# What is the mathematical relationship of brightness and distance

### Luminosity and Apparent Brightness | Astronomy Planets, Stars, Galaxies, and the Universe

The relationship between the intensity of light at different distances from the same light source can be found by dividing one from the other. The formula for this is. The inverse square law. As the distance increases, the amount of light decreases by a factor of the square of the distance. brightness of light varies with distance from the source and compare that result Determine the mathematical relationship between intensity and distance from a.

However, you and your partner should switch roles so that everyone gets a chance to do every measurement. When you make measurement, hold the null-photometer between the lights, and move it back and forth along an imaginary line between them until both halves of the photometer's window appear the same. Your partner can check to make sure the photometer really is on a line between the two lights, and then measure the distances Da and Db.

Ideally, these distances should be measured from the center of each light-bulb to the nearest side of the photometer, as shown in the diagram. Once both distances have been recorded, flip the photometer over so the left face is now the right face, and vice versa. Re-position the photometer between the lights, move it so both halves appear the same, and again measure the distances. Repeat two more times, again flipping the photometer each time. You should now have four separate measurements of the two distances.

Each set of four measurements can be averaged to get a more precise value; you can also look at the range of values for each measurement to get some idea of the accuracy of your work. Before moving on to the next pair of lights, be sure to record the luminosities La and Lb. When you write up your lab report, first compute averages for your measurements of Da and Db for each pair of lights. If the last two columns of each row are equal, allowing for experimental error, then the inverse-square law passes the test.

Measuring luminosity The same procedure can be used to measure the luminosity of a light-bulb. We will set up a pair of lights and tell you the luminosity of one light; your job is to calculate the luminosity of the other.

Follow the same procedure you used when testing the law: Record your measurements for Da and Db, along with the known luminosity La. When you write up your lab report, compute averages for your measurements of Da and Db just as you did when testing the law. Then plug your averages and the known luminosity La into the equation In astronomy, we sometimes know the distance to a star but not its luminosity. A measurement like this can be used to find the star's luminosity.

## Luminosity and Apparent Brightness

Measuring distance A similar procedure can be used to measure an unknown distance, given the luminosities of both light-bulbs. We will set up one last pair of lights and tell you both luminosities.

Once again, repeat another three times, flipping the photometer each time. Record your measurements for Da, along with the given luminosities La and Lb. When you write up your lab report, compute averages for your measurements of Da, and plug your result into the equation In astronomy, stars come in a range of luminosities, and we can sometimes figure out the luminosity by measuring the star's color.

So, everyone will measure a different apparent brightness for the same star if they are all different distances away from that star. For an analogy with which you are familiar, consider again the headlights of a car. When the car is far away, even if its high beams are on, the lights will not appear too bright.

However, when the car passes you within 10 feet, its lights may appear blindingly bright.

To think of this another way, given two light sources with the same luminosity, the closer light source will appear brighter. However, not all light bulbs are the same luminosity. If you put an automobile headlight 10 feet away and a flashlight 10 feet away, the flashlight will appear fainter because its luminosity is smaller.

Stars have a wide range of apparent brightness measured here on Earth. The variation in their brightness is caused by both variations in their luminosity and variations in their distance. These are related through the inverse square law of brightness described above. At a particular Luminosity, the more distant an object is, the fainter its apparent brightness becomes as the square of the distance.

### Brightness and Distance

Appearances can be deceiving Does a star look "bright" because it is intrinsically very luminous? To know for sure, you must know either the distance to the star, or some other, distance-independent property of the star that clues you in. Measuring Apparent Brightness The process of measuring the apparent brightnesses of objects is called Photometry. Two ways to express apparent brightness: Stellar Magnitudes Absolute Fluxes energy per second per area Both are used interchangeably by astronomers.

Magnitude System Traditional system dating from classical times, invented by Hipparchus of Nicaea, c. Rank stars into "magitudes":

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