Module 9 / Lecture 1 : Apparent Brightness, Luminosity, and Distance

Summary

This lecture covers the concepts of apparent brightness, luminosity, and distance of stars. It explains that a star's apparent brightness is how bright it appears to us, while luminosity is the total power it emits. The relationship between distance and brightness is described using the inverse square law. The magnitude system is introduced, including both apparent and absolute magnitudes, to compare stars' brightness. Stellar parallax is discussed as a method to measure star distances, which in turn helps determine their luminosity. Further topics like stellar temperature and mass will be covered in future lectures.

Takeaways

• 🌟 Apparent brightness and luminosity are two different things; brightness is how we perceive a star, while luminosity is the total light it emits.
• 🌍 The apparent brightness of a star depends on its distance and the amount of light it emits.
• 🔭 Example: Betelgeuse appears as bright as Procyon, though Betelgeuse emits much more light because Procyon is much closer.
• 💡 Apparent brightness is measured as the amount of power reaching us per square meter.
• 🔆 Luminosity refers to the total energy a star radiates into space.
• 📏 The inverse square law governs how apparent brightness diminishes with increasing distance.
• 🔢 The magnitude system classifies stars based on their apparent brightness; higher magnitudes indicate dimmer stars.
• 🌙 Objects brighter than magnitude zero have negative values; for instance, the full Moon has an apparent magnitude of -13.
• 🧑‍🚀 Parallax is a method used to determine the distance of nearby stars by measuring their apparent shift in position over six months.
• 📐 The distance to a star in parsecs can be calculated using its parallax angle in arcseconds.

Q & A

What is the difference between apparent brightness and luminosity?

Apparent brightness is how bright a star appears from Earth, while luminosity is the total amount of power a star emits into space.

Why do some stars appear brighter than others in the night sky?

The brightness of a star in the night sky depends on both its luminosity and its distance from Earth. A star may appear bright because it is very luminous or because it is close to Earth.

What example does the lecture give to explain the difference in brightness and luminosity?

The lecture compares Procyon and Betelgeuse, which appear equally bright in the sky, but Betelgeuse emits 15,000 times more light than Procyon because it is much farther away.

How is apparent brightness defined?

Apparent brightness is defined as the amount of power reaching us per unit area, or per square meter.

What is the inverse square law of light?

The inverse square law of light states that the apparent brightness of a light source is inversely proportional to the square of its distance from the observer.

How does the lecture illustrate the inverse square law of light?

The lecture uses an example of counting photons on imaginary spheres around a star. Moving to a sphere twice as far away means each square meter receives only a quarter of the light.

What is the magnitude system and who developed it?

The magnitude system classifies stars based on their apparent brightness and was developed by the Greek astronomer Hipparchus over 2000 years ago.

How do astronomers denote apparent and absolute magnitudes?

Apparent magnitudes are denoted with a lower-case 'm' and absolute magnitudes with an upper-case 'M'.

What is the relationship between apparent magnitude numbers and brightness?

A larger number for apparent magnitude means a dimmer apparent brightness. For example, a star of apparent magnitude 4 appears dimmer than a star of magnitude 1.

What is stellar parallax and how is it used to measure distances?

Stellar parallax is the apparent shift in position of a nearby star against the background of distant stars, observed from two points in Earth's orbit. The parallax angle is used to calculate the star's distance.

How is the distance to a star related to its parallax angle?

The distance to a star in parsecs is equal to 1 divided by the parallax angle in arcseconds. For example, a star with a parallax angle of 0.5 arcseconds is 2 parsecs away.

Why couldn't ancient Greeks measure stellar parallax?

Ancient Greeks couldn't measure stellar parallax because even the nearest stars have parallax angles smaller than 1 arcsecond, which is below the angular resolution of the human eye.

Outlines

00:00

✨ Apparent Brightness, Luminosity, and Distance

This paragraph introduces the concepts of apparent brightness, luminosity, and distance in astronomy. It begins by explaining that the brightness of stars in the sky varies and that this does not necessarily indicate how much light they are generating, as it also depends on their distance from Earth. For instance, Procyon and Betelgeuse appear similarly bright, even though Betelgeuse emits far more light, because Procyon is much closer. Apparent brightness refers to the power reaching us per unit area, while luminosity is the total power a star emits into space. The relationship between these quantities follows the inverse square law, where apparent brightness decreases with the square of the distance from the light source. The paragraph also discusses how apparent brightness and luminosity are related, noting that while apparent brightness is easily measured from Earth, determining the distance to a star is often more challenging. The concept of the magnitude system, introduced by the Greek astronomer Hipparchus, is used to classify stars based on their brightness, with lower magnitudes corresponding to brighter stars. Additionally, the modern magnitude system distinguishes between apparent magnitude (brightness as seen from Earth) and absolute magnitude (brightness as it would appear from 10 parsecs away).

05:04

📏 Measuring Stellar Distances with Parallax

This paragraph explains how astronomers measure the distances to nearby stars using stellar parallax. Parallax is the apparent shift in a star's position when observed from two different points in Earth's orbit, six months apart. This shift occurs because of the different viewpoints. The parallax angle, denoted by p, is half the star's total shift over a year, and it becomes smaller as the star's distance increases. The nearest stars have parallax angles less than 1 arcsecond, too small to be detected by the human eye. The distance to a star in parsecs can be calculated by taking the reciprocal of the parallax angle in arcseconds. For example, a star with a parallax angle of 0.5 arcseconds is 2 parsecs away. Once the distance is known, astronomers can calculate the star's luminosity using its apparent brightness. This method allows astronomers to determine the intrinsic brightness of a star. The paragraph concludes by mentioning that future lectures will cover how astronomers measure stellar temperature and mass.

Keywords

💡Apparent Brightness

Apparent brightness refers to how bright a star or light source appears to an observer from Earth. It is measured as the amount of power per unit area reaching us. The script explains that a star's apparent brightness can be deceiving because it depends on both the star’s luminosity and its distance from Earth, as illustrated with the stars Procyon and Betelgeuse.

💡Luminosity

Luminosity is the total amount of power or light a star emits into space. It reflects the intrinsic brightness of a star, independent of distance. In the video, luminosity is distinguished from apparent brightness by showing that stars like Betelgeuse, though appearing as bright as Procyon, actually emit far more light.

💡Inverse Square Law

The inverse square law describes how the apparent brightness of a light source decreases with the square of the distance from the observer. As you move further away from a star, the light spreads out over a larger area, reducing its apparent brightness. The script uses the example of counting photons at different distances to illustrate this concept.

💡Magnitude System

The magnitude system is a way of classifying stars based on their brightness. Originating from the ancient Greek astronomer Hipparchus, it ranks stars by apparent brightness. Stars with lower magnitudes are brighter, while higher magnitudes indicate dimmer stars. The system is now used to describe both apparent and absolute magnitudes.

💡Apparent Magnitude

Apparent magnitude refers to how bright a star appears from Earth, denoted by a lowercase 'm'. The scale is such that lower numbers indicate brighter stars, with negative values representing extremely bright objects like the Moon. The video mentions how apparent magnitude was historically based on human visual perception but is now more precisely defined.

💡Absolute Magnitude

Absolute magnitude is a measure of a star's luminosity, defined as the apparent magnitude a star would have if it were 10 parsecs away from Earth. This concept helps compare the intrinsic brightness of stars. For example, the Sun’s absolute magnitude is 4.8, even though its apparent magnitude is much brighter due to its proximity.

💡Parsec

A parsec is a unit of distance used in astronomy, equivalent to about 3.26 light-years. It is defined by the distance at which a star would have a parallax angle of 1 arcsecond. The video introduces parsecs when discussing stellar distances, showing how they are calculated using parallax angles.

💡Stellar Parallax

Stellar parallax is the apparent shift in the position of a nearby star when observed from two different points in Earth’s orbit, six months apart. By measuring this shift, astronomers can calculate the star’s distance. The script explains how parallax angles help determine the distances to stars, which are essential for calculating luminosity.

💡Parallax Angle

The parallax angle is the angle that represents the shift in a star’s position due to stellar parallax. It is half of the total shift observed over a year. The script explains how smaller parallax angles correspond to greater distances, making it more challenging to measure distant stars.

💡Photons

Photons are particles of light. In the script, they are used to explain the inverse square law, showing that as you move further from a light source, fewer photons pass through a given area, which decreases the apparent brightness. This concept is central to understanding how light spreads out over distance.

Highlights

The difference in a star's apparent brightness does not directly indicate how much light it emits, as distance affects its perceived brightness.

Procyon and Betelgeuse appear equally bright in the sky, but Betelgeuse emits 15,000 times more light; Procyon appears bright because it's much closer.

Apparent brightness is the amount of power (light) reaching us per unit area, measured in watts per square meter.

Luminosity refers to the total amount of power a star emits into space, independent of its distance from Earth.

The inverse square law of light explains that apparent brightness decreases with the square of the distance from the source.

Apparent brightness equals luminosity divided by 4π times the distance squared.

The magnitude system, developed by Greek astronomer Hipparchus, classifies stars based on how bright they appear to the human eye.

Apparent magnitudes (denoted by 'm') describe how bright a star appears, with larger magnitudes indicating dimmer stars.

Absolute magnitude (denoted by 'M') refers to a star's brightness if it were located at a standard distance of 10 parsecs from Earth.

The Sun's apparent magnitude is -27, but its absolute magnitude is 4.8 if it were placed 10 parsecs away.

Stellar parallax is the apparent shift in the position of a nearby star relative to distant stars due to Earth's orbital motion.

A star’s parallax angle (p) is half of its apparent annual shift, with smaller parallax angles indicating greater distances.

The distance to a star in parsecs can be calculated as the inverse of its parallax angle in arcseconds (distance = 1/p).

Stars with parallax angles smaller than 1 arcsecond are too distant for the human eye to detect without telescopic assistance.

If a star's distance and apparent brightness are known, its luminosity (intrinsic brightness) can be determined.

Transcripts

This lecture is all about apparent brightness, luminosity, and distance.

We'll begin with apparent brightness and luminosity.

If you go outside on any clear night, you'll immediately see that some stars are brighter

than other stars.

The difference in brightness does not by itself tell us anything about how much light these

stars are generating, because the brightness of a star depends on its distance as well

as on how much light it actually emits.

For example, the stars Procyon and Betelgeuse appear about equally bright in our sky, but

Betelgeuse emits about 15,000 times as much light as Procyon.

Procyon appears as bright because it's over 50 times closer.

Because two similar-looking stars can be generating very different amounts of light, we need to

distinguish clearly between a star's brightness in our sky and the actual amount of light

that it emits into space.

A star's apparent brightness is how it appears to our eyes.

We define apparent brightness as the amount of power reaching us per unit area, or per

square meter.

Luminosity is the total amount of power that a star emits into space.

When we talk about how bright stars are in an absolute sense, regardless of their distance,

we're talking about luminosity.

For example, a 100-watt light bulb always puts out the same amount of light.

Its luminosity doesn't vary.

But its apparent brightness will depend on how far away you are from the bulb.

The apparent brightness of a star, or any light source obeys an inverse square law with

distance, much like the inverse square law for the force of gravity.

In equation form, the inverse square law of light says that the apparent brightness equals

luminosity over four pi times the distance squared.

Consider this figure.

The same a total amount of light must pass through each imaginary sphere surrounding

the star.

Pretend you're standing on the first sphere.

You draw a square meter on its surface and you count the number of photons that pass

through your square each second.

Let's say you measure 4 photons.

Now move to the sphere that is twice as far away and draw a square the same size.

If you count the number of photons that pass through this square, you'll only count 1.

Because of the inverse square law, the light spreads out.

Each square on the sphere twice as far away receives only a quarter of the light as the

square on the first sphere.

A star's luminosity depends on apparent brightness and distance.

In most cases we can easily measure apparent brightness from Earth.

The distance is often more difficult to determine, but we need it if we want to determine luminosity.

We'll discuss distance measurements in just a bit.

To describe apparent brightness and luminosity, we use what is called the magnitude system.

It was developed by the Greek astronomer Hipparchus over 2000 years ago.

The magnitude system originally classified stars based on how bright they look to human

eyes.

The brightest stars were called "first magnitude", the next brightest "second magnitude" and

so on.

The faintest visible stars were magnitude 6.

These descriptions are called apparent magnitudes because they compare how bright different

stars appear in the sky.

We denote apparent magnitudes with a lower-case m.

The magnitude scale is such that a larger number for apparent magnitude means a dimmer

apparent brightness.

A star of apparent magnitude 4 appears dimmer in the sky than a star of magnitude 1.

Objects brighter than magnitude zero go negative.

For example the full Moon has an apparent magnitude of minus 13.

The original magnitude scale was based on the human eye.

Astronomers use a more precisely defined system today.

The modern magnitude system also defines absolute magnitudes as a way of describing stellar

luminosities.

A star's absolute magnitude is the apparent magnitude it would have if it were at a distance

of 10 parsces for Earth.

We denote absolute magnitudes with an upper-case M.

For example, the Sun's apparent magnitude - how bright it appears to us is minus 27.

If we were to move the Sun 10 parsecs away, it would appear dimmer and we would measure

an apparent magnitude of 4.8.

Therefore, the absolute magnitude of the Sun is 4.8.

Remember, if we want to get at luminosity, we need to know distance.

The most direct way to measure a stars distance is with stellar parallax.

We'll discuss other methods of determining distance later in the semester.

You may recall that parallax is the apparent shift in position of a nearby object against

the background of more distant objects.

Astronomers measure stellar parallax by comparing observations of a nearby star made six months

apart.

A nearby star will appear to shift against the background of more distant stars because

we are observing it from two points of Earth's orbit.

We can calculate a star's distance if we know the precise amount of the star's annual shift

due to parallax.

This means measure the angle p, which we call the star's parallax angle.

Note that p is equal to half the star's annual back and forth shift.

The farther the star is, the smaller the parallax angle becomes.

Therefore more distant stars have smaller parallax angles.

Even the nearest stars to us have parallax angles smaller than 1 arcesecond, well below

the angular resolution of the human eye.

This is why ancient Greeks were never able to measure parallax.

By definition, the distance to an object with a parallax angle of 1 arcsecond is 1 parsec.

If we use units of arcseconds for the parallax angle, p, the distance in parsecs is simply

1 over the parallax angle.

For example, for a star with a parallax angle of one-half of an arcsecond, the distance

is two parsecs.

Remember, if you know a star's distance you can determine its luminosity.

For a star you have measured the parallax angle for, you can calculate the distance,

and then you can measure the apparent brightness.

You have everything you need to determine luminosity- the intrinsic brightness of the

star.

That's all for now.

We'll learn how astronomers measure stellar temperature and mass in the next lecture.

Take care, I'll talk to you soon.