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GPS (Global Positioning System) Accuracy of Measurement

The 24 satellites that orbit the earth and define the Global Positioning System use
precision atomic clocks that are accurate to 1 x 10-9 s, or 1 nanosecond (1ns). A person on the earth, using their mobile phone, can usually “see” 4-12 of the 24 satellites at any one time.

An animation depicting the orbits of GPS satel...
An animation depicting the orbits of GPS satellites in medium Earth orbit. (Photo credit: Wikipedia)

The satellites are moving, relative to the surface of the earth, at 1.4 x 104 km/h.
a- Calculate  for one of these satellites,
Civilian GPS measurements have to be accurate at the level of 5-10m. How accurate must our knowledge of the clocks on the satellites be in order to achieve this level of accuracy in our position measurement?
[HINT: light signals are used by your phone and the satellites to perform the triangulation]
c-If we measure the passage of 1 day on earth using a clock that is identical to the clocks on the GPS satellites, how much time have the clocks on the satellites measured? What about for the passage of 2 days on earth? For this problem, it will be useful to apply the Binomial Expansion again

Mona asked

A Problem from Gravitation

An artificial satellite is revolving around the earth in circular path at height equal to the radius of the earth.Find the speed of the satellite.The mass and radius of Earth are respectively 5.98 x 1024 kg and 6 x 103 km.

(Asked by Rehmat)

Answer:

Will be answered soon

Why gravitational force of attraction is necessary for a satellite to revolve around earth?

The question was posted by Raj Kumar.

The satellite has a velocity. To revolve around, the direction of velocity must change. In the absence of a force it can move only in a straight line. It is the gravitational force which helps the satellite top change direction and revolve around the earth.

In other words, for a satellite to revolve in a circular path, a centripetal force is required. This centripetal force is provided by the force of gravitation only.

NAVSTAR : GPS NAVIGATION SYSTEM

Anjum Haseeb asks:

What is NAVSTAR navigation system?

Answer:

NAVSTAR stands for Navigation System using Timing And ranging.

It consists of  at least 24 satellites in 6 orbital planes.

Each satellite circles the Earth twice every day at an altitude of 20,200 kilometers.

The satellites are equipped with atomic clocks . They continuously broadcast the precise time according to their own clock, along with information including the orbital elements of their own motion, as determined by a set of ground-based observatories.

Find more details at

 

 

 

BMMD – Body Mass Measuring Device

Priyanka asked

What is a BMMD? How does it work?

Ans:

BMMD stands for Body Mass Measuring Device used by astronauts, which is basically a spring mounted chair which measures mass as a measure of inertia. As you know, one experiences weightlessness inside a satellite and normal methods of measuring mass do not work. (like a common balance or a spring balance). The time period of oscillations which depends on the force constant and mass is used in measuring mass in BMMD used by an astronomer

Time Period of a Simple Pendulum in Space

Mary Beth asked:

“if you set up a pendulum aboard an orbiting space vehicle, would the period be less than, the same as, or greater than it would be in our lab? explain.”

Ans:

In a space vehicle orbiting around the earth, the apparent weight is zero as the entire gravitational pull is being utilized in providing the centripetal force required for revolving. This is called weightlessness in space.

i.e; in effect, the acceleration due to gravity is zero which make the time period of the satellite infinity. The pendulum will not oscillate at all.

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Tailpiece:

However, in manned space vehicles, there is an option to simulate gravity by making the system rotate at a particular rate so as to make the inhabitants feel as if there is weight and gravity.

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