Welcome, Guest. Please Login.
Gravity Simulator
11/20/14 at 12:27:03
News: Registration for new users has been diabled to discourage spam. If you would like to join the forum please send me an email with your desired screen name to tony at gravitysimulator dot com.
Home Help Search Login


Pages: 1 2 
Send Topic Print
Mercury (Mercury Closest Approaches to Earth?) (Read 16871 times)
kheider
Junior Member
**


Wikipedia is a
MMORPG

Posts: 86
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
03/01/09 at 11:46:52
 
On Wikipedia we are trying to update the data on Mercury's distance from Earth since Mercury has a varying eccentric orbit.  Last year I used Horizons to generate "Mercury Closest Approaches to Earth from 1950 to 2200" showing that currently Mercury does not come closer than 0.5489AU (82 million km):
http://home.comcast.net/~kpheider/Mercury.txt (see bottom section)
 
According to NASA Mercury never comes closer to Earth than 77.3 million:
http://nssdc.gsfc.nasa.gov/planetary/factsheet/mercuryfact.html   (under Mercury Observational Parameters)
 
Under http://en.wikipedia.org/wiki/Mercury_(planet)#Observation (cut and paste link) someone using Solex 10 suggests, "In 871, the nearest approach was the first in about 41,000 years to be closer than 82.2 Gm, something that has happened 68 times since then, as of 2008. After much longer gaps, the next approach to within 82.1 Gm is in 2679, and to 82 Gm in 4487. But it will not be closer to Earth than 80 Gm until 28,622." (Edited)
 
Can GravSim generate a plot of the distance of Mercury from Earth over say a 50,000 year period? Smiley  This would hopefully help illustrate some concepts.
-- Kevin
Back to top
 
« Last Edit: 03/02/09 at 18:10:44 by kheider »  
View Profile WWW   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
Reply #1 - 03/01/09 at 13:15:08
 
Difficult question to plot a graph for this time period autmatically !  
I guess JPL ends at 2200.  
I gave it a try using the Taylor integrator ( Picard) . After some manipilation with Excel I got the following graph for the next 1000 years .  
The output was split in timeframes of 10 years starting at 1 feb 2007 . The minimum value of each 10 year period ( if smaller then before ) is represented in the graph .  
So the next close approach in the coming 10 years will be 31th may 2015 .  
It's nice to see how the close approaches seem to gather each time beginnig of june .  
The minimum value I got at the end is 82.080.535.160 m  
 
Edit : I see the figure herunder gives a match in the year 2679 with the Solex Integration  Wink
Back to top
 

Distance_Mercury-Earth.jpg
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
Reply #2 - 03/02/09 at 12:57:58
 
This is a really tricky task Kevin .  
It requires a very good accurancy to perform this . Not only the orbits should be integrated very accurate in terms of orbital elements , but also the true anomaly should be very precise for both bodies . If this isn't the case the close approaches will miss.  
I've been to quick to run the above graph , as I noticed that runnig it at a higher accurancy the results vary a little . The graph herunder was run at an accurancy 10 times higher than the one above .  
Contrary to the Solex integration which was mentionned above the minimum distance keeps decreasing after 2679 .  
I think its hard to be confident about results after more than a couple of hundred years ( lets say thousand year ) given the accumulating errors .
Back to top
« Last Edit: 03/02/09 at 22:10:17 by frankuitaalst »  

Mercury-Earth_distance_2500_y.jpg
Email View Profile   IP Logged
kheider
Junior Member
**


Wikipedia is a
MMORPG

Posts: 86
Gender: male
Re: Mercury (Mercury Closest Approaches to Earth?)
Reply #3 - 03/02/09 at 18:19:07
 
Ahh.  This is why I like multiple sources.  The Solex 10 comment on the Mercury article had a few typos.  The comment has been changed to say, "After much longer gaps, the next approach to within 82.1 Gm is in 2679, and to 82 Gm in 4487. But it will not be closer to Earth than 80 Gm until 28,622."
 
We should keep in mind:
1. the prediction of the motions of Mercury was an important factor in the early acceptance of Einstein's General Theory of Relativity.
http://www.nineplanets.org/mercury.html
2. The eccenticity of Mercury can vary from nearly 0 to more than 0.45
http://www.worldscibooks.com/phy_etextbook/6178/6178_chap01.pdf  (Correia and Laskar 2004)
http://www.nature.com/nature/journal/v429/n6994/fig_tab/nature02609_F1.html
http://www.nature.com/nature/journal/v429/n6994/full/nature02609.html
http://www.obspm.fr/actual/nouvelle/jul04/merc.en.shtml
http://arxiv.org/abs/0901.1843 (Correia and Laskar 2009 core-mantle friction)
 
-- Kevin
Back to top
 
« Last Edit: 03/03/09 at 08:05:27 by kheider »  
View Profile WWW   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
Reply #4 - 03/04/09 at 10:17:53
 
Hereunder a graph of Mercury's distance to Earth which I ran at high accurancy .  
This result is I think in accordance with the Solex 10 simulation mentionned above .  
The distance seems to be decreasing with time .  
Reasons for this behaviour are variations in the eccentricity of Mercuries orbit , the precession of its orbit , but also the change in inclination ....But also Earths orbit changes in this time period .  
I'll try to post some additional info about this variations .
Back to top
 

MercuryDistanceToEarth22000y.jpg
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
Reply #5 - 03/04/09 at 11:57:57
 
The decreasing distance between Mercury and Earth is partially due to the changing inclination and eccentricity of Mercuries orbit ( see graph below) .  
But also Earths orbit changes . In this timeperiod the inclination of Earth rises to more than 2°.
Back to top
 

MercuryEvolution_Inc_and_Ecc.jpg
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
Reply #6 - 03/04/09 at 14:18:35
 
As a final picture of Earth's relation to Mercury an animation which clearly shows the dynamics of both orbits :  
The orbits seem to be static at first sight , till the animation starts again .  
Clearly visible is the precession of the perihelion of Mercury , but also Earth orbit seems to shift upwards.  
The animation was run over 22000 years .  
Unfortunately due to downsizing the sun isn't visible anymore in this screenshots .
Back to top
 

EarthandMercury22000y.gif
Email View Profile   IP Logged
kheider
Junior Member
**


Wikipedia is a
MMORPG

Posts: 86
Gender: male
Re: Mercury (Mercury Closest Approaches to Earth?)
Reply #7 - 03/04/09 at 16:03:00
 
Quote from frankuitaalst on 03/04/09 at 11:57:57:
The decreasing distance between Mercury and Earth is partially due to the changing inclination and eccentricity of Mercuries orbit ( see graph below) .
But also Earths orbit changes . In this timeperiod the inclination of Earth rises to more than 2°.

Wow Frank.  Those are very nice charts.  I am impressed.  I can really see how Mercury gets closer since the inclination drops as the eccentricity increases.
-- Kevin
Back to top
 
 
View Profile WWW   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
Reply #8 - 04/02/09 at 12:02:19
 
Kevin , as asked hereby the evolution of Earths Inc and Ecc in comparison with Mercurys over a timespan of more than 26000 years . Graph was generated using the Picard Integration . The result should be comparable with the results you get with the Solex10 program .  
The broad variation in Ecc of Earths orbit is due to our Moon .  
The result is also availabe in .xls format .  
Back to top
 

MercuryEarthincEccPlot.jpg
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
Reply #9 - 04/05/09 at 07:53:48
 
I've extended the above picture to the four rocky planets  and extended also the time period (0= now ) .
Back to top
 

Inclination_rocky_planets.jpg
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Re: Mercury (Mercury Closest Approaches to Earth?)
Reply #10 - 04/05/09 at 07:55:15
 
The evolution of eccentricity shows the following pattern :
Back to top
 

Eccentricity_rocky_planets.jpg
Email View Profile   IP Logged
kheider
Junior Member
**


Wikipedia is a
MMORPG

Posts: 86
Gender: male
Re: Mercury (Mercury Closest Approaches to Earth?)
Reply #11 - 04/05/09 at 18:43:19
 
Quote from frankuitaalst on 04/05/09 at 07:55:15:
The evolution of eccentricity shows the following pattern :

 
Solex 10 shows the same endpoints for eccentricity/inclination after 50,000 years...
Note: In Franks plots the point 50,000 is the year 52,007 since he set the 0 point as 2007-02-01.
 
-- Kevin
Back to top
« Last Edit: 04/07/09 at 12:49:13 by kheider »  

Mercury52009d.gif
View Profile WWW   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Mercury (Mercury Closest Approaches to Earth?)
Reply #12 - 04/17/09 at 12:33:05
 
It took some time to have the full solar system simulated for a period of 250.000 years from "now" .  
But here's the plot of the innermost planet ...
Inclination reaches a maximum of 10° , while eccentricity is generally decreasing .  
Something happens around 100.000 years from now for the Sma.  
Edit : above simulation was run under Newtonian gravity and does not take into account any oblateness .
Back to top
 

MercuryOrbitalParam_250000y.jpg
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Venus orbital parameters
Reply #13 - 04/17/09 at 13:01:06
 
Even more mysterious is the evolution of the orbital parameters of our sister planet Venus .  
The plot was generated with the full solar system .
Back to top
 

VenusOrbitalParam_250000y.jpg
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1415
Gender: male
Earth and Venus inclination
Reply #14 - 04/17/09 at 13:43:00
 
Some part of the mystery of Venus' inclination may become clear if we take a look  at the following picture:  
Earth and Venus are more closely related than I've previously thought .  
Their inclinations vary in counterphase . The period seems to be around 70.000y
Back to top
 

Earth_and_Venus_inclination_250000y.jpg
Email View Profile   IP Logged
Pages: 1 2 
Send Topic Print