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Satellite speed is $35\ \mathrm{km/s}$ after burn for $500\ \mathrm{ sec}$ and after some days or months this speed is reduced automatically $34$, $33$, $32$ respectively.

Questions:

  1. How the satellite speed is reduced automatically in the vacuum? (as per Newton's 1st law this is wrong)

  2. How do we calculate the speed of a satellite in space?

  3. How much accurate they are?

I'm assuming they calculate by sending(ACK) radio wave to satellite from ground (earth) or space(other satellite) and by calculating how much time it has taken(t) to receive back those signal(ACK).

$\text{Distance}= \text{speed of radio wave}\times\large \left(\frac{t}{2}\right)$ as it was round trip ACK signal.

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How the satellite speed is reduce automatically in vacuum?

Perhaps they are not in hard vacuum.

Many objects are in low earth orbit (LEO) between 160 and 2000 km. Therefore they experience atmospheric drag.

The Earths atmosphere has a layer called the exosphere which extends from about 700 km out to 10000 km. However this is pretty thin stuff.

The thermosphere extends from about 80 up to 500-1000 km (depending on solar activity). This definitely causes drag.

How do we calculate speed of satellite in space?

NASA and other organisations track satellites and orbital debris using radar and optical measuring systems.

For some large objects in orbit you can just look up and time how long it is between appearances of the object overhead.

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  • $\begingroup$ what happens if satellite cross thin stuff(above 1000km)? assume it is going to Saturn. $\endgroup$ – editinit Dec 2 '15 at 9:40
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    $\begingroup$ @editinit: If it is going to Saturn it isn't a satellite. Also, this site is optimised for asking one question at a time, not for conducting discussion of follow up questions in comments. $\endgroup$ – RedGrittyBrick Dec 2 '15 at 9:42
  • $\begingroup$ @RedGrittyBrick - I think they use Doppler effects and interferometry to get the attitude/orbit information... $\endgroup$ – honeste_vivere Dec 2 '15 at 14:12
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I am only going to address the third question since @RedGrittyBrick already answered the first two.

How much accurate they are?

The accuracy of the speed and location of spacecraft depends upon the distance from Earth and the amount of money spent on the attitude systems.

The distance matters because when close to Earth, they can use interferometry between multiple ground stations. Then the accuracy is limited by the accuracy of the spacecraft and ground station clocks. On GPS spacecraft, the clocks are incredibly accurate and we can determine their location very accurately. On other spacecraft like Wind, located at the $L_{1}$ point, the location does not need to be known to better than few tens to few hundred kilometers. This may sound like a large uncertainty, but the spacecraft is located ~230-250 $R_{E}$ (or ~1.5 million km) away from Earth (or something like ~0.007% uncertainty).

The speed of the spacecraft can be determined using a combination of the interferometry, Doppler effects from the transmitter signal and/or radar, and orbital element predictions (see more in this article on orbital mechanics and this article on flight dynamics). Again, the accuracy depends upon the distance from Earth and the amount of money spent on the attitude systems.

Some missions buy specific atttitude systems to ensure high accuracy in their attitude/orbit determinations while other missions rely upon some of the methods I mentioned above using the Deep Space Network or the Near Earth Network, depending on altitude.

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35 km/s is faster than the escape velocity of the Earth (11 km/s) but slower than the escape velocity of the Sun (42 km/s). So this satellite is heading toward the outer planets but still in orbit around the Sun.

While heading away from the Sun, the gravitational force of the Sun is causing the satellite to slow down -- per Newton's first law.

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