Exploring Central Forces: Orbital Mechanics Practice Problems

In summary, the conversation discusses three problems related to a satellite orbiting the Earth and a comet orbiting the Sun. The first problem involves finding the angular momentum, potential, kinetic and total energy, and orbital period of a satellite with a given mass and circular path around the Earth. The second problem explores the effect of a change in velocity on the satellite's angular momentum, total energy, and orbit shape. The third problem focuses on determining the shape of a comet's orbit and its closest approach to the Sun based on given distance and velocity measurements. The equations used to solve these problems are L = r x p and E = Ek + U(r), and the link provided by the teacher is used as a reference for solving the exercises.
  • #1
Otto31
1
0

Homework Statement



1) A satellite having a mass of 5000 kg describes a circular path around the Earth of radius
8000 km. Find (a) its angular momentum and (b) its potential, (c) kinetic and (d) total
energy. Also calculate (e) the orbital period.

2) Assume the satellite in the previous problem is given an horizontal velocity 20% greater
than the velocity required to achieve a circular orbit. Find (a) its new angular momentum
and (b) total energy, and determine (c) the shape of the orbit, including its maximum and/or
minimum distance to the Earth's center.

3) A comet is observed at a distance of 1011 m from the Sun, traveling toward it with a velocity
5.16 x 104 m/s at an angle of 45° with the radius vector from the Sun. Determine (a) the
shape of the orbit and (b) its closest approach to the Sun.

Homework Equations



L = r x p

E = Ek + U(r)

Our teacher gave us the following link in order to resolve the exercises:
http://www-physics.ucsd.edu/students/courses/fall2010/physics110a/LECTURES/CH09.pdf

The Attempt at a Solution



My attemp at a solution was first, calculate the angular momentum and the Total Energy in each problem, then with the graphic E(r) I should calculate the shape of the orbit, but this is where the problem get stuck. In all three exercises I know how to calculate L and E, but I can't "imagine" the proper way to continue solving the problems. Sorry if It something is wrong with this thread, but this is my first post.
 
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  • #2
For question I I think it doesn't need to be so complicated, after all in the case of a circular orbit there is an easy identity to exploit(U= -2T)
 

What is a central force?

A central force is a type of force that acts on an object towards or away from a fixed point, known as the center. This type of force is always directed along the line connecting the center and the object. Examples of central forces include gravity, electrostatic forces, and magnetic forces.

What are some common examples of central forces?

Some common examples of central forces include the gravitational force between two objects, the electrostatic force between two charged particles, and the magnetic force between two magnets. These forces are all directed along the line connecting the two objects and are dependent on the distance between them.

How do central forces affect the motion of an object?

Central forces cause an object to move in a curved path, rather than a straight line. This is because the force is always directed towards or away from the center, causing the object to continuously change direction. The exact path of the object depends on the strength and direction of the force, as well as the initial velocity of the object.

What is the difference between a conservative and non-conservative central force?

A conservative central force is one that conserves energy, meaning that the total energy of the object remains constant as it moves. Examples of conservative central forces include gravity and electrostatic forces. Non-conservative central forces, on the other hand, do not conserve energy and can cause the object to lose or gain energy as it moves, such as friction or air resistance.

How are central forces calculated and represented mathematically?

Central forces are often represented using vector equations, with the magnitude and direction of the force determined by the distance between the two objects and the strength of the force. The equations used to calculate central forces vary depending on the type of force and the specific scenario, but typically involve the use of Newton's laws of motion and the principles of conservation of energy and momentum.

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