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Martin Hoecker-Martinez's Answer is correct for perfectly noiseless observations of a two body Kepler system, i.e. the force between the bodies is directed along the vector linking them and the force magnitude follows and inverse square law with distance. An alternative to Martin's answer is that perfectly known position and velocity will determine all ...

10

An ideal Kepplerian orbit is defined by six (6) parameters: angular momentum (3) total energy (1) Laplace–Runge–Lenz vector which is perpendicular to angular momentum (2) Therefore you need at least six (6) independent observations. Astronomical observations are direction (but not range usually) given by a pair (2) of angles therefore three (3) ...

5

$G$ was historically calculated from the Cavendish experiment, involving balls and a torsion balance. The earth's mass was actually calculated before the sun's mass. Using the assumption that the earth was a sphere, its circumference and thus its radius could be determined through geodesy, as was done historically even before Newton. The acceleration of an ...

4

The little $h$ is a historical artifact, one that will probably die out soon enough. The thing is, $H_0$ was extremely difficult to measure precisely for many decades after its importance was realized. At some point, cosmologists were divided between the "$H_0 = 50\ \mathrm{km/s/Mpc}$" and the "$H_0 = 100\ \mathrm{km/s/Mpc}$" camps. Because the quantity ...

3

An infinite number of observations are needed because a comet does not have a well defined orbit. It is strongly deflected from ideal Newtonian orbits by outgassing, solar wind etc., so if you want to know where it is, and especially where it will be, at a given time in the future, you have to keep observing.

3

Olbers’ Paradox says that in an infinite universe every line of sight will end on a star. That statement is incomplete. The paradox requires not only an infinite universe, but also one that is both static and infinitely old. Neither of the second two statements are true for our universe. Your question considers the effect of aging. As our position ...

3

I don't think there is an exact definition. The term is used as a means of referring to an array of observation times of some astronomical phenomenon. In common usage, the terms "long cadence", or less often "low cadence", means that there is generally a longer time interval between observations. On the other hand, a "short cadence" or "high cadence" means ...

1

In the search by parameters screen you'll notice you can set limits on the morphological type. The types are given names, but the limits are input as though they are ordered. A little experimenting confirms the numbers you see reported as "type" correspond to the limits options, in the order of the drop-down menu. That is, we have: -3: dS0 5: Sb ...

1

This relation is quite important, non trivial, and mathematical, and was proved by Etherington along with the other closely related theorem in this paper I. M. H. Etherington (Philosophical Magazine ser. 7, vol. 15, 761 (1933)) This theorem only depends on photon conservation and the fact that photons only travel in null geodesics in Reimannian ...

1

You use units to make it convenient to talk about numbers. It's easy to do mental arithmetic with small numbers and hard to do mental arithmetic with scientific notation. So we tend to choose units where values of interest have numerical values between one-tenth and ten thousand (with a lot of give and take). For instance, we use the non-SI "astronomical ...

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