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How to Find Distance Using Cepheids

Astronomers use a technique termed parallax to determine the distance of stellar objects from Earth. The parallax technique is only effective within about 200 parsecs. A parsec is equivalent to 3.26 light years. To grasp the magnitude of a light year, you need to know that the Sun is approximately 91 million miles (91 X 10^6) from Earth, and light travels from the Sun to the Earth in about eight minutes. One light year is 65,700 minutes, so that yields that a light year represents approximately 6 X 10^12 miles. To measure distances beyond the 200-parsec limit of the parallax technique, astronomers use Cepheids. Cepheids are pulsating stars. A Cepheid from the same region of space as other stellar objects of interest will act as a reference to determine the distance of those stellar objects from Earth. The brightness and period of pulsation allow the use of the distance-modulus formula to calculate their relative distance.

Instructions

- 1
  Observe a section of space with a telescope until you find a Cepheid. Due to the distances involved and the dimness of these stars, most astronomers use photographic plates or photoelectric CCD devices to capture the light images.
- 2
  Isolate the Cepheid of interest and monitor it over time until you can distinguish the period of pulsation. Periodicity of pulsation can range from just a few days to as long as approximately 100 days. By plotting the luminosity of the Cepheid over time, you can visually distinguish a pattern of increasing intensity of brightness followed by a decrease in intensity. This rise and fall of intensity defines the periodicity of pulsation. To quantify the period, measure the time between peaks or troughs of two consecutive peaks or troughs.
- 3
  Estimate a Cepheid’s apparent luminosity based on its brightness or intensity on photographic films or photoelectric CCD images. The difference between apparent luminosity and the absolute luminosity allows the distance to be calculated. Determine the apparent luminosity of the Cepheid by taking the average luminosity over time.
- 4
  Determine the Cepheid’s absolute brightness from the period-luminosity plots that have existed since 1912. Initial plots for Cepheids within the Milky Way galaxy provided the basis for plots. The parallax technique is usable for many of these Cepheids and serve as a check of the validity of the plots. Over the years since its discovery, further verification and refinement of the plots has occurred.
- 5
  Plug in the values of the absolute brightness (M) and the apparent brightness (m) to the distance-modulus formula to calculate the distance (D). The formula reports distance in parsecs. For example, assume that the apparent brightness of a Cepheid is 15 (based on a period of 4.76 days) and the absolute brightness of -3.57 (from the period-luminosity plot). The distance-modulus formula is D = 10^ (m – M + 5) / 5. Substitute the values given into the formula to find the distance of the object from Earth in parsecs. D = 10^ (15 – (-3.57) +5) / 5. D = 10^ (23.57/5). D = 10^ (4.71). The distance of the Cepheid is 51,760 parsecs away, which is 168,740 light years away.

Astronomy