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Chaos Game

Planet Applet Applet Details Planetary Events Solutions

Solar, lunar, and planetary events to discover and to explore
(read the explanatory details before)

Solutions:

1. Watch the rare constellation of the bright planets Mar/Apr 2004 Details:
Rare constellation of the bright planets Mar/Apr 2004

2. Find the date and time of spring equinox for 2004

3. How long is a Tropical Year ?
2004, Mar 20 at about 06:37 UT, JD 2453084.776
2005, Mar 20 at about 12:24 UT, JD 2453450.017
2005, Mar 20 at about 18:18 UT, JD 2453815.263
intervalls: 365.241 days, 365.246 days.
In 1994-98, the tropical year was 365.242190 days long.
Link: Seasons

4. Find the date and time of summer solstice

summer solstice (northern hemisphere):
Sun reaches 90° in geocentric ecliptical longitude and maximum declination (+23° 26' 22'')
winter solstice (northern hemisphere):
Sun reaches 270° in geocentric ecliptical longitude and minimum declination (-23° 26' 22'')

2004, Jun 21 at about 00:50 UT
2004 Dec 21 at about 12:32 UT
Open the "Data Sun, Moon" window from the view menu.
Link: Earth's Seasons (USNO Data Services)
The deviation from USNO results (00:57 UT, 12:42 UT) is not more than 10 minutes.
Link: Seasons

5. How long are the seasons ?
2004, Mar 20 at about 06:37 UT, JD 2453084.776
2004, Jun 21 at about 00:45 UT, JD 2453177.531
2004, Sep 22 at about 16:18 UT, JD 2453271.179
2004, Dec 21 at about 12:24 UT, JD 2453361.017
2005, Mar 20 at about 12:24 UT, JD 2453450.017
Spring: 92.755 days
Summer: 93.648 says
Autumn: 89.838 days
Winter: 89.000.
Link: Seasons

6. Find the altitude of the noon Sun at summer and winter solstice:

In Berlin (52.52° N, 13.41° E), 2004:
Jun 20, the sun culminates at 12:08 at an altitude angle of 60.9°,
Dec 21, the sun culminates at 12:04 at an altitude angle of 14.1°,
noon altitude = 90° - latitude +/- declination
= 90° - 52.52° + 23.44° = 60.9°
= 90° - 52.52° - 23.44° = 14.0°
Animation

7. Determine the azimuth of the rising Sun at summer and winter solstice:

In Berlin (52.52° N, 13.41° E), 2004:
sunrise is at 03:43 on June 20,
the azimut angle of the rising Sun is 48°,
sunrise is at 08:15 on Dec 21,
the azimut angle of the rising Sun is 129°,
(closest to the south)
Animation

8. Find the date and time of perihelion 2004

Perihelion: 2004, January 4 at about 18 UT
Aphelion: 2004, July 5 at about 10 UT
Or: open the "Data Sun, Moon" window from the view menu.
Link: Earth's Seasons (USNO Data Services)
USNO: Jan 4, 17:42

9. Find the date of Easter 2004

1) 2004, Mar 20, 2) Mon 2004, Apr 5,
3) Easter: Sun, 2004, Apr 11
Link: Date of Easter

10. Explore the Transit of Venus on 2004, June 8

The transit will be visible from Europe
Eclipse begins at about 5:20 UT
Maximum eclipse at about 8:20 UT
Eclipse ends at about 11 UT
Link: Transit of Venus

11. Explore the visibility of the inner Planets

Mercury: before sunrise from end of Mar to beg. of Apr
Mercury: after sunset mid of Sep
Diagram Mercury, Venus

12. Find the duration of the longest day of 2004 for your location

Berlin (52.51° N):
15:51 hours on Jun 20,
07:39 hours on Dec 21.

13. Find the the day of earliest and latest sunrise 2004 for your location:

For Berlin (52.51° N), 2004:
2004 June 17 sunrise at 3:43,
and December 30 at 8:17
(not the days of solstice !)
Link: Sun or Moon Rise/Set Table for One Year (USNO Data Services)

14. Find the date and time of New Moon 2004

Jan 21, 21:05 UT, LSun=LMoon=301.17° (21:05)
Feb 20, 09:19 UT, LSun=LMoon=331.08° (9:18)
Mar 20, 22:44 UT, LSun=LMoon=0.67° (22:41)
Apr 19, 13:24 UT, LSun=LMoon=29.83° (13:21)
May 19, 04:56 UT, LSun=LMoon=58.56° (04:52)
Or: open the "Data Sun, Moon" window from the view menu.
Link:
Phases of the Moon (USNO Data Services)
The deviation from USNO results (brackets) ist not more than 4 minutes.

15. Check the duration of a Synodic Month

This is the period of time which elapses between the New Moon and the next.
New Moon 2004:
Jan 21, 21:05 UT, JD=2453026.378
Feb 20, 09:19 UT, JD=2453055.887
Mar 20, 22:44 UT, JD=2453085.447
Apr 19, 13:24 UT, JD=2453115.058
May 19, 04:56 UT, JD=2453144.706
The intervalls:
Jan/Feb: 29.509 days
Feb/Mar: 29.560 days
Mar/Apr: 29.611 days
Apr/May: 29,648 days
The mean duration is 29.53059 solar days (or 29 days 12 hours 44 minutes approximately). The synodic month is also called a lunation. Any particular phase cycle may vary from the mean by up to seven hours (29.27152 d to 29.83263 from 1600 to 2400).
Or: open the "Data Sun, Moon" window from the view menu.
Links:
Moon Phase Applet,
Synodic Month (Eric Weisstein's World of Science)

16. Determine the duration of a Draconic Month

The Draconic (Draconitic or nodical) Month is the interval of time between two successive transits of the Moon through its ascending node (heliocentric latitude changing from - to +):
2004 Feb 26 at 00 UT JD 2453061.5
2004 Mar 24 at 05 UT JD 2453088.71
2004 Apr 20 at 12 UT JD 2453116.0
2004 May 17 at 18 UT JD 2453143.25
The intervalls:
27.21 days
27.29 days
27.25 days
In 1994-2000, it was 27.212221 days.
Or: open the "Data Planets" window from the view menu.
Link:
Draconic Month (Eric Weisstein's World of Science)

17. Determine the duration of an Anomalistic Month

The anomalistic month is the time between perigee passages.
Perigees 2004:
Jan 19 at 19 UT, JD 2453024.292
Feb 16 at 08 UT, JD 2453051.833
Mar 12 at 04 UT, JD 2453076.667
Apr 08 at 02 UT, JD 2453103.583
May 06 at 05 UT, JD 2453131.708
Jun 03 at 13 UT, JD 2453160.042
Jul 01 at 23 UT, JD 2453188.458
Jul 30 at 06 UT, JD 2453216.75
Aug 24 at 06 UT, JD 2453244.75
The intervalls:
27.541 days
24.834 days
26.916 days
28.125 days
28.344 days
28.416 days
28.292 days
28.000 days
Mean: 27.55455 days (in 1900-2078, SD 1.136).
Or: open the "Data Sun, Moon" window from the view menu.
Link: Anomalistic month (Eric Weisstein's World of Science)

18. Explore the Total Lunar Eclipse of 2004, Oct. 28

Maximum eclipse at about 3:10 UT
All eclipse visible from South America, and from the mid and western parts of USA,
from western Europe at moonset
Link:
2004 Oct 28: Total Lunar Eclipse (Fred Espenak)

19. Watch the declination of the Moon and the azimuth at rise and set
2004 Jan 20: declination -27.1°
Moonrise in Berlin at an azimuth of 139°
(close to south!)
2004 Jan 06: declination +26.8°
Moonrise in Berlin at an azimuth of 61°
(closest to the north!)
Or: open the "Data Sun, Moon" window from the view menu.
Links:
Sun & Moon Polar Applet
Sun or Moon Altitude/Azimuth Table for One Day (USNO Data Services)

Predictable Periodic Events

Tropical Month: period of revolution of the moon around the earth in reference to the vernal equinox
2004, Geocentric Longitude L=0°:
Jan 26 03:07 UT JD 2453030.630
Feb 22 12:45 UT JD 2453058.301
Mar 20 21:30 UT JD 2453085.396
Apr 17 04:26 UT JD 2453112.685
May 14 10:03 UT JD 2453139.919
27,671
27,095
27.289
27.234

Month Intervall d d h m s

Synodic
new 29.53059 29 12 44 3

Anomalistic
perigee 27.55455 27 13 18 33

Draconitic
node 27.21222 27 5 5 36

Sidereal
fixed star 27.32166 27 7 43 12

Tropical
vernal equinox 27.32158 27 7 43 5

Month (Wikipedia)

Celestial Observer (CalSky)

To be continued ...

1. Watch the rare constellation of the bright planets Mar/Apr 2004	Details: Rare constellation of the bright planets Mar/Apr 2004
2. Find the date and time of spring equinox for 2004
3. How long is a Tropical Year ?	2004, Mar 20 at about 06:37 UT, JD 2453084.776 2005, Mar 20 at about 12:24 UT, JD 2453450.017 2005, Mar 20 at about 18:18 UT, JD 2453815.263 intervalls: 365.241 days, 365.246 days. In 1994-98, the tropical year was 365.242190 days long. Link: Seasons
4. Find the date and time of summer solstice	summer solstice (northern hemisphere): Sun reaches 90° in geocentric ecliptical longitude and maximum declination (+23° 26' 22'') winter solstice (northern hemisphere): Sun reaches 270° in geocentric ecliptical longitude and minimum declination (-23° 26' 22'') 2004, Jun 21 at about 00:50 UT 2004 Dec 21 at about 12:32 UT Open the "Data Sun, Moon" window from the view menu. Link: Earth's Seasons (USNO Data Services) The deviation from USNO results (00:57 UT, 12:42 UT) is not more than 10 minutes. Link: Seasons
5. How long are the seasons ?	2004, Mar 20 at about 06:37 UT, JD 2453084.776 2004, Jun 21 at about 00:45 UT, JD 2453177.531 2004, Sep 22 at about 16:18 UT, JD 2453271.179 2004, Dec 21 at about 12:24 UT, JD 2453361.017 2005, Mar 20 at about 12:24 UT, JD 2453450.017 Spring: 92.755 days Summer: 93.648 says Autumn: 89.838 days Winter: 89.000. Link: Seasons
6. Find the altitude of the noon Sun at summer and winter solstice:	In Berlin (52.52° N, 13.41° E), 2004: Jun 20, the sun culminates at 12:08 at an altitude angle of 60.9°, Dec 21, the sun culminates at 12:04 at an altitude angle of 14.1°, noon altitude = 90° - latitude +/- declination = 90° - 52.52° + 23.44° = 60.9° = 90° - 52.52° - 23.44° = 14.0° Animation
7. Determine the azimuth of the rising Sun at summer and winter solstice:	In Berlin (52.52° N, 13.41° E), 2004: sunrise is at 03:43 on June 20, the azimut angle of the rising Sun is 48°, sunrise is at 08:15 on Dec 21, the azimut angle of the rising Sun is 129°, (closest to the south) Animation
8. Find the date and time of perihelion 2004	Perihelion: 2004, January 4 at about 18 UT Aphelion: 2004, July 5 at about 10 UT Or: open the "Data Sun, Moon" window from the view menu. Link: Earth's Seasons (USNO Data Services) USNO: Jan 4, 17:42
9. Find the date of Easter 2004	1) 2004, Mar 20, 2) Mon 2004, Apr 5, 3) Easter: Sun, 2004, Apr 11 Link: Date of Easter
10. Explore the Transit of Venus on 2004, June 8	The transit will be visible from Europe Eclipse begins at about 5:20 UT Maximum eclipse at about 8:20 UT Eclipse ends at about 11 UT Link: Transit of Venus
11. Explore the visibility of the inner Planets	Mercury: before sunrise from end of Mar to beg. of Apr Mercury: after sunset mid of Sep Diagram Mercury, Venus
12. Find the duration of the longest day of 2004 for your location	Berlin (52.51° N): 15:51 hours on Jun 20, 07:39 hours on Dec 21.
13. Find the the day of earliest and latest sunrise 2004 for your location:	For Berlin (52.51° N), 2004: 2004 June 17 sunrise at 3:43, and December 30 at 8:17 (not the days of solstice !) Link: Sun or Moon Rise/Set Table for One Year (USNO Data Services)
14. Find the date and time of New Moon 2004	Jan 21, 21:05 UT, LSun=LMoon=301.17° (21:05) Feb 20, 09:19 UT, LSun=LMoon=331.08° (9:18) Mar 20, 22:44 UT, LSun=LMoon=0.67° (22:41) Apr 19, 13:24 UT, LSun=LMoon=29.83° (13:21) May 19, 04:56 UT, LSun=LMoon=58.56° (04:52) Or: open the "Data Sun, Moon" window from the view menu. Link: Phases of the Moon (USNO Data Services) The deviation from USNO results (brackets) ist not more than 4 minutes.
15. Check the duration of a Synodic Month	This is the period of time which elapses between the New Moon and the next. New Moon 2004: Jan 21, 21:05 UT, JD=2453026.378 Feb 20, 09:19 UT, JD=2453055.887 Mar 20, 22:44 UT, JD=2453085.447 Apr 19, 13:24 UT, JD=2453115.058 May 19, 04:56 UT, JD=2453144.706 The intervalls: Jan/Feb: 29.509 days Feb/Mar: 29.560 days Mar/Apr: 29.611 days Apr/May: 29,648 days The mean duration is 29.53059 solar days (or 29 days 12 hours 44 minutes approximately). The synodic month is also called a lunation. Any particular phase cycle may vary from the mean by up to seven hours (29.27152 d to 29.83263 from 1600 to 2400). Or: open the "Data Sun, Moon" window from the view menu. Links: Moon Phase Applet, Synodic Month (Eric Weisstein's World of Science)
16. Determine the duration of a Draconic Month	The Draconic (Draconitic or nodical) Month is the interval of time between two successive transits of the Moon through its ascending node (heliocentric latitude changing from - to +): 2004 Feb 26 at 00 UT JD 2453061.5 2004 Mar 24 at 05 UT JD 2453088.71 2004 Apr 20 at 12 UT JD 2453116.0 2004 May 17 at 18 UT JD 2453143.25 The intervalls: 27.21 days 27.29 days 27.25 days In 1994-2000, it was 27.212221 days. Or: open the "Data Planets" window from the view menu. Link: Draconic Month (Eric Weisstein's World of Science)
17. Determine the duration of an Anomalistic Month	The anomalistic month is the time between perigee passages. Perigees 2004: Jan 19 at 19 UT, JD 2453024.292 Feb 16 at 08 UT, JD 2453051.833 Mar 12 at 04 UT, JD 2453076.667 Apr 08 at 02 UT, JD 2453103.583 May 06 at 05 UT, JD 2453131.708 Jun 03 at 13 UT, JD 2453160.042 Jul 01 at 23 UT, JD 2453188.458 Jul 30 at 06 UT, JD 2453216.75 Aug 24 at 06 UT, JD 2453244.75 The intervalls: 27.541 days 24.834 days 26.916 days 28.125 days 28.344 days 28.416 days 28.292 days 28.000 days Mean: 27.55455 days (in 1900-2078, SD 1.136). Or: open the "Data Sun, Moon" window from the view menu. Link: Anomalistic month (Eric Weisstein's World of Science)
18. Explore the Total Lunar Eclipse of 2004, Oct. 28	Maximum eclipse at about 3:10 UT All eclipse visible from South America, and from the mid and western parts of USA, from western Europe at moonset Link: 2004 Oct 28: Total Lunar Eclipse (Fred Espenak)
19. Watch the declination of the Moon and the azimuth at rise and set	2004 Jan 20: declination -27.1° Moonrise in Berlin at an azimuth of 139° (close to south!) 2004 Jan 06: declination +26.8° Moonrise in Berlin at an azimuth of 61° (closest to the north!) Or: open the "Data Sun, Moon" window from the view menu. Links: Sun & Moon Polar Applet Sun or Moon Altitude/Azimuth Table for One Day (USNO Data Services)
Predictable Periodic Events
	Tropical Month: period of revolution of the moon around the earth in reference to the vernal equinox 2004, Geocentric Longitude L=0°: Jan 26 03:07 UT JD 2453030.630 Feb 22 12:45 UT JD 2453058.301 Mar 20 21:30 UT JD 2453085.396 Apr 17 04:26 UT JD 2453112.685 May 14 10:03 UT JD 2453139.919 27,671 27,095 27.289 27.234

Month	Intervall	d	d	h	m	s
Synodic	new	29.53059	29	12	44	3
Anomalistic	perigee	27.55455	27	13	18	33
Draconitic	node	27.21222	27	5	5	36
Sidereal	fixed star	27.32166	27	7	43	12
Tropical	vernal equinox	27.32158	27	7	43	5