Error Propagation Gravity
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Speed Of Propagation Of Gravity
the planet! Everyone who loves science is here! Finding error on gravitational acceleration how fast does gravity propagate Page 1 of 2 1 2 Next > Oct 6, 2012 #1 peripatein How may the error on gravitational
Error Propagation Example
acceleration (g) be determined, given a set of measurements of time (t) and distance (d)? It is stated that the distances are measured precisely and time with an accuracy of 0.01 error propagation division sec. I have applied Least Squares on t = √(2/g) * √d and found (σ of √g) albeit was unsuccessful at deducing (σ of g). I have also tried using Error Propagation, hence (σ of t)^2 = [(∂t/∂g) * (σ of g)]^2 → (σ of t)^2 = (d/2g^3) * (σ of g)^2, yet what value would d have? Please advise! peripatein, error propagation physics Oct 6, 2012 Phys.org - latest science and technology news stories on Phys.org •Game over? Computer beats human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength Oct 6, 2012 #2 Simon Bridge Science Advisor Homework Helper Gold Member How did you get the different measurements? Simon Bridge, Oct 6, 2012 Oct 7, 2012 #3 Simon Bridge Science Advisor Homework Helper Gold Member Back to you ... you have y=√g and σy and you want to find σg ... is that it? so what is stopping you from putting g=y2 and finding the uncertainty on that the usual way? Simon Bridge, Oct 7, 2012 Oct 7, 2012 #4 peripatein Thank you! :-) peripatein, Oct 7, 2012 Oct 7, 2012 #5 Simon Bridge Science Advisor Homework Helper Gold Member No worries. In general, if ##y=f(x)## and you have ##x\pm \sigma_x## and you need ##\sigma_y## then: ##\sigma_y = \sigma_x f^\prime(x)## Proof: expand f(x) in a power series $$y=f(x)=\sum_{n=0}^\infty a_n x^n$$ You know how to find the uncertainty on each of the terms: $$\frac{\sigma(x^n)}{x^n}=n\frac{\sig
calculate important results. For example, you might: - Measure a room’s linear dimensions (length, width, height) and calculate its volume. - Measure the time and distance a ball falls from rest, and calculate the gravitational acceleration it was experiencing as
Error Propagation Calculus
it fell. - Measure the distance a spring is pulled away from its equilibrium error propagation khan academy position, and the force needed to pull it, to calculate the “spring constant k”. In every case, you will have some uncertainty in
Error Propagation Average
the values you measure, as every measurement in science has some inherent uncertainty due to the instrument, technique, and/or observer involved. How will those uncertainties in what you measured affect the derived quantity? There are https://www.physicsforums.com/threads/finding-error-on-gravitational-acceleration.641717/ some easy brute-force techniques you can use in every lab to estimate the uncertainty of any calculated quantity, and some wonderful mathematical principles you can apply that show why those techniques are valid. Example: Calculating Volume Suppose you want to calculate the volume of a regular, rectangular solid, like a physics book! You measure the length (l), width (w), and height (h) of the solid, in centimeters, to two (2) significant figures, and https://www.chabotcollege.edu/faculty/shildreth/physics/4alectures/Uncertainty1.htm record the data as shown below in the table. You have some uncertainty in the measured values of l, w, and h, which you have estimated to be 1 mm for each dimension. We’ll use the greek letter “delta” (d) to indicate that uncertainty in a measurement. (l) Length (cm) (dl) Uncertainty in measuring l (cm) (w) Width (cm) (dw) Uncertainty in measuring w (cm) (h) Height (cm) (dh) Uncertainty in measuring h (cm) 28.7 0.1 21.1 0.1 5.4 0.1 What does d mean? The uncertainty in a measurement reflects a range in values that might be possible. In your measurement of length for the book, you found l = 28.7 cm, but it might have been as little as 28.65 cm, or as much as 28.75 cm. You could capture this uncertainty by writing your measurement as: Length = 28.7 +/- 0.1 cm In general, your measurements should always be recorded as: x +/- dx (units) For the regular rectangular solid, calculating the volume is easy – Volume = Length x Width x Height. From your measurements, a calculator will give you: Volume = 28.7 cm x 21.1 cm x 5.4 cm = 3270.078 cm3 Two questions should immedi
Explore this journal > Explore this journal > Previous article in issue: Twentieth century constraints on sea level change and earthquake deformation at http://onlinelibrary.wiley.com/doi/10.1111/j.1365-246X.2010.04669.x/abstract Macquarie Island Previous article in issue: Twentieth century constraints on sea level change and earthquake deformation at Macquarie Island Next article in issue: Swarms of microearthquakes associated with the 2005 Vulcanian explosion sequence at Volcán de Colima, México Next article in issue: Swarms of microearthquakes associated with the 2005 Vulcanian explosion sequence at Volcán de Colima, México View issue TOC error propagation Volume 182, Issue 2 August 2010 Pages 797–807 Propagation of atmospheric model errors to gravity potential harmonics—impact on GRACE de-aliasingAuthorsL. Zenner, Institute for Astronomical and Physical Geodesy, Technische Universität München, Arcisstr. 21, 80290 Munich, Germany. E-mail: zenner@bv.tum.deSearch for more papers by this authorT. Gruber, Institute for Astronomical and Physical Geodesy, Technische Universität München, Arcisstr. 21, 80290 Munich, Germany. E-mail: zenner@bv.tum.deSearch for error propagation gravity more papers by this authorA. Jäggi, Astronomical Institute, University of Bern, Sidlerstr. 5, 3012 Bern, SwitzerlandSearch for more papers by this authorG. Beutler Astronomical Institute, University of Bern, Sidlerstr. 5, 3012 Bern, SwitzerlandSearch for more papers by this authorFirst published: 23 June 2010Full publication historyDOI: 10.1111/j.1365-246X.2010.04669.xView/save citationCited by: 0 articles Citation tools Set citation alert Check for new citations Citing literature SUMMARYHigh-frequency, time-varying mass redistributions in the ocean and atmosphere have an impact on GRACE gravity field solutions due to the space–time sampling characteristics of signal and orbit. Consequently, aliasing of these signals into the GRACE observations is present and needs to be taken into account during data analysis by applying atmospheric and oceanic model data (de-aliasing). As the accuracy predicted prior to launch could not yet be achieved in the analysis of real GRACE data, the de-aliasing process and related geophysical model uncertainties are regarded as a potential error source in GRACE gravity field determination. Therefore, this study aims to improve the de-aliasing process in order to obtain a more accurate GRACE gravity field time-series. As these time