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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!
aluminum-copper alloy96 atom al 4 atom cu is solution-annealed at 550c and then aged at 450c. at 450c a cual2
If the pressure before the contraction is 415 kPa, calculate the pressure in the smaller tube.
A symmetric 3 by 3 matrix [M] has the eigenvalues (lambda)_1 = 1, (lambda)_2 = 2, and (lambda)_3 = 5. The eigenvector associated with eigenvalue 1 is Determine matrix [M]
Calculate the theoretical power in kW to 1 DP developed by a fluid motor. The formula is: theoretical power = Volumetric Displacement * Angular Speed * pressure where the volumetric displacement = 102 cubic centimetres / revolution, the Angular Speed..
A turbine uses steam at 25MPa and 650°C at the turbine inlet to generate 17.5MW of power. The steam enters the turbine at a rate of 90000kg/h. A portion of the steam passing through the turbine is removed for the purposes of feedwater heating (Figure..
Suppose noise levels of a tape recorder are stated as -55 dB, while another figure is given as -60 dB "A-weighted." Explain the two statements. Why would one specification be preferred over the other?
one mole of ideal gas with known constant volume specific heat is confined in the cylinder by the weightless
a consider the steady operation of a refrigeration package for a shipping container on a train truck or ship. the
040 kg automobile is accelerated from 5 kmph to 70 kmph. What is the average power (in hp) required if this is done in 7 s?
How many hours would it take, on average, to find that DES key, using an exhaustive search approach and a collection of 2" processors?
an aircraft has a glide ratio of 12 to 1 meaning the plane drops 1m for every 12m it travels horizontally. a buildng
At a certain location in a duct, moist air at 35 C, 125 kPa and a relative humidity of 50% flows at a volume flow rate of 50 m^3/s. using tabular data, determine the following: i)the humidity ratio ii)the dry air mass flow rate (kg/s) iii) the water ..
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