Editing 1633: Possible Undiscovered Planets

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Stating the obvious, this {{w|log–log plot}} shows that for an object to be an unknown planet it has to be very far away, since planets are big, to explain why we haven't seen it yet. With the log scale it is possible to go from a diameter of less than 1 mm to an {{w|astronomical unit}} (AU) on the Y-axis and from a distance of just 1 cm up to thousands of AU on the X-axis.
 
Stating the obvious, this {{w|log–log plot}} shows that for an object to be an unknown planet it has to be very far away, since planets are big, to explain why we haven't seen it yet. With the log scale it is possible to go from a diameter of less than 1 mm to an {{w|astronomical unit}} (AU) on the Y-axis and from a distance of just 1 cm up to thousands of AU on the X-axis.
  
Randall's chart is somewhat humorously parochial (if not downright {{w|egocentric}}) in that it purports to measure distance not "from Earth" or from an arbitrary observer, but specifically from himself ("from me"). There is also more detail (e.g. a differentiation between bird, bugs, and skin flora) in the zone closest to the observer, somewhat reminiscent of the classic New Yorker cover illustration ''{{W|View of the World from 9th Avenue}}''.
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Randall's chart is very {{w|egocentric}} as it categorizes objects based on size but also on their distance from himself ("from me"). This distance starts at 1 cm, and an item on the chart reads "skin flora", thus distance is measured from the surface of Randall's body (skin/eyes) rather than from his center of mass. All the planets (and moon) that are marked on the chart are so far away that it will not matter if the distance is measured from Randall's surface, his center of mass, or by the way anywhere on {{w|Earth}}. Also, the planets' diameters are so much smaller than the distance from Earth that their real size would hardly take up any space in the chart due to the {{w|Logarithmic scale|log-scale}}. The dots marking these 7 planets are thus not drawn to scale that should represent their actual size compared with the other planets. But their distance from Earth (and Randall) is not constant even on the log-scale, especially not for the nearest planets, as they can be on either side of the {{w|Sun}} compared to Earth.
 
 
The distance calculations are somewhat problematic (see more on this below). Close distances seem to be measured from the surface of Randall's body (skin/eyes) rather than from his center of mass. All the planets (and moon) that are marked on the chart are so far away that it will not matter if the distance is measured from Randall's surface, his center of mass, or by the way anywhere on {{w|Earth}}. Also, the planets' diameters are so much smaller than the distance from Earth that their real size would hardly take up any space in the chart due to the {{w|Logarithmic scale|log-scale}}. The dots marking these 7 planets are thus not drawn to scale that should represent their actual size compared with the other planets. But their distance from Earth (and Randall) is not constant even on the log-scale, especially not for the nearest planets, as they can be on either side of the {{w|Sun}} compared to Earth.
 
  
 
The chart correctly states that if there was a planet that was at a distance from him smaller than its diameter, he would be inside it (although at the bottom of that region, it's more like the planet that would be inside him, as this line goes down to a diameter of 1 cm). If the distance is to the planets center, this would also fit if he was only a radius away from the planet. As Randall is not inside the Earth but really close to it, Earth is correctly positioned on this line. However, for Earth, which is marked with the largest of the dots, he seems to have put himself a full Earth diameter away from Earth. Even using the center of mass of Earth as its position he should only have been 6,350 km away from it, but now he places the measuring point of his distance to Earth on the opposite side of the Earth so his distance to it is equal to its diameter (which would make a choosing a distance of 0 km just as correct). Earth is just left of the 10,000 km line on both axis, and Earth has a diameter of 12,700 km, which will fit fine with the center of the dot, but not with the distance which should have been the maximum distance Randall could be from it (0 or 6350 km depending on the definition of distance from Randall).
 
The chart correctly states that if there was a planet that was at a distance from him smaller than its diameter, he would be inside it (although at the bottom of that region, it's more like the planet that would be inside him, as this line goes down to a diameter of 1 cm). If the distance is to the planets center, this would also fit if he was only a radius away from the planet. As Randall is not inside the Earth but really close to it, Earth is correctly positioned on this line. However, for Earth, which is marked with the largest of the dots, he seems to have put himself a full Earth diameter away from Earth. Even using the center of mass of Earth as its position he should only have been 6,350 km away from it, but now he places the measuring point of his distance to Earth on the opposite side of the Earth so his distance to it is equal to its diameter (which would make a choosing a distance of 0 km just as correct). Earth is just left of the 10,000 km line on both axis, and Earth has a diameter of 12,700 km, which will fit fine with the center of the dot, but not with the distance which should have been the maximum distance Randall could be from it (0 or 6350 km depending on the definition of distance from Randall).

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