1.2. MEASURING DISTANCES IN SPACE 11
Earth orbit
Venus orbit
∆t
1
∆t
2
Figure 1.6: Parallax was used to measure the distance between Earth and Venus, by making
observations from two different locations on Earth of a transit of Venus across the Sun’s disk.
(Illustration by Duckysmokton, Ilia, Vermeer, CC BY-SA 3.0.)
because of the slightly different vantage points, different observer’s saw the planet transit at
different solar latitudes, and so require different amounts of time.
It is possible to relate those time differences, given the known angular diameter of the Sun,
to the small angle (much exaggerated in the illustration) of the triangle that is formed by the
geometry. e distance between the two observation points on Earth, then, is like the right side
of the triangle in Figure 1.4. We can thus use the small-angle formula to calculate the distance,
d , to Venus:
d D B; (1.14)
where B is the baseline—the physical distance between the two observation points.
Using parallax to triangulate the true distance to Venus provided the scale factor for the
entire solar system. us, these eighteenth-century studies of transits of Venus allowed for the
first real measurements of the Earth–Sun distance—the astronomical unit (AU).
Another transit of Venus occurred in June of 2012; see Figure 1.7 for my photograph of
one stage of the transit. e dark circular disk is the silhouette of Venus, while the smaller not
completely dark spots are sunspots. e true size of Venus is not much bigger than the largest
of these sunspots. It appears much larger that that because it is much closer than the Sun.
12 1. TOOLS FOR UNDERSTANDING SPACE
Figure 1.7: My photograph of the June, 2012 transit of Venus. Contrast the perfectly round
silhouette of Venus with the irregular and less-dark sunspots. Since Venus is much closer than
the Sun, it appears much larger than its true size, which is similar to that of the largest sunspots
shown here.
1.2.4 STELLAR PARALLAX
We can use the method of parallax to measure the distances to nearby stars. But a far larger
baseline, B, is needed because the distance, d , is so much greater than for the case discussed in
Section 1.2.3. Instead of observing from different locations on the surface of Earth, we allow
our planet’s orbital motion about the Sun to carry us to different parts of Earth’s orbit. us, our
baseline over the course of a year is a full 2 AU; Figure 1.8 shows the basic geometry.
ere are many circumstances where angles measured in astronomy are extremely small—
a minuscule fraction of a degree. Such is the case for the parallax angle measured for even the
closest of stars. Since the radian is already a large angle (over 57
˝
), it is inconvenient for everyday
descriptions of these tiny angles. And so astronomers commonly use other units of angle instead,
only converting to radians when a calculation is needed. e most common units for tiny angles
are the arcminute (or minute of arc) and the arcsecond (or second of arc). ese units have nothing
per se to do with time; they are simply fractions of a degree: there are 60 arcminutes per degree,
and 60 arcseconds per arcminute. ey are commonly denoted with single and double quotes,
1.2. MEASURING DISTANCES IN SPACE 13
Earth's Motion Around the Sun
Distant Stars
Near Star
Near Star Parallax Motion
Parallax Angle
p
Figure 1.8: Stellar parallax: a relatively nearby star appears in slightly different directions as seen
(against the backdrop of very distant stars) from two vantage points on opposite sides of Earth’s
orbit about the Sun. (Graphic public domain)
just like minutes and seconds of time. And so we have the following:
1 arcminute
D
1
1
D
0:01667
˝
(1.15)
1 arcsecond D 1
2
D 0:01667
1
D 0:0002778
˝
(1.16)
1 radian D 57:296
˝
(1.17)
1
˝
D 3600
2
(1.18)
1 radian D 206; 265
2
: (1.19)
Astronomers take a practical approach to measurements of stellar parallax, taking advantage of
the following.
• e baseline is always the same for measurements of stellar parallax—the diameter of
Earth’s orbit.
• e stellar parallax angle is always very tiny, and so it is measured in arcseconds. Even for
the nearest star, this angle is less than one arcsecond.
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.