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You can only know that a Foucalt pendulum demonstrates the rotation of the earth by way of astronomical observations - that is, it is by observing the motion of the stars that you can tell how long the day is. That being so, you can determine that the motion of a Foucalt pendulum corresponds to the position of a distant star, that is, it corresponds to a ...

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According to Constraints on Dark Matter in the Solar System the following upper limits have been placed on dark matter in the solar system, based upon orbital motion of bodies in the solar system: At the radius of Earth's orbit: $1.4 \times 10^{-19} g/cm^3$ At the radius of Mars's orbit: $1.4 \times 10^{-20} g/cm^3$ At the radius of Saturn's orbit: $1.1 ... 9 Surprisingly it's quite easy to answer this because we can use the cosmic microwave background as a reference. The CMB gives us an average inertial frame for the universe so our motion relative to it is the closest we can come to defining the Solar System's motion through space. The CMB is isotropic, but because we are moving relative to it the radiation is ... -3 Planck: 13.82 Gyr; 68.3% dark energy, 26.8% dark matter, 4.9% baryonic matter. http://arxiv.org/abs/1306.5534 There is no dark matter in the solar system. Dark matter inside Saturn's orbit is less than 1.7×10^(-10) M_solar. Dark matter is repeatedly reparatmeterized curve-fitting with no empirical composition. Dark matter phenomenology is wholly ... 8 The answer is because dark-matter has relatively constant density, as has been given explicitly in another answer. Then, it logically follows that the impact on the Milky Way due to this low density. To show this step, I will establish a figure of merit. $$FOM = \frac{M_{dark}}{M_{normal}}$$ That is, the ratio of dark matter within the area of ... 2 Dark matter collects in larger quantities (thus a higher proportion relative to matter) in the centre of galaxies compared to in the centre of stellar systems such as the solar system. galaxies are not very dense, as stellar systems are sparsly spaced. So even though on a galactic scale the dark matter is in high ratios, on a stellar scale the ratio is ... 12 Dark matter would affect planetary motion, but the influence of dark matter on planets in our solar system is too small to detect even currenlty, due to the low concentration of dark matter compare to ordinary matter in our solar system. See Constraints on Dark Matter in the Solar System. The density of dark matter is very low,$ <~10^{-19} grams/cm^3$, ... 26 You've used the gravitational constant with only three significant digits. So it's no surprise that your answer isn't accurate to five significant digits. Instead of$G$and$M_\odot$separately, you should use the product$GM_\odot$, known as the standard gravitational parameter. Its value is known very accurately: in the link, you'll find $$GM_\odot = ... 11 To expand on Prahar's answer, let me run some numbers to try and convince you this is reasonable. Your answer is correct to within one part in 104:$$ \frac{365.256363004}{365.2075}\approx 1.000133795.$$The main perturbing influence on Earth's orbit is the gravitational pull of Jupiter, whose mass is about 1000 times smaller than the Sun, and which orbits ... 10 Kepler's 3rd law assumes that the Earth travels in a perfect ellipse with the only gravitational force on it being from the Sun. Further, Kepler's laws are derived from Newtonian gravitation. In reality, the orbit of the Earth is affected by the gravitational pull of other planets, and by the effects of General Relativity and is therefore not quite ... 0 I think your definition of sphere of influence is not correct. You could also be confusing the sphere of influence with the Hill sphere. The sphere of influence has mainly an application in the patched conic approximation. And the word sphere is even another approximation. A related question asks about the derivation of the radius of this sphere. I also ... 1 I thought the tilt was caused by the formation of the earth. When the earth formed from the gas of the pre-solar system, the gasses rotated and created a disk with an axis of near 23 degrees. When the disk got dense enough, it condensed it to spheroid we know know and love, keeping its tilt from its gassy days. Taking into consideration a collision that ... 1 There is a reasonable chance that yes, planets can form before the star "ignites" (which I take to mean the fusion of hydrogen into helium, not the very brief phase of deuterium burning which certainly will take place before planets can form). Planets form in a disk of circumstellar material around their parent protostars. The "core-accretion" model of ... 0 This would be better in astronomy since the earth collided with another planet size rock and the moon was the result. Since the center of the earth is fluid, the tilt of the axis would vary considerable, but the moon has a stabilizing effect. 1 An impact, possibly the same impact that caused material from earth to fly off to space and create the moon, tilted the earth to$23.5^o\$

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It's not constant, so there is no magic about it. It varies within a range, reflecting stabilising interactions with the moon and the sun, and the equatorial bulge.

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The planets appear to have formed by accretion of dust and gas around initially-small nuclei in orbit around the sun. As orbital radius (distance from the sun) increases, more material is available (in a uniform dust/gas disc) to accrete, so you get bigger planets further out; bigger planets sweep up more of their neighbors, so they tend to be spaced further ...

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