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2

Judging by the fact that after cubing the distance you have ended up with an exponent of 1021 (21 = 6×3+3) at the first point you have substituted the numbers into the equation, you appear to be assuming that 1 km3 is 1000 m3. However, if you write the same linear quantity in metres and kilometres and cube them, you can see this is not ...


5

Here's how I would do it. I'd convert everything to a single, standard set of units as recommended in the comments, and also stick to one digit before the decimal in scientific notation: $$ T^2=\frac{4\pi^2r^3}{G\cdot M_{Sun}}$$ Using all numbers in the same units: $r \ 4.5 \times 10^{11} \ (m) $ $G = 6.674 \times 10^{-11} \ (m^3 \ kg^{-1} s^{-2}) $ $M ...


6

According to Oxford Dictionary of English, the word "modulus" is the diminutive of the Latin modus, meaning measure (modus, in turn, comes from Proto-Indo-European mod-os, Nocentini & Parenti 2010. Hence, the distance modulus is a "measure of distance", just like the modulus of a vector is a way of measuring its size, and Young's modulus is a way of ...


5

The axis type ‘FELO’ is regularly gridded in frequency but expressed in velocity units in the optical convention. The unit here is $m/s$. This means that the wavelength/frequency has already been expressed as velocity corresponding to a Doppler shift around a reference wavelength. This velocity is given by $$ v = c \ \frac{\lambda - \lambda_0}{\lambda_0 ...


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