The relativistic effect in Global Navigation Satellite System satellites has two parts, of which the first part is the time dilation due to the shift in the fundamental frequency of the satellite clock. The second part is due to the satellite’s semi-major axis and __________
The relativistic effect in Global Navigation Satellite System satellites has two parts, of which the first part is the time dilation due to the shift in the fundamental frequency of the satellite clock. The second part is due to the satellite’s semi-major axis and __________
Show Hint
In GNSS, relativistic time corrections consist of constant (gravitational) and periodic (orbital eccentricity-related) terms. Remember: a satellite's eccentric orbit causes changing velocity and altitude—both impacting clock time.
- eccentricity
- inclination
- argument of perigee
- right ascension of the ascending node
The Correct Option is A
Solution and Explanation
The first part of the relativistic effect comes from the general relativity principle where time dilation occurs because satellites orbit in a weaker gravitational field compared to the Earth's surface.
The second part arises from periodic variations in the satellite’s speed and distance from Earth, which are caused by the satellite’s orbital eccentricity. These variations cause periodic shifts in the satellite's clock due to special relativity.
Hence, the relativistic correction includes terms that are directly related to both the semi-major axis and the eccentricity of the satellite orbit.
Top Questions on Waves
- In an open organ pipe \( \nu_3 \) and \( \nu_6 \) are 3rd and 6th harmonic frequencies, respectively. If \( \nu_6 - \nu_3 = 2200\ \text{Hz} \), then the length of the pipe is _________ mm. (Take velocity of sound in air as \(330\ \text{m s}^{-1}\).)
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- The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \( \frac{5}{x} \). The value of \( x \) is ________.
Two loudspeakers (\(L_1\) and \(L_2\)) are placed with a separation of \(10 \, \text{m}\), as shown in the figure. Both speakers are fed with an audio input signal of the same frequency with constant volume. A voice recorder, initially at point \(A\), at equidistance to both loudspeakers, is moved by \(25 \, \text{m}\) along the line \(AB\) while monitoring the audio signal. The measured signal was found to undergo \(10\) cycles of minima and maxima during the movement. The frequency of the input signal is _____________ Hz.
(Speed of sound in air is \(324 \, \text{m/s}\) and \( \sqrt{5} = 2.23 \))
- 5th harmonic of a closed organ pipe matches with 1st harmonic of an open organ pipe. Find ratio of their lengths.
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