Trajectories, equation of motion and forces....

In summary, the study of trajectories involves analyzing the path of an object through space, while the equation of motion describes the mathematical relationship between an object's position, velocity, and acceleration. Forces, such as gravity and friction, can affect an object's trajectory and are represented in the equation of motion. By understanding these concepts, scientists and engineers are able to predict and control the motion of objects in various scenarios.
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Setting a cartesian system how can i get the equation of the trajectory of an object knowing the forces acting on that object?

Example: If F= GMm/r^2 and let be the sun at the center (point (0,0,0)) of the cartesian system how do i get the equation of an ellipse in this system? ( x^2/a^2 + y^2/b^2 = 1)

Where x and y define the position of the planet in the chosen system centred in the sun
 
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1. What is a trajectory in physics?

A trajectory in physics refers to the path that an object takes through space as it moves. It is often described as the line or curve that an object follows through space, and can be affected by various forces such as gravity, friction, and air resistance.

2. How is the equation of motion related to trajectories?

The equation of motion is a mathematical formula that describes the motion of an object in terms of its position, velocity, and acceleration. By using this equation, we can determine the trajectory of an object by calculating its position at different points in time.

3. What are some factors that can affect a trajectory?

There are several factors that can affect the trajectory of an object, including the object's initial velocity, the forces acting on it, and the shape of the object. Other factors such as air resistance, wind, and temperature can also play a role in determining the trajectory of an object.

4. How do forces impact an object's trajectory?

Forces can have a significant impact on an object's trajectory. Depending on the direction and magnitude of the force, it can alter the object's velocity and direction of motion, resulting in a change in trajectory. Forces such as gravity, friction, and air resistance can all affect an object's trajectory.

5. How does the concept of inertia relate to trajectories?

Inertia is the tendency of an object to resist changes in its state of motion. In terms of trajectories, this means that an object will continue to move in a straight line at a constant speed unless acted upon by an external force. This concept is important in understanding how an object's trajectory can be affected by different forces.

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