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1

John gave a nice explanation of what we mean by "expansion", "acceleration" etc. as it concerns cosmology. I just wanted to connect this a bit more to what you're describing. It seems natural to beginners to associate $H$ with the "expansion rate", however this is not totally accurate and it often leads to confusion like this. ...

2

We describe the expansion of the universe with a scale factor that we conventionally call $a$. We take $a=1$ right now, so if in the future the universe has doubled in size that means $a=2$, or if we look back to a time when in the past when the universe was half the size $a = \tfrac12$. To understand what this scale factor means we can relate it to any ...

0

The average temperature of the Earth is the result of a radiative balance--the Sun adds energy, and the Earth radiates energy at the same average rate (call that rate the power $P$). Approximating the Earth as a blackbody, the Stefan-Boltzmann law says: $$P \propto T^4$$ If you increase $P$ by a small amount $dP$ and call the resulting increase in ...

1

It isn't a convolution, you are just integrating the product. I.e. if your (normalised) filter bandpass is $b(\lambda)$ and the spectral flux from the star is $f(\lambda)$, then the thing you are trying to calculate is a magnitude, which will be given by $$m_b = -2.5 \log_{10}\left[ \int b(\lambda) f(\lambda)\ d\lambda \right] + 2.5\log_{10} f_0 ,$$ where ...

1

The definition of the magnitude $M$ is such that smaller values correspond to brighter objects. Hence, the larger the luminosity $L$ the smaller the absolute magnitude $M$.

3

The $G$ magnitude is the apparent magnitude of the star seen through the broadest of the Gaia photometric bandpasses. The Gaia photometric band is much broader than a $V$ filter, so although $G$ and $V$ are monotonically related, the difference between the two does depend on the intrinsic colour/spectral type of the star and the extinction-related reddening ...

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