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The closest planet to Earth

On several occasions I met the interesting question Which planet is closest to Earth and decided to answer it. As a matter of fact any of the terrestrial planets can be the closest to Earth at any instant. But which planet is closest to us most of the time ? To answer this question I generated positions of Mercury, Venus, Earth and Mars at 0h TT for all dates, beginning AD 1001-Jan-01 and ending AD 3001-Jan-01 and compared distances at which the planets are. Two millennia should be large enough timespan to answer the question. Most amazingly its neither Venus nor Mars, but it's Mercury that is closest to Earth most of the time - 46.8%. Second place is for Venus - it's closest planet to Earth in 36.7% of the time, and Mars is third with 16.5%.

During 2009 and 2010 closest planet to Earth at different periods can be found below. All times are in Terrestrial Time and indicate the first instant at which specified planet becomes closest to Earth. Please note: distances between planets centers of mass are used in this computation.

2009-Jan-01 00:00:00 Venus  
2009-May-18 05:20:08 Mercury
2009-Jun-06 22:55:14 Venus  
2009-Aug-06 14:18:38 Mercury
2009-Oct-19 11:15:58 Mars   
2009-Dec-28 22:22:32 Mercury
2010-Jan-10 23:30:59 Mars   
2010-Apr-03 00:57:29 Mercury
2010-Jun-15 08:04:59 Venus  
The closest planet to other planets

Table below summarizes results for closest to each planet. In the first column is home planet, in other columns are other planets and percent of time they are closest one's. For instance, Mars is closest planet to Mercury during 1.4% of the investigated period, while Mercury is closest planet to Mars during 34.4% of it. Lack of percentage denotes technical impossibility given planet to be the closest planet. It might be curious to note that Uranus and Neptune are the only two planets for which at different instants any planet might be the closest.

          Mercury   Venus    Earth    Mars    Jupiter  Saturn   Uranus   Neptune 
Mercury             72.9%    25.7%     1.4%                                      
Venus      66.4%             27.3%     6.3%                                      
Earth      46.8%    36.7%             16.5%                                      
Mars       34.4%    32.2%    33.5%                                               
Jupiter    14.5%    19.1%    25.7%    35.2%              5.5%                    
Saturn      8.8%    12.2%    17.1%    24.4%    36.7%              0.9%           
Uranus      3.5%     5.6%     7.6%    12.0%    24.5%    32.4%             14.4%  
Neptune     2.3%     3.8%     5.5%     9.3%    19.2%    27.8%    32.1%           

Below are times of closest approaches between all planetary pairs during the two millennia timespan, AD 1001 - AD 3000. All times in Terrestrial Time, dates prior to 1582 are in Julian calendar.

Planetary pair     Distance     Calendar Date  
                    mln.km.                    
                                               
Mercury  Venus       39.100   2911-Nov-13 11:22
Mercury  Earth       82.080   2942-Jun-14 02:41
Mercury  Mars       144.188   1089-May-12 04:44
Mercury  Jupiter    686.296   2615-Sep-12 23:00
Mercury  Saturn    1296.871   1355-Feb-09 08:52
Mercury  Uranus    2672.292   2556-Jul-20 17:12
Mercury  Neptune   4407.886   2870-Oct-14 17:33

Venus    Earth       39.463   1137-Nov-28 16:26
Venus    Mars        97.748   2904-Aug-19 01:30
Venus    Jupiter    630.604   2616-Feb-26 21:27
Venus    Saturn    1235.308   1355-Jan-30 14:39
Venus    Uranus    2622.892   2555-Jul-10 04:27
Venus    Neptune   4347.127   2871-Jul-11 08:40

Earth    Mars        55.651   2729-Sep-08 04:50
Earth    Jupiter    589.507   2734-Oct-17 11:54
Earth    Saturn    1195.818   1354-Dec-02 06:47
Earth    Uranus    2581.866   2555-Mar-22 01:14
Earth    Neptune   4307.074   2870-Nov-20 08:41

Mars     Jupiter    525.458   2617-Mar-04 01:16
Mars     Saturn    1104.805   1473-Nov-10 15:30
Mars     Uranus    2482.187   2555-Oct-23 21:58
Mars     Neptune   4230.109   1071-Mar-21 19:59

Jupiter  Saturn     567.561   1504-Apr-24 20:54
Jupiter  Uranus    1917.716   2977-Aug-07 09:06
Jupiter  Neptune   3697.595   1089-Mar-04 03:03

Saturn   Uranus    1302.509   1216-Apr-23 11:40
Saturn   Neptune   3009.487   2491-Sep-22 01:29

Uranus   Neptune   1460.984   2852-Aug-05 15:17