Try again. In order to use spectroscopic parallax, you must first have a well defined H-R diagram.
Correct. In order to use spectroscopic parallax, you must first have a well defined H-R diagram. The luminosities of nearby stars can be calculated using the inverse square law of light, since we have measured their distances using stellar parallax. An H-R diagram can be plotted using these nearby stars.
Incorrect. In order to use spectroscopic parallax, you must first have a well defined H-R diagram. The luminosities of nearby stars can be calculated using the inverse square law of light, since we have measured their distances using stellar parallax. An H-R diagram can be plotted using these nearby stars.

Summary

Unfortunately, neither stellar parallax nor spectroscopic parallax allows astronomers to measure distances to objects outside of our Galaxy, but as we'll see, they are the first steps towards measuring distances to objects farther and farther away.

24.3 Cepheid Variables

Cepheid Variable
A Cepheid Variable detected in M100 allows astronomers to determine a distance of 17 Mpc (17 million parsecs) to this galaxy.

In 1908, while cataloguing the brightnesses of stars in the Small Magellanic Cloud, Henrietta Leavitt noted that a number of stars varied in brightness, and that their period of variation was directly related to their apparent brightness. Once the distance to the Small Magellanic Cloud was determined, the apparent brightnesses were converted into luminosities, and a Period-Luminosity relation was derived. For this particular type of star, known as Cepheid variables after the first of its type to be observed - δ Cephei, the Period-Luminosity relation states that the longer the period of variability, the more luminous the star on average. Cepheid Variables are useful distance indicators, since their periods of variability give us their luminosities.

Question 24.3

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3
Try again. The luminosity of a Cepheid is directly related to the period of variation. The greater the period, the more luminous the star.
Correct. Since Cepheid A has a longer period of variation, it must be more luminous, yet appears as bright as Cepheid B. In order for this to happen, it must be farther away.
Incorrect. Since Cepheid A has a longer period of variation, it must be more luminous, yet appears as bright as Cepheid B. In order for this to happen, it must be farther away.

Summary

Suppose you observe a Cepheid variable in another galaxy, such as the one observed in M100 as shown to the right, how would you determine its distance? Well, first you would observe it over a number of days to determine how long it takes to change from brightest to dimmest to brightest again. The period of variation for Cepheids ranges from 1 to about 50 days. Given the period, you then use the Period-Luminosity relation to determine the Cepheid's luminosity. Next, you take the average of its apparent brightness as observed from Earth. (Apparent brightness is what you were observing in order to determine the period of variability.) Finally, given its luminosity and apparent brightness, you can use the inverse square law of light to determine its distance. The best part is that Cepheid variables are observable out to around 25 Mpc (25,000,000 parsecs), allowing us to measure distances to nearby galaxies.

24.4 Tully-Fisher Relation

In 1977, two astronomers, R. Brent Tully and J. Richard Fisher discovered a relationship for spiral galaxies, which also provides a useful distance indicator. They discovered a strong correlation between two galactic properties. It turns out that the rotation speed of a spiral galaxy is highly correlated with its total luminosity. Based on this relation, if you can measure the rotation speed of a spiral galaxy, then you can determine its luminosity. Then, you observe its apparent brightness and use the inverse square law of light to determine its distance.

Question 24.4

2U0Zubzzc4vZQCpu6FdyQVjoBRLuakp/DPSCoYxAFQsF19madijNhAOw57+6xDbwKPcWeCPiJv4WLfUKiPM5XUwcCZcQYOCgElDN4Gl0rO77eLIRF65ZWdGIgR7I+9prDB+KiTgnPBgZaWVS2sTkwV485Z+8nvy1wfBNskLD6r8kh/UillMtZ8qzfsArDd2+baPhOW7d/Prg2lP8YFnGdngKjnPBwoSKJRYLbPKk+RntYt44aR0Iby2+qm2FfDAXI/bx6KOrBGi0/o0RwLETRvwH6OEDtTfhSJhji7s+fn+heJg22DEj53GS1rBwzGdEGpIkjLnHMxUsJxDrYZTE+vjoEVO7gFjU35hmR4xmNMc0PyXc6yt7zMNtd/DZhI7bi/uK3eAEL2urBAEBiNOM2g+LeltjIfNTeBfcLw==
3
Try again. Recall what happens to the wavelengths of light emitted by an object moving radially towards or away from us.
Correct. When an object exhibits radial motion relative to us, we detect a Doppler shift in its spectrum. If an object is moving towards us, its light will be blueshifted to shorter wavelength.
Incorrect. When an object exhibits radial motion relative to us, we detect a Doppler shift in its spectrum. If an object is moving towards us, its light will be blueshifted to shorter wavelength.

How do you determine the rotation speed of a galaxy? As a galaxy rotates, one side of the galaxy is moving towards us, while the other side is moving away. Cool hydrogen gas in the galaxy emits 21-cm radiation, but as the gas moves either towards us or away from us, the light it emits is Doppler shifted to either longer or shorter wavelength, a redshift or a blueshift. As we observe the total light from a galaxy, we see all of the light emitted from the hydrogen gas in the galaxy at the same time.

The animation above depicts a rotating spiral galaxy giving off light at 21 cm. The side moving towards us is blueshifted while the side moving away from us is redshifted. At the top of the animation is a slide that will allow you to adjust the rotation speed of the galaxy. Use the slider to change the speed such that the galaxy spins faster. Observe the effects on the spectral line. Then change the speed such that the galaxy spins slower.

Question 24.5

i4ogwQ6+eNYm2YGSpongGVoaK+Is/38/0olIXWfuIHJNJpfdNqOs0b5tGSkMDM5lTw5CYam5PyKvd0jgjexOm5s2bbK1Au5oEVS+zSx+S6IeQHW2DrHXk+phx6ztQEU7mc30YOxwGcyJfTco+ubeCM+e7tQqGkJE0T5brLTWrx1JR4wHggNCKWmn2f+NaP7RGAXxM1soqBYWiiErRcZGXr3CoXyHmMqPTOE2fWSS3VS63wKSJZZ+b2MGXWMGymoq6vYoVLWXbhDCeLgiFZwa3tRVdfiwQkiORjTiULcXueKeDQnVNIgUjtXXgnN6P8FWK7l3BQXqyeQ9oN4D44/0ZSfD4aJPBOQDTXqvqLUiRD8jCJ0aBcLMivjhhRPDpGcpkO7Q9qDqiue1NcthnNwxOeZFvljZdC+GpE0MypSYgwUMEqR1A38oJ111SW0Xa6xEyUu36hb+vBqSTGRN495RlKn555U=
3
Try again. Vary the rotation speed of the galaxy in the animation above and watch what happens to the observed emission line.
Correct. As the galaxy spins faster, the light from the sides of the galaxy are Doppler shifted more. Because some of the light is redshifted and some is blueshifted, the net result is a broadening of the spectral line.
Incorrect. As the galaxy spins faster, the light from the sides of the galaxy are Doppler shifted more. Because some of the light is redshifted and some is blueshifted, the net result is a broadening of the spectral line.

Summary

As you can see in the animation, by measuring the width of the 21-cm emission line from a galaxy, you can determine its rotational speed, which is highly correlated with its luminosity. But why are these two properties of a spiral galaxy related? Does it make sense that the luminosity of a galaxy should depend on its rate of rotation? It turns out that rather than one of these properties being caused by the other, they are both different "effects" of the same "cause". In other words, there is one property that influences both the luminosity and the rotation rate of a galaxy: mass. The more mass a galaxy has, the more light it gives off. Also, the more mass a galaxy has, the more gravity it exerts, causing objects within the galaxy to move faster. This is why the two properties are so well correlated, and why the Tully-Fisher relation is a good distance indicator, out to around 100 Mpc.

24.5 Faber-Jackson Relation

Elliptical galaxy
Elliptical galaxies don't spin, so astronomers found another method for measuring distances to these galaxies.

While the Tully-Fisher relation is useful in spiral galaxies, it cannot be used with elliptical galaxies, like M87 shown to the right, because ellipticals do not rotate in an orderly fashion. Stars orbit, but in a variety of directions and orientations. Fortunately, a similar method, known as the Faber-Jackson relation, can be used with them. Although elliptical galaxies do not rotate, the stars within them still have orbits through the galaxy. According to the Faber-Jackson relation, the total luminosity of an elliptical galaxy is correlated with the dispersion of velocities (deviations from the average velocity) of stars near the center of the galaxy; the greater the dispersion, the more luminous the galaxy. Therefore, by using the Doppler effect to measure the various speeds of the stars and determining how they deviate from the average motion, we can use the Faber-Jackson relation to determine the luminosity of the galaxy. Then, by measuring the galaxy's apparent brightness, we can use the inverse square law of light to determine its distance.

Question 24.6

0TOTWdD0Z8nz3VXki4dWd1tXpklUhuL4RyiJvjg+6smqCAvaspSP7J7vWtllZoYJ1TeZ3e6kS1iHbYytkIPPrHx4D5PWP4DlujsLihCSONgJhHexvvBljpTN/wDrjktP9h1TWjP+eBoiQf1CnRy74XsvbsdFoA5gaglB+NyOJOlqfaHhkrImSnZz7W58YOwjHxWP3jqs6O9eHPQQr9vCwKPqZiUmIkrUe2enKojFfcEKPYTl07+zkRxohh8EGldycEGrRaAdF6/4FYqqR3W8qEV0lRROr/WmC2GLh47ZKinF2TJie0kwtg==
3
Try again. Remember, the mass of a galaxy determines its gravitational influence, which controls many of its properties.
Correct. As in spiral galaxies, the mass of an elliptical galaxy directly influences its total luminosity. It also influences the speeds at which the stars with the galaxy move, causing a correlation between these two properties.
Incorrect. As in spiral galaxies, the mass of an elliptical galaxy directly influences its total luminosity. It also influences the speeds at which the stars with the galaxy move, causing a correlation between these two properties.

24.6 Type Ia Supernovae

Type Ia Supernova
In 2006, a Type Ia Supernova was detected in M100, shown here before and after the event. (The two images were taken with different filters, hence the color difference).

One of the most useful distance indicators for galaxies is the Type Ia Supernova. A Type Ia supernova occurs when a white dwarf in a binary system funnels material off of its binary companion, causing it to gain mass until eventually it exceeds the Chandrasekhar limit of 1.4 solar masses. At this mass limit, the white dwarf's electron degeneracy pressure can no longer balance the inward force of gravity, and the white dwarf explodes. Because all white dwarfs explode at the same mass limit, their explosions are very similar, causing their light curves (a plot of light intensity as observed from Earth over time) to be remarkably similar as well. A typical light curve for a Type Ia supernova is shown below. Specifically, all Type Ia supernovae peak at around the same luminosity. Just observe a Type Ia supernova event at its peak of maximum emission, and it can be used as a distance indicator. Because Type Ia supernovae are so luminous, they can be observed at great distances, out to 1 Gpc, 1 billion parsecs away.

Light Curve for a type Ia supernova
Light Curve for a type Ia supernova (http://www.cortinastelle.it/)

Question 24.7

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3
Try again. Remember that 1 Gpc is equal to 109 pc. The log of a number written as a power of 10 is simply equal to the exponent (for example: log 106 = 6).
Correct. Plugging in M = -20 and d = 109, we get: m = M + 5log(d) - 5 = -20 + 5(9) - 5 = +20. This is the threshold limit of a 1-meter class telescope, and would be observable with the Hubble Space Telescope.
Incorrect. Plugging in M = -20 and d = 109, we get: m = M + 5log(d) - 5 = -20 + 5(9) - 5 = +20. This is the threshold limit of a 1-meter class telescope, and would be observable with the Hubble Space Telescope.

24.7 Standard Candles

Many of the objects we've featured in this activity are useful distance indicators because, at least at one point in their evolution, they have a well-known luminosity. We call objects like these standard candles. If you can observe a standard candle at the moment in its life when we know its luminosity and also determine its apparent brightness, then you can use the inverse square law of light to determine the distance to that object, as well as the galaxy in which it resides.

In order for a standard candle to be effective, it must satisfy a number of criteria. First, it should be luminous, so that it may be observed as far away as possible. Second, its luminosity must be very well known, at least at one point in its life, so that it may yield an accurate distance measurement. Third, it must be easy to observe. In other words, it can't look like every other star in the galaxy. It must stand out, either by how its light varies over time, or in some other manner. Finally, it should be common enough that we can find them in other galaxies so that we can measure their distances. Given all of these criteria, some standard candles can be used to measure distances much further away than the methods already discussed. Astronomers have found that the following objects can be used as standard candles: variable stars, eclipsing binaries, stars that lie in the tip of the red giant branch on the H-R diagram, planetary nebulae, globular star clusters, and X-ray bursters.

The animation above depicts three galaxies at various distances from Earth. Each one has a distance indicator present. Hover over each galaxy and see happens and how astronomers can determine each galaxy's distance.

Question Sequence

Question 24.8

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3
Try again. Click on the galaxies in the animation above again to see which one is furthest away.
Correct. Galaxy B represents a galaxy in the Coma cluster, almost 100 Mpc away from us.
Incorrect. Galaxy B represents a galaxy in the Coma cluster, almost 100 Mpc away from us.

Question 24.9

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3
Try again. Click on galaxy B again to see what information we are able to gather from it.
Correct. In this galaxy, a star was observed to explode in a Type Ia supernova event. By measuring its apparent brightness at the moment of its peak luminosity, we were able to determine its distance.
Incorrect. In this galaxy, a star was observed to explode in a Type Ia supernova event. By measuring its apparent brightness at the moment of its peak luminosity, we were able to determine its distance.

24.8 Uncertainty Grows with Distance

A problem arises when using these various techniques to measure distances to galaxies very far away. In general, the greater the distance to an object, the more uncertainty there is in the measurement. The reason is that the accuracy of a distant measurement depends on the accuracies of measurements to closer objects. For example, if you remember the story of Henrietta Leavitt, when she first studied Cepheid Variables in the Small Magellanic Cloud, she was only able to determine their apparent brightnesses, and compare those values to their periods of variation. How did astronomers determine their luminosities? To do so, they had to use another distance measurement technique (for example, spectroscopic parallax). Any uncertainty in this method would create an uncertainty in the measured distances to the Cepheid variables used to calculate their luminosities, which in turn would create an uncertainty in the period-luminosity relationship.

How did Tully & Fisher determine the luminosities of galaxies in order to correlate this value with their rotation rates? They knew the distances to nearby galaxies, which were determined using observations of Cepheid variables and in some cases Type Ia supernovae. Any uncertainty in these measurements created an uncertainty in the Tully-Fisher relation.

Question 24.10

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
3
Try again. The error in the measurements is compounded. Look at the extremes in the distance to the first galaxy and determine how that would affect the distance measured to the second galaxy. For example, if the distance to the first galaxy is only 0.9 Mpc, and the second galaxy is only 90 times farther away, at what distance does it lie?
Correct. Let's look at the two extremes. First, what if both measurements are 10% shorter than measured. The first galaxy would lie only 0.9 Mpc away, and the second galaxy would be 90 times farther, or 81 Mpc. If both measurements are 10% farther than measured, then the first galaxy would lie 1.1 Mpc away, and the second galaxy would be 110 times farther, or 121 Mpc. Because the second measurement depends on the accuracy of the first measurement, its error is larger.
Incorrect. Let's look at the two extremes. First, what if both measurements are 10% shorter than measured. The first galaxy would lie only 0.9 Mpc away, and the second galaxy would be 90 times farther, or 81 Mpc. If both measurements are 10% farther than measured, then the first galaxy would lie 1.1 Mpc away, and the second galaxy would be 110 times farther, or 121 Mpc. Because the second measurement depends on the accuracy of the first measurement, its error is larger.

Summary

As you can see, the farther away an object is, the more uncertain we are of its exact distance. Because one distance measurement technique depends on the accuracy of previous techniques, we call this series of distance measurement the Distance Ladder, since you need to be able to measure distances to closer objects before you can measure distances to farther objects.

In one of the other activities associated with this chapter, we will investigate the top step of the distance ladder: Hubble's Law. This relationship between the apparent recessional velocity of a galaxy and its distance is the method astronomers use to measure distances to the most distance objects in our universe.

24.9 Quick Check Quiz

Indepth Activity: The Distance Ladder

Question 24.11

E9L6CHC6e0maKHi/SvFIcn7aMWHOIgFPbFu6+1yzOCySOcahjmkEpyzMj2Kfu6QUvB06Er34exj57rp2vft2U28Sv7sDzrbpQzO5mjjxJhBy+Z8Pv5B+XFoxts0e82gf9chwvXJnr++MT9Px6vBFoo4Tsp9cLGSi2G8qzbCAf0VRkIjhZPjbewb8Z8p0RkTGkHBxf/xv+A80//XV1CsT2uzsZezN0HaqmDUzsib2HuAe3OvUF8iN7fOdMVKXOmtXjZSGL7mp+Yk7Z+QPFWzoDQDjWykjcJeKqDIgdwkIPvOqppoNEVr2NhZPAyRL4rPjnklYOG2+DDr8i7skSvtSZ9Sw8SOqgLBU/OwmGdDr0Cp17UUMwGudEGxTV5NCReJW9rlIAhFJZK2GgF/3VHh4tKbW/ngQbFABNHXda+ig8QSnIld+MsCydlZ+5HERHLYuEnPQOxF9E34=
Correct.
Incorrect.

Question 24.12

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
Correct. In order to determine the distance to a spiral galaxy, we need to be able to determine its rotation rate, which we cannot do if, as it rotates, parts of it are not moving towards us or away from us.
Incorrect. In order to determine the distance to a spiral galaxy, we need to be able to determine its rotation rate, which we cannot do if, as it rotates, parts of it are not moving towards us or away from us.

Question 24.13

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Correct. While we cannot use the Tully-Fisher relation to determine the distances to spiral galaxies, we can use the Faber-Jackson relation to do so.
Incorrect. While we cannot use the Tully-Fisher relation to determine the distances to spiral galaxies, we can use the Faber-Jackson relation to do so.

Question 24.14

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Correct. Because the distance measurements of distant galaxies rely on the accuracy of distance measurements to closer galaxies, the error in measurements increases with distance.
Incorrect. Because the distance measurements of distant galaxies rely on the accuracy of distance measurements to closer galaxies, the error in measurements increases with distance.

Question 24.15

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Correct. Type Ia supernovae can be observed as far away as 1 Gpc.
Incorrect. Type Ia supernovae can be observed as far away as 1 Gpc.

Question 24.16

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Correct. The Tully-Fisher relation demonstrates that the rotation speed of a galaxy and its total luminosity are highly correlated, due to the fact that both are affected by the mass of the galaxy.
Incorrect. The Tully-Fisher relation demonstrates that the rotation speed of a galaxy and its total luminosity are highly correlated, due to the fact that both are affected by the mass of the galaxy.

Question 24.17

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Correct. Cepheid Variables are stars that change in brightness, and the longer it takes a Cepheid to complete one cycle, the more luminous it is.
Incorrect. Cepheid Variables are stars that change in brightness, and the longer it takes a Cepheid to complete one cycle, the more luminous it is.

Question 24.18

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Correct. All Type Ia supernovae have essentially the same peak luminosity.
Incorrect. All Type Ia supernovae have essentially the same peak luminosity.

Question 24.19

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Correct. Measurements only need to be taken at one point in the object's life in order to use it as a standard candle.
Incorrect. Measurements only need to be taken at one point in the object's life in order to use it as a standard candle.

Question 24.20

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Correct. Because Cepheid X has a longer period, it is also more luminous. Since the two Cepheids are the same distance away, the more luminous one appears brighter.
Incorrect. Because Cepheid X has a longer period, it is also more luminous. Since the two Cepheids are the same distance away, the more luminous one appears brighter.