Why aren’t planets always perfect circles in telescopes?
The distance determines how big the disk is, and the oblateness and viewing angle determine how flat it is.
Planets and Small Solar System Objects
A flatter sphere looks like an ellipse when viewed from the equator, and more like a circle when viewed from the pole. Let’s try it first with the actual disk of Saturn; we don’t include the rings in this lesson.
Guess first
Will an oblate sphere be more round when viewed from the pole than from the equator?
Show answer and explanation
meeting — A disc is a projection of a three-dimensional shape.
Then connect experience and science
Two tables in the original book
A and B are the historical constants listed in the original book.
sE=a/Δ
polar radius
Saturn's projection is corrected with observation latitude.
sP=√(b²cos²B+a²sin²B)/Δ
Jupiter approximation
The Earth's latitude relative to Jupiter is small, so polar radius is usually used directly in books.
sP≈b/Δ
Zoom
A fixed angle scale is used for the same planet; if the distance is too close, it will exceed the indicated field of view and will not be forcibly retracted to the original size.
Picture pixels cannot be used as arc seconds
Expand the calculation
sequatorial = a/Δ s极向 = √(b²cos²B + a²sin²B)/Δ dequatorial = 2sequatorial；d极向 = 2s极向
a and b are the equatorial and poloidal angular radii (arcseconds) at 1 AU, and Δ is in AU. When B=0°, the body oblateness can be seen, and the angular radii of the two directions are the same when looking toward the polar axis. Picture pixels do not represent arc seconds.
give it a try
Select Saturn and compare 0° at the equator with 90° at the pole. Switching the visible distance of other planets affects the visual size.
No need to memorize symbols
- Δ
- Assume that the distance from the center of the earth is AU
- B
- Latitude of the Earth as seen from the center of Saturn
- sE/sP
- Projected equatorial/polar radius arc seconds
Algorithm, accuracy and scope of application
Covers Chapter 55 Planetary Table A/B and Saturn Polar Radius Projection. The equatorial/polar radii of Jupiter and Saturn are listed separately; the moon surface or Saturn rings are not mixed into the main body. The original Pluto book B value of 2.07″/Δ is stated outside the source code table and can be calculated as the same formula; not applicable to group A. The local AA+ ApparentSaturnPolarSemidiameterB uses the polar radius as a pre-factor, which is inconsistent with the equatorial radius pre-factor in p390 of the original book; this site adopts the original book formula and independently verifies it with the geometric boundary that should be circular when viewed poleward.
my understanding check
Does the Saturn ellipse in this lesson contain the rings?
Not included — Only the body angular radius is calculated.
If the same planet is twice as far away, the angular radius will be similar?
halved — The original book uses s₀/Δ.
Can the output change slightly by changing a set of radius constants?
Can — Data definitions and versions are part of the calculation.
The oblate shape in front of you is the result of a combination of shape, distance and viewing direction.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 55 chapter
Planets and Small Solar System Objects · All interactive courses