Re: most mileage

Leo Barhorst (leobarhorst@pi.net)
Thu, 09 Oct 1997 21:17:40 +0200

In a private message to me Jeff Kosecki wrote:
> 
> hi,
> 
> Interesting stuff about the history of satelites.  I thought of a question the 
> other day?  What man made object would have the most mileage?  And how much 
> mileage would that be....
> 
> thanks
> \
> jeff

Hello Jeff and all you Seesatters,

That is an interesting question and interesting for more people, so I take the
liberty to answer this private mail in public.

The second question was cut short due to a singe long line in which your message
arrived.
I assume you mean the total mileage by one sat, regardless its distance to 
the earth at this moment, october 8th 1997 (question 1) and when it finally decays
(question 2).

Question 1:

As far as I now recall it's Voyager 1 that is fartest away from earth; travelling
faster than Pioneer 10 that passed 50 AU from the sun in 1990 and is travelling at
about 2.7 AU/year and thus now about 69 AU away. 1 AU is the distance Sun-Earth, 
some 150 million km. So Pioneer 10 is now at 10.350.000.000 km distance.

The oldest sat still in orbit is Vanguard 1.
Launched 17th march 1958 in a 650 by 3968 km orbit, period 134.2 min. This data is 
not much different than the data for July 1, 1993: 653 by 3870 km, 133.2 min.
The mean orbit is then: 651 by 3920 km and 133.7 min.

Using 'simple' formula's for ellipses:

a=R+{(H+h)/2}=6371+{(3920+651)/2}=8657 km -> semi-major axis

e=(H-h)/(H+h+2R)=(3920-651)/(3920+651+2*6371)= 0.26402 -> eccentricity

the semi-minor axis: b*b=a*a(1-e*e) -> b=8350 km


Circumference of the ellipse = (2*pi*a+2*pi*b)/2 = 53.248 km

from 17-3-1958 till 8-10-1997 is 14.450 days and 1440 min/day; 133.7 min/revelution
we get: 14.450*(1440/133.7)=1.676.157 revs since launch

total travelled distance:
1.676.157 * 53.248 km = 89.553.716.000 km or almost 60 milliard (billion) miles.

Although this seems quite a distance it is very small compared to the lightyear:
60*60*24*365.25*300.000=9.467.280.000.000 km

or less than 1 percent of a lightyear and only about 0.2 percent of the distance to
the sun-closest star at 4 lightyears.

The oldest satellite in an almost circular orbit is Tiros 1 in an orbit of 658 by
695 km and a period of 98.3 min and launched 01-04-1960.

Using a mean radius of the orbit : (658+695)/2=677 km + R earth = 7048 km
Circumference = 2*pi*7048 = 44.283 km

Revs since launch: 13704 days * (1440/98.3) = 200.750 revs

total distance travelled: 200.750 * 44.283 = 8.898.812.200 km or about a tenth of 
the total distance travelled by Vanguard 1.

Question 2:
The estimated lifetime of sats depends ond many factors, such as  orbit disturbance
by the sun, moon, planets, atmospheric density when they come closer to the earth.
The orbit gets closer to the earth so the period decreases and the circumference
gets smaller. So an accurate estimate is not possible.

For Vanguard 1 a lifetime is estimated of 300 years or some 109.575 days. 
Not regarding the above the total mileage would be

  (109.575 / 14.450) * 89.553.716.000 ~ 7.58 * 89.55 * 10^9 ~ 680 * 10^9 km

or still only 7 percent of a lightyear !
 

Although the above calculations are not super precise they give a good idea of the
mileage of these old sats.
Travelling to the stars is not possible in this way.

Can someone inform me about the current status of the Pioneer 10, 11 and Voyager
1, 2 spacecraft? How far away are they at the moment?

Greetings 

-- 
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Leo Barhorst    Alkmaar   The Netherlands
52.65 North   4.77 East   3 m asl
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Every day I wonder about what I see in the sky