Aspacecraft in a trapped orbit is observed to be at an altitude of 1000 km with a velocity of 10.3 km/s. the velocity vector is orthogonal to the radius vector (from the center of the earth).

a. find the specific energy, semi-major axis, eccentricity, and the parameter.
b. find the specific kinetic energy, potential energy, and angular momentum at perigee and apogee.
c. find the altitude and velocity of the spacecraft at its furthest position from earth.
d. given that the average earth-moon distance is 385,000 km, what type of maneuver might this orbit be classified as? hint: search online for maneuvers.
e. assume the moon is in a circular orbit around the earth with a period of 27.3 days. what is the phase angle, that is, the angle between the spacecraft and the moon relative to earth at the time of the first burn to ensure a successful rendezvous?
f. suppose the spacecraft starts at the same altitude and has the same velocity direction as given in the problem statement. determine the range of speeds that would place this spacecraft on a ballistic trajectory with the earth (i. e. spacecraft impacts the surface). ii. determine the minimum speed that would place this spacecraft on an escape (e. g., interplanetary) trajectory

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

total distance/total time

(85 + 82)/(5+3)

167/8

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