B Variation of Apparent Luminosity with Distance

AI Thread Summary
Apparent luminosity is measurable and varies with distance, which can be determined using parallax methods. The relationship between true luminosity and distance is expressed as ##A_X = \frac{T_X}{D_X^2}##, indicating that apparent luminosity decreases with the square of the distance from the observer. This means true luminosity can be calculated using the formula ##T_X = A_X \times D_X^2##. Additionally, if two objects have the same apparent luminosity, their distances can be compared using the ratio of their true luminosities. Understanding these relationships is crucial for accurately assessing the luminosity and distance of celestial objects.
Agent Smith
Messages
345
Reaction score
36
True luminosity of object X = ##T_X##
Apparent luminosity object X = ##A_X##
Distance of object X from observer = ##D_X##
True luminosity of object Y = ##T_Y##
Apparent luminosity of object Y = ##A_Y##
Distance of object Y from observer = ##D_Y##

Apparent luminosity is something measurable I suppose. Distance is measured by means that don't depend on luminosity (parallax?)

Assuming ##A_X = \frac{T_X}{D_X}## and ##A_Y = \frac{T_Y}{D_Y}##

So we can find ...
1. True luminosity: ##T_X = A_X \times D_X## and ##T_Y = A_Y \times D_Y##
2. The relative distance of luminous objects: Assuming ##A_X = A_Y##, we have ##\frac{D_X}{D_Y} = \frac{T_X}{T_Y}##
 
Astronomy news on Phys.org
Agent Smith said:
Distance is measured by means that don't depend on luminosity (parallax?)
https://en.wikipedia.org/wiki/Cosmic_distance_ladder
Agent Smith said:
Assuming ##A_X = \frac{T_X}{D_X}## and ##A_Y = \frac{T_Y}{D_Y}##
No, the measured luminosity drops with the square of distance. The light emitted in a short time period forms an expanding sphere around the source. The total energy of the light is constant, but spread over the area of the sphere which grows with the square of distance.
 
  • Like
Likes berkeman and Agent Smith
So ##A_X = \frac{T_X}{D_X {^2}}##. So I'd be underestimating the true luminosity.
 
Today at about 4:30 am I saw the conjunction of Venus and Jupiter, where they were about the width of the full moon, or one half degree apart. Did anyone else see it? Edit: The moon is 2,200 miles in diameter and at a distance of 240,000 miles. Thereby it subtends an angle in radians of 2,200/240,000=.01 (approximately). With pi radians being 180 degrees, one radian is 57.3 degrees, so that .01 radians is about .50 degrees (angle subtended by the moon). (.57 to be more exact, but with...
This thread is dedicated to the beauty and awesomeness of our Universe. If you feel like it, please share video clips and photos (or nice animations) of space and objects in space in this thread. Your posts, clips and photos may by all means include scientific information; that does not make it less beautiful to me (n.b. the posts must of course comply with the PF guidelines, i.e. regarding science, only mainstream science is allowed, fringe/pseudoscience is not allowed). n.b. I start this...
Back
Top