Celestial Mechanics

Use Equation v2= (r/m)Fc [1] and [4] to solve for T. From this equation, determine what should happen to T as Fc is increased. Circle it on Data Sheet A.

When it comes to Euclidean Geometry, Spherical Geometry and Hyperbolic Geometry there are many similarities and differences among them. For example, what may be true for Euclidean Geometry may not be true for Spherical or Hyperbolic Geometry. Many instances exist where something is true for one or two geometries but not the other geometry. However, sometimes a property is true for all three geometries. These points bring us to the purpose of this paper. This paper is an opportunity for me to demonstrate my growing understanding about Euclidean Geometry, Spherical Geometry, and Hyperbolic Geometry.

Figure 3.4, located below, shows the theoretical acceleration of the rocket as a function of time. Figure 3.4 was created using modified code from the Eagle Space Flight Team. The modified code is not included in Appendix I because it contains many sub functions and would make the length of this lab longer than 20 pages. The code is available upon request by emailing Carl Leake at leakec@my.erau.edu.

During this phase of the cycle a base of fire is established along with identifying the enemy capability. During this phase the object is to suppress the enemy for maneuver. As an example this is when a Marine may use a frag grenade to eliminate/shock/suppress the enemy position.

β A = D/V βD + E/V βE = .5 × 0 + .5 × 1.4 = .7

6) The moons altitude increased from each other by 10 in the first two observations, and after that there was a short decrease of

Using case 2, we calculated ratios of mass and velocity for each configuration. Using the following formula, we compared the ratio of mass and ratio of velocity. We compared the ratios to see if momentum was conserved by seeing if the ratios agree within three times the percent uncertainty in the velocities.

In the equation above, I_ring^this the theoretical moment of inertia of the Ring, Mr is the mass of the ring, R_1^2 is the inner radius of the ring, and R_2^2 is the outer radius of the ring.

Next, theoretical velocity values were calculated, first by finding starting value, then by multiplying it by reference velocities according to equation (10) and Table1:

The objective of the experiment is to understand the meaning of displacement, average velocity, instantaneous velocity, average acceleration and instantaneous in one-dimensional motion. The first experiment was to calculate the average and instantaneous velocity. We first

(g) The steps (c) and (d) were repeated to obtain new values of Ŝe and then step (e) to obtain a new curve III.

where x, y are the coordinates of the robot (point o) in the inertial frame. If the linear speed and angular velocity of the robot are v and ω, respectively, assuming no-slip on the wheels, the velocity components can be written as

The missile acceleration should nullify the line-of-sight (LOS) rate between the target and interceptor that is basic philosophy behind PN. Originally, PNG law creates angular velocity or acceleration commands perpendicular to the LOS (line of sight). If two bodies are closing on each other eventually they will intercept when there is no rotation in the line of sight (LOS) between the two bodies relative to the inertial space.

Department of Mechanical Engineering MENG 263 TUTORIAL 1 Q1. The motion of a particle is defined by the relation x 2t3 6t2 10, where x is expressed in m and t in seconds. Determine the time, position, and acceleration when v 0. ( Ans. x 2m, a 12 m/s2 ) Q2. The motion of a particle is defined by the relation x 2t3 -15t2 24t 4, where x is expressed in meters and t in seconds. Determine (a) when the velocity is zero, (b) the position and the total distance traveled when the acceleration is zero. (Ans. (a) 1s ,4s (b) 1.5m,24.5m) Q3. A motorist is traveling at 54 km/h when she observes that a traffic light 240 m ahead of her turns red. The traffic light is timed to stay red for 24 s. If the motorist wishes

For an impulsive transfer case, there are several works, which focused on finding an ana-lytical solution to the primer vector equation. In 1669, Prussing published his work on the analytical solution of the out of plane component circular rendezvous problem [27]. In 1991, Carter published his studies of the xed time linearised impulsive rendezvous