Performing the calculations required to move a vehicle from one circular orbit to another.

A space vehicle is in a circular orbit about the earth. The mass of the vehicle is 3,000 kg and the radius of the orbit is 2Re= 12,800km. The vehicle must be transferred to a circular orbit of radius 4Re. a) What is the minimum energy expenditure required for the transfer? b) An efficient way to accomplish the transfer is to use a semielliptical orbit (Hohmann transfer orbit). What velocity changes are required at the points of intersection between the original orbit and the semiellipse called A, and between the semiellipse and new circular orbit B?

Determining the distance of Halley's Comet from the sun at perihelion and aphelion and its speed when closest to the sun.

Halley's comet is in an elliptic orbit about the sun. The eccentricity of the orbit is 0.967 and the period is 76 years. The mass of the sun is 2 x 10^30 kg and G=6.67 x 10^-11 Nm^2/kg^2. a) Using this data, determine the distance of Halley's Comet from the sun at perihelion and at aphelion. b) What is the speed of Halley's Comet when it is closest to the sun?

Calculating the energy that will make the motion circular and finding the frequency of radial oscillations.

A particle of mass m moves under as an attractive central force Kr^4 with angular momentum l. For what energy will the motion be circular, and what is the radius of the circle? Find the frequency of radial oscillations if the particle is given a small radial impulse.

Needing help for a problem of friction

A half section of pipe, weighting 200 lb, is to be moved to the right along the floor without tipping. Knowing that the coefficient of friction between the pipe and the floor is 0.40, determine the largest allowable value of «alpha». My part of the answer: Sum Fy=0 -200 + N + T*sin(alpha)= 0 N = 200 - T*sin(alpha) Sum Fx=0 T*cos(alpha)- F = 0 T*cos(alpha) = F We know that F = 0.4*N T*cos(alpha) = 0.4*(200 - T*sin(alpha)) T*cos(alpha)-80 = -0.4*T*sin(alpha) -2.5*T*cos(alpha)+200 = T*sin(alpha) -2.5*T*cos(alpha)+200 = T*(1-cos^2(alpha))^1/2 (-2.5*T*cos(alpha)+200)^2 = (T*(1-cos^2(alpha))^1/2)^2 7.25*T^2*cos^2(alpha)-500*T*cos(alpha)+200^2=T^2 For verificatio... click for more

Problem of friction

Here is the asking problem relating to the cylinder drawing: Find the moment of the largest couple M which may be applied to the cylinder if it is not to spin. The cylinder has a weight W and a radius r, and the coefficient of static friction (Us) is the same at A and B. I give you the answer of this problem: M=W*r*Us*(1+Us)/(1+Us^2)