PDF Gravitational Field of a Static, Spherically Symmetric Source

The energy density carried by an electromagnetic field can be computed by adding the square of the electric field intensity to the square of the magnetic field intensity. As another example, a beam of light produced from, say, a laser consists of an electromagnetic field, and it will exert a force on charged particles. Thus the electromagnetic field carries momentum. Because an electromagnetic field contains energy, momentum, and so on, it will produce a gravitational field of its own.

This gravitational field is in addition to that produced by the matter of the charge or magnet. A simple example of the gravitational or space-time curvature effect of electric charges arises in the "Reissner-Nordstrom" solution to Einstein's gravitational field equations. This solution describes the gravitational field in the exterior of a spherical body with non-zero net electric charge. The solution describing the special case in which the net electric charge is zero is the famous "Schwarzschild solution" to the gravitational field equations.

• DNA Data Storage Innovation Reduces Write Times, Boosts Density?
• The Language of Speech and Writing (Intertext).
• Categories and Case: The Sentence Structure of Korean?

From the Reissner-Nordstrom solution, it is clear that the motion of test particles in the gravitational field of the spherically symmetric body depends on whether or not the body carries a charge. Just as the Schwarzschild solution can be extended to describe the famous phenomenon of a "black hole," the Reissner-Nordstrom solution can be extended to describe a "charged black hole.

I do not know and I doubt whether this aspect of gravitational theory that electromagnetic fields produce gravitational fields has been directly tested by experiment. The difficulty is that the gravitational field produced by a typical electromagnetic field you can produce in a laboratory is predicted to be very, very weak.

A better place to look for gravitational effects due to electromagnetic fields would be in astrophysical objects carrying a significant net electric charge. Unfortunately, to my knowledge, such objects are expected to be hard to come by.

Physical Review D - Accepted Paper: Imaging extended sources with the solar gravitational lens

So while the answer to the question is definitely "yes" according to theory, the experimental status of this effect appears to be somewhat open. This book is aimed at non-specialists. For a more detailed mathematical treatment, you can consult any text on the general theory of relativity. Newsletter Get smart. This upper bound is used to estimate the total uncertainty in a gravity or geoid anomaly.

Signal spectra represent the amplitude of expected signals in the Earth's gravity field. We also show error spectra that are analogous quantities derived from the estimated degree variances of the uncertainties in the anomalous potential coefficients expected for various missions or gravity field models.

External gravitational field of a non-static spherically symmetric body

In Chapter 2 of this report we estimate the resolving power of various satellite gravity missions. Our estimates are obtained under the assumption that the power spectral density PSD of the errors in the observable is white and that the orbit distributes the errors isotropically over the surface of a sphere. Under these assumptions, equations given by Jekeli and Rapp and a chosen mission duration can be used to obtain the degree variances of the observable on a sphere at satellite altitude. Rummel and van Gelderen discuss further the properties of isotropic distributions as used in geodesy.

The observable is , the "range rate," the time derivative of the line-of-sight distance between the two spacecraft. An SGG mission will measure second derivatives of the gravity potential at the spacecraft altitude. We approximate the errors in the gravity field obtained in such a mission by assuming that the dominant source of gravity-field error is the error in the second radial derivative of the potential, V rr.

We obtain the degree. We follow Jekeli in using a spherical approximation to an isotropic Gaussian convolution filter weighted average as follows. Define the weight function. The leading constant in A17 normalizes the weight function so that its integral over the surface of a sphere is one. In order to form Gaussian-weighted averages from degree variances, we need the Legendre expansion of the weight function. These are adjusted, as explained in Chapter 2 , so that if the degree variance of the error from a satellite mission exceeds the degree variance of the signal in the.

The root-mean-square accuracy of the Gaussian-averaged geoid height, e geoid , is given by. For the past three decades, it has been possible to measure the earth's static gravity from satellites. Such measurements have been used to address many important scientific problems, including the earth's internal structure, and geologically slow processes like mantle convection.

In principle, it is possible to resolve the time-varying component of the gravity field by improving the accuracy of satellite gravity measurements. These temporal variations are caused by dynamic processes that change the mass distribution in the earth, oceans, and atmosphere. Acquisition of improved time-varying gravity data would open a new class of important scientific problems to analysis, including crustal motions associated with earthquakes and changes in groundwater levels, ice dynamics, sea-level changes, and atmospheric and oceanic circulation patterns.

This book evaluates the potential for using satellite technologies to measure the time-varying component of the gravity field and assess the utility of these data for addressing problems of interest to the earth sciences, natural hazards, and resource communities. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

Jump up to the previous page or down to the next one.

• THE DANCE OF TWO BLACK HOLES.
• Yoga for a New You.
• River Conservation and Management.
• Shell theorem.

Also, you can type in a page number and press Enter to go directly to that page in the book. Switch between the Original Pages , where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

Solution # 13/ Gravitational field due to solid sphere & spherical shell/ GRAVITATION/ olagynulehyb.gq