Cover Sheet: Activity: Extra
Transit of Venus
Name:________________________________________________________________ Date Submitted:____________________________________________________ Returned for Revision:____________________________________________ Resubmitted:________________________________________________________ Date Recorded as Satisfactory:___________________________________ By :_____________________________________________________________ PHYS 1000 /AST 1040
Self Paced
Activity: June 5, 2012 Transit of Venus
Objective: To make measurements of the Solar System from observations of the June
5, 2012 transit of Venus.
Background: When an inferior planet (Venus or Mercury) is at a place in the solar
system called inferior conjunction, it is passing the Earth on the way around the Sun.
Another point in the orbit (relative to the Earth) is superior conjunction, where the planet
is aligned with the Sun but farther than it. These points are in contrast to opposition,
which occurs when a superior planet is opposite the Sun in the sky.
For the inferior planets, the vast majority of the passes in front of the sun do not
transit the sun, but traverse north or south of it. Occasionally one does: the tables
below show the transits for Mercury and Venus.
Source: http://eclipse.gsfc.nasa.gov/transit/transit.html
Transits of Mercury:
1901-2050
Date
Universal Time
1907 Nov 14
12:06
1914 Nov 07
12:02
1924 May 08
01:41
1927 Nov 10
05:44
1937 May 11
09:00
1940 Nov 11
23:20
1953 Nov 14
16:54
1957 May 06
01:14
1960 Nov 07
16:53
1970 May 09
08:16
1973 Nov 10
10:32
1986 Nov 13
04:07
1993 Nov 06
03:57
1999 Nov 15
21:41
2003 May 07
07:52
2006 Nov 08
21:41
2016 May 09
14:57
2019 Nov 11
15:20
2032 Nov 13
08:54
2039 Nov 07
08:46
2049 May 07
14:24
Transits of Venus:
1601-2400
Date
Universal Time
1631 Dec 07
05:19
1639 Dec 04
18:25
1761 Jun 06
05:19
1769 Jun 03
22:25
1874 Dec 09
04:05
1882 Dec 06
17:06
2004 Jun 08
08:19
2012 Jun 06
01:28
2117 Dec 11
02:48
2125 Dec 08
16:01
2247 Jun 11
11:30
2255 Jun 09
04:36
2360 Dec 13
01:40
2368 Dec 10
14:43
Equipment and Supplies: Ruler, calculator.
Data:
Sun’s diameter: DSun= 1.39 x 106 km
Distance from the Sun to Earth: dSun-Earth= 1.496 x 108 km
Distance from the Sun to Venus: dSun-Venus= 1.082 x 108 km
Section I: Find the diameter of Venus.
1) Measure the diameter of the solar disk with a millimeter ruler. Take several
measurements and find the average. LSun = _____________ mm.
2) Measure the diameter of Venus with the ruler. (It is the large black dot on the
face of the Sun.) Take several measurements and find the average. LVenus =
______________mm
3) If Venus were crossing the Sun at the distance to the Sun, then the diameter of
Venus would be equal to the product: DVenus =(LVenus/LSun) x DSun. BUT, Venus is
closer to the Earth than the Sun is, so the occultation disk appears larger than
that. How many times farther away is the Sun from the Earth compared to Venus
(from the Earth)? Let’s call this number M = _______________.
4) This factor needs to be introduced into the previous calculation since Venus is
actually smaller by this amount.
DVenus = (LVenus/LSun) x (DSun/M) = _______________ km.
5) Compare your measurements to the standard value of the diameter of Venus:
12100 km. Find your percent error via the equation
| Standard - Observed|
%error =
×100.
Standard
%error = ________________________.
6) Compare the diameter you calculate to the diameter of the Earth: 12800 km. Do
your measurements support the claim that Venus is Earth’s sister planet (due to
them having similar sizes?)
7) What are sources of error? How could this experiment be improved?
Section II: Estimate the orbital speed of Venus.
Here we will attempt to estimate how fast Venus is moving in its orbit by the formula
distance
.
time
speed =
Even though we know that the planets move in curved trajectories called ellipses, for
short periods of time we can approximate the path of a planet as a straight line.
From http://eclipse.gsfc.nasa.gov/OH/transit12.html : The principal events occurring during a transit are conveniently characterized by
contacts, analogous to the contacts of an annular solar eclipse. The transit begins
with contact I, the instant the planet's disk is externally tangent to the Sun.
Shortly after contact I, the planet can be seen as a small notch along the solar limb.
The entire disk of the planet is first seen at contact II when the planet is
internally tangent to the Sun. Over the course of several hours, the silhouetted
planet slowly traverses the solar disk. At contact III, the planet reaches the
opposite limb and once again is internally tangent to the Sun. Finally, the transit
ends at contact IV when the planet's limb is externally tangent to the Sun. Contacts I
and II define the phase called ingress while contacts III and IV are known as egress.
Position angles for Venus at each contact are measured counterclockwise from the north
point on the Sun's disk.
1) How long does it take Venus to go from Contact I to Contact III? Convert the
answer to seconds:
ΔtI − III
= _____________ s.
2) Over this short amount of time, it is fair to approximate the path of Venus as a
straight line. Using similar triangles, estimate how far Venus has traveled in
this time (see the figure below.) The similar triangles share the Earth at one
vertex.
ΔxVenus-estimate = _____________________________ km.
3) This estimation is wrong. The Earth has also moved during the transit. We can
approximate the extra distance the Earth has covered by knowing that the
Earth moves at
time using
vEarth = 30 km/s. Calculate how far the Earth moved during that
ΔxEarth = vEarth tI − III .
ΔxEarth = ____________________________ km.
4) Since both Earth and Venus moved over the transit, some extra distance has to
be added to the estimate of Venus’s motion. The amount to add is
approximately Δxextra
=
dSun-Venus
ΔxEarth = ___________________km.
dSun-Earth
5) Sum these two values to get the total distance Venus has moved in this time.
Δxtotal = ΔxVenus-estimate + Δxextra = ________________ km.
6) This estimate is still wrong- why? Because it was assumed that Venus transited
across the diameter of the sun. However, it didn’t go that far, it went across
from one point to another. Use a ruler to measure the diagram ‘2004 and 2012
Transits of Venus’ (above). Measure the distance (in mm) of the track of
Venus, and also across the diameter of the Sun. Call the ratio of the length of
Venus’s track to the length of the diameter p, where p should be a number less
than 1. p = _________________________.
7) The final estimate of the distance that Venus has traveled is obtained by
multiplying the result in part (5) by the multiplicative factor in part (6).
Δxfinal = pΔxtotal = ________________ km.
8) The speed of Venus is therefore
vVenus
Δxfinal
=
=
Δt I − III
______________________ km/s.
9) Compare your answer to the standard value of the orbital speed of Venus:
vstandard = 35.0 km/s . Find the percent error as you did in Section I
%error = ___________________________________.
Section III: Discussion
1) Look at the tables that give the calendar for the transits of Mercury and Venus.
Do you notice any trends amongst the dates? What kind of transits occur more
often, those of Venus or those of Mercury? What is a plausible explanation for
this?
2) The Kepler space mission (kepler.nasa.gov) is designed to discover planets
around other stars by studying the brightness of those stars during planetary
transits. Kepler is sensitive to brightness changes of 1/10000 which occur when a
planet blocks out a tiny fraction of the light being emitted by the star it orbits.
Given the area of Venus and the Sun, do you think that Kepler would be able to
detect a transit of Venus? Why or why not?