A spaceship of mass 142kg is going to use a planet for a gravitational assist - that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 205m/s and at an angle of∘ϕ0=61.8∘ at a distance 11500km from the center of the planet, as shown in the figure. Given an expression for the angular momentum of the spacecraft, using the coordinate system specified, in terms of m, r0, v0, ϕ0, and unit vectors i^, j^, and k^. If the spaceship whips around the planet to the other side so that the angle is ϕ = 33.9 degrees is moving at 83 m/s, how far, in kilometers, from the planet is it?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
A spaceship of mass 142kg is going to use a planet for a gravitational assist - that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 205m/s and at an angle of∘ϕ0=61.8∘ at a distance 11500km from the center of the planet, as shown in the figure.
Given an expression for the
If the spaceship whips around the planet to the other side so that the angle is ϕ = 33.9 degrees is moving at 83 m/s, how far, in kilometers, from the planet is it?
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