Editing 2707: Astronomy Numbers
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==Explanation== | ==Explanation== | ||
− | Space [https:// | + | Space [https://www.youtube.com/watch?v=Hv1spjsvu-A is big] and the things that are in space can also end up being very big themselves. As a result, most quantities in astronomy have huge scales. For example, Earth has a mass 10<sup>23</sup> times more than the average human, and the Sun is 10<sup>5</sup> times more than that, which itself is 10<sup>12</sup> times less massive than the Milky Way. The same applies to speeds, distances, and time, which can often be measured in terms of light speed, light-years, and millions or billions of years. Because of this, it's a truly unusual occurrence for anything in space to end up in the fairly narrow range of scales of mass, size, speed, or time that humans can easily grasp. |
− | + | [[Ponytail]], apparently a scientist researching something related to Earth's orbit, finds that on the date in question (January 1, although the year is not specified), Earth will be approaching the sun at a velocity of 65 miles per hour—an extremely common and normal-sounding velocity to American ears, often used as a speed limit on highways in the US. Ponytail is clearly a little thrown off by this, and remarks that she finds it "suspicious" when reasonably human-scaled numbers come up. | |
− | [[ | + | She then extends this discomfort to things that should be measured in regular numbers, such as the weight of cats. The vet, [[Megan]], is seemingly used to this problem (perhaps she gets a lot of astronomers, or Ponytail has a hypochondriac cat), so she restates the 12-lb weight of Ponytail's cat in solar masses. Since using this unit yields an ''incredibly'' small number, 3×10<sup>-30</sup> (a three preceded by a decimal point and 29 zeroes), it evidently sounds more plausible to the astronomer. This weight is in fact about 13 lb 2 oz (about 5.5 kilograms), slightly heavier than the initial figure given for the cat, but within [[2585: Rounding|rounding error]] for the single digit of precision that Megan uses. According to [[2205:_Types_of_Approximation | 2205: Types of Approximation]] that rounding error is unusually small for an astronomer, though. Also, the usage of weight gives the word "scales" in "scales should all be incomprehensible" a double meaning because scales are used to weigh things, including cats. A scale that returns weights in solar masses would indeed be incomprehensible to most people. However, this could be unintentional on Randall's part. |
− | + | The Earth's orbital velocity around the Sun is far above any "normal" scales (around 30 kilometers per second or 108,000 kilometers per hour). However, Earth has a pretty circular orbit around the Sun, so most of this speed ends up being tangential (sideways) rather than radial (towards or away from) the Sun, which is the value relevant for Ponytail's calculations. On January 1, Earth's radial velocity is close to its smallest value because we reach our closest point to the Sun in the first few days of January each year (in 2023, {{w|Perihelion|perihelion}} happens on January 4) so by January 1, it's nearly come to a standstill before it starts traveling away from the Sun again. On the other hand, by April 3, 2023, Earth will be receding from the Sun by almost 500 meters per second or 1800 kilometers per hour, a less normal speed for the average person to encounter in everyday life.{{citation needed}} 65 miles per hour is approximately equal to 105 kilometers per hour, although the even more typical scientific value (in {{w|International System of Units|SI}} derived units) would be 29 meters per second. | |
− | The | + | The title text suggests that laser pointers "love chasing" a new cat with a weight of 12 solar masses (an inversion of the typical cat behavior of [[729: Laser Pointer|chasing laser pointer dots]]). A 12 solar mass cat would have the dominant gravitation well in our solar system, which would make everything fall towards the cat – including laser pointers. Furthermore, all gravitational fields bend light towards their center; a 12 solar mass object could bend light quite a lot. The path of the light from a laser pointer aimed near such a cat would bend towards it or "chase" it. In fact, anything with 12 solar masses would have a Schwarzschild radius of around 36 kilometers, so any cat-sized thing with that mass would be a black hole, drawing all light within a 72-kilometer sphere around it into its singularity. |
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==Transcript== | ==Transcript== | ||
− | :[Ponytail is standing in front of a whiteboard writing on it with a pen, while Cueball looks over her shoulder from behind her. On the board is an almost circular ellipse with a cross that centers on a dot towards the left side of it. On the right side there is a small circle on the ellipse's line. There are several lines of wiggles representing unreadable text. To the left of the ellipse there are two lines near the top of and four near at the bottom of the ellipse. Ponytail is writing a fifth line below these almost under the ellipse. At the bottom to the left there is a rectangular frame with a line of text beneath it and at the bottom left corner there is a line forming a half | + | :[Ponytail is standing in front of a whiteboard writing on it with a pen, while Cueball looks over her shoulder from behind her. On the board is an almost circular ellipse with a cross that centers on a dot towards the left side of it. On the right side there is a small circle on the ellipse's line. There are several lines of wiggles representing unreadable text. To the left of the ellipse there are two lines near the top of and four near at the bottom of the ellipse. Ponytail is writing a fifth line below these almost under the ellipse. At the bottom to the left there is a rectangular frame with a line of text beneath it and at the bottom left corner there is a line forming a half closes rectangle around two dots.] |
:Ponytail: …And we need to correct for our elliptical orbit. On January 1<sup>st</sup>, Earth will be approaching the sun at a rate of ...let's see... | :Ponytail: …And we need to correct for our elliptical orbit. On January 1<sup>st</sup>, Earth will be approaching the sun at a rate of ...let's see... | ||
:Ponytail: 65 miles per hour. | :Ponytail: 65 miles per hour. | ||
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:Ponytail: Scales should all be incomprehensible. | :Ponytail: Scales should all be incomprehensible. | ||
− | :[ | + | :[Megan in a lab-coat raised her hand palm up towards an animal carrier cage standing on her desk. The cage has a handle and five air holes are at the top. Behind two of them something black inside the cage can be seen. Ponytail is standing on the other side of the desk looking at Megan. Above the top of the panels frame there is a panel with a label:] |
:Earlier, at the vet: | :Earlier, at the vet: | ||
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:Megan: Your cat weighs 12 lbs. | :Megan: Your cat weighs 12 lbs. | ||
:Ponytail: Ridiculous, nothing weighs "12". You must mean 10<sup>-20</sup>? Or 10<sup>40</sup>? | :Ponytail: Ridiculous, nothing weighs "12". You must mean 10<sup>-20</sup>? Or 10<sup>40</sup>? |