pointing (in practice one would use a combination of accelerometers to obtain readings in three orthogona directions). The direction is measured independently using gyroscopes, which we will study in future lectures the location (required to extract the value of the gravity force) is tracked by integrating the acceleration The final ingredient is an accurate map, or model, for the gravity field as a function of position Let us consider an accelerometer, or system of accelerometers, capable of providing readings along two(or three, when we consider a 3D space)orthogonal directions n'y A=B The external forc the test mass, m, will be F=R+ mg, where R is the total force exerted by the springs, and g is the gravity acceleration vector. If the mass has an acceleration a, the inertial force for an observer B moving with the mass will be simply Inertial=-ma. Thus, F+ Inertial =R+mg-ma=0 (g-a)=(a-9) The quantity (a-g) is called the specific force and is the actual measurement that we will obtain from the accelerometer. Note that if we are dealing with a single axis accelerometer, with the axis parallel to the unit vector ea, then the accelerometer will only provide the component of R along that axis, i. e. Ra =ea. R. Thus from the above equation, we have Ra Newtonian Relativity(from Hollister) Although relativistic corrections are not necessary for most aerospace engineering applications(with the possible exception of the very large scale GPS systems), one concept of Einsteins General Relativity is helpful in understanding gravity. It is called the Principle of equivalence. The concept is that, since the pecific force (a-g) is the only quantity that can be measured, gravity and inertial acceleration cannot be distinguished by measurement only. Once again, this can be illustrated with the example of the boy in the elevator. If the boy did not know his weight before getting into the elevator, once inside the elevator he would not be able to tell the difference between gravitational acceleration and inertial acceleration. That is, for an accelerated observer, inertial forces and gravity appear to be of exactly the same form. It is thenpointing (in practice one would use a combination of accelerometers to obtain readings in three orthogonal directions). The direction is measured independently using gyroscopes, which we will study in future lectures; the location (required to extract the value of the gravity force) is tracked by integrating the acceleration. The final ingredient is an accurate map, or model, for the gravity field as a function of position. Let us consider an accelerometer, or system of accelerometers, capable of providing readings along two (or three, when we consider a 3D space) orthogonal directions x ′y ′ . The external force on the test mass, m, will be F = R + mg, where R is the total force exerted by the springs, and g is the gravity acceleration vector. If the mass has an acceleration a, the inertial force for an observer B moving with the mass will be simply Finertial = −ma. Thus, F + Finertial = R + mg − ma = 0 , or, R m = −(g − a) = (a − g) . The quantity (a − g) is called the specific force and is the actual measurement that we will obtain from the accelerometer. Note that if we are dealing with a single axis accelerometer, with the axis parallel to the unit vector ea, then the accelerometer will only provide the component of R along that axis, i.e. Ra = ea · R. Thus, from the above equation, we have Ra m = ea · (a − g) = (aa − ga) . Newtonian Relativity (from Hollister) Although relativistic corrections are not necessary for most aerospace engineering applications (with the possible exception of the very large scale GPS systems), one concept of Einstein’s General Relativity is helpful in understanding gravity. It is called the Principle of Equivalence. The concept is that, since the specific force (a − g) is the only quantity that can be measured, gravity and inertial acceleration cannot be distinguished by measurement only. Once again, this can be illustrated with the example of the boy in the elevator. If the boy did not know his weight before getting into the elevator, once inside the elevator he would not be able to tell the difference between gravitational acceleration and inertial acceleration. That is, for an accelerated observer, inertial forces and gravity appear to be of exactly the same form. It is then 2