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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!
one mole of ideal gas with known constant volume specific heat is confined in the cylinder by the weightless
a piston-cylinder device initially contains 0.07 m3 of nitrogen gas at 130 kpa and 120 oc. the nitrogen is now expanded
a tank of 50 cubic feet contains saturated ammonia at 100 f and a quality of 50. vapor is withdrawn from the top of the
A bullet of mass m is shot at speed v toward a pendulum bob of mass M. The bullet penetrates through the block and emerges on the other side traveling at speed v/2.
Explain why it is difficult to validate a reusable component without the component source code. In what ways would a formal component specification simplify the problems of validation?
A golf ball is driven off a tee that is elevated 30 ft above the fairway and hits the ground that is below 30 ft from the tee. The initial velocity of the ball is 120 ft/s at an angle of 40 degrees from the horizontal.
Plot the lift and drag forces exerted on an airfoil as a function of velocity. Use velocity values going from 0 to 45 m/s on a log-linear plot (log-scale on the y axis).
you are blanking a square using a straight edge punch. if the punch is angled to be at a shear angle of 10 degrees how
Determine the current through the capacitor just before and just after the switch is closed in Figure P5.23. Assume steady-state conditions for t 0.
what is the actual speed of the pitch? Assume the pitch follows a straight-line path, and express your answer in terms of s: Note that the value s measured by the radar gun is the rate of change of the distance between point A and the ball.
An ideal gas expands isentropically through a converging nozzle from a large tank at 120 lbf/in.2, 6008R, and discharges into a region at 60 lbf/in.2 Determine the mass flow rate, in lb/s, for an exit flow area of 1 in.2, if the gas is
In air-conditioning systems, streams of cold and warm air are mixed to get air with the right temperature. Consider a mixing chamber into which cold air enters at 8 degree C and 100 kPa at a rate of 0.55 m3/s and warm air enters at 30 degree C and 10..
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