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See the advance of the perihelion of Mercury It is possible to ‘see' the advance of the perihelion of Mercury predicted by general relativity by direct numerical solution. Take Einstein's path equation
(d2v/dθ2) + v = (1/1-e2) + ηv2,
where υ = au. Here a and e are the semi-major axis and eccentricity of the non-relativistic elliptic orbit and η = 3MG/ac2 is a small dimensionless parameter.
For the orbit of Mercury, η = 2.3 × 10-7 approximately. Solve this equation numerically with the initial conditions r = a(1 + e) and r· = 0 when θ = 0; this makes θ = 0 an aphelion of the orbit.
To make the precession easy to see, use a fairly eccentric ellipse and take η to be about 0.005, which speeds up the precession by a factor of more than 104!
a 356 mm diameter main services a section of a mine and carries 4.8 kgs of compressed air at peak periods. if the main
the reynolds number of a fluid flowing through a 5-cm-diameter, square-edged orifice plate meter within a 15-cm pipe is 250,000. Find the discharge coefficient for flange taps.
The use of commercial software packages has allowed Life Cycle Assessments to be undertaken more rapidly and easily. Your task is to investigate the software packages that are available, and give an overall review of the ways in which they make t..
Assume that h0 = 20 m, H = 10 m, and Q0/2πkH = 1 m. What is the limiting value of the head when the radius of the tube is very small, rw → 0?
when drilling a hole in a table leg a furniture maker uses a hand-operated drill with a bit of diameter d4.0mm.a. if
A 5-ft 3 rigid tank contains a saturated mixture of refrigerant-134a at 50 psia. If the saturated liquid occupies 20 percent of the volume, determine the quality and the total mass of the refrigerant in the tank
Model the earth as a sphere with a diameter of 8,000 miles. Using 14.7 psia as the average pressure at the earth's surface and ignoring variation in g with altitude, estimate the weight of the earth's atmosphere in lbf, and its mass in lbm.
If the pressure drop through a cyclone is assumed to be 1 in. of water, estimate the diameter of cyclone required for various air-flow rates to remove 1-in.-diameter aluminum chips
the masses of a b and c are 5 kg 15 kg and 100 kg respectively. the coefficient of friction between all contacting
water is supplied steadily at 150 ft2s to a hydraulic turbine through a 3ft diamter inlet pipe and discharged through a
The 12-kg uniform bar AOB is pinned to the carriage at O. The bar is at rest in the vertical position at t = 0 when the harmonic displacement y(t) = Y sin pt is imposed on the carriage, where p is the resonant frequency for small amplitudes and Y ..
determine the cycle efficiency of steam power plant working under the following data boiler pressure 80 bar condenser
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