Relative Error | Lecture Note - Edubirdie

University:
Massachusetts Institute of Technology
Course:
18.01SC | Single Variable Calculus
Academic year:

2019
Views:

438

Pages:

1
Author:

flokkdyrz57

Relative Error We continue with our example of time dilation in GPS satellite operation. We started with the following formula from special relativity: T Tm = � 1− v2 c2 and used a linear approximation to ﬁnd that: � � �� 1 v2 Tm ≈ T 1 + . 2 c2 This formula describes the diﬀerence due to time dilation between clocks on the ground and on the satellite. Algebraically, the diﬀerence is ΔT = Tm − T ; it turns out that there’s a very simple relation between T , ΔT , v and c: � � �� 1 v2 Tm ≈ T 1 + 2 c2 � � 1 v2 Tm ≈ T + T 2 c2 � 2� 1 v Tm − T ≈ T 2 c2 � � 1 v2 ΔT ≈ T 2 c2 � � ΔT 1 v2 ≈ T 2 c2 In other words, the relative or percent error ΔTT caused by time dilation is v2 proportional to the ratio 2 , which relates the speed of the satellite to the c speed of light. As in the example of falling stock prices, this value ΔTT gives us an idea of the relative size of the error introduced by time dilation.

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