Gravitational Orbits: Circular vs. Elliptical

[Fredley_Banyo]

Homework Statement

1. Which of the following statements about a circular orbit are true? (The planet is orbiting around the star.)


a. At any instant the momentum of the planet is tangent to the planet's trajectory.

b. The magnitude of the planet's momentum is constant.

c. At every instant, dvector p/dt points from the planet to the star.

d. The direction of the planet's momentum is changing at every instant.

e.The gravitational force on the planet due to the star always acts at a right angle to the planet's momentum.




2. Which of the following statements about an elliptical orbit are true? (The planet is orbiting around the star.)


a. At any instant the momentum of the planet is tangent to the planet's trajectory.

b. The magnitude of the planet's momentum is constant.

c. At every instant, dvector p/dt points from the planet to the star.

d. The direction of the planet's momentum is changing at every instant.

e.The gravitational force on the planet due to the star always acts at a right angle to the planet's momentum.





I want to know which choice applies to each so i can better understand the concepts of gravitational orbits.

The Attempt at a Solution

My guess for a circular orbit was a,b,d and e because the momentum's magnitude is constant but is constantly changing direction. The gravitational force from the star is pointed towards the center of the orbit so that is why i thought e was true as well. As for an elliptical orbit i really have to idea except for the fact that the magnitude of momentum is not constant which makes it elliptical and not circular.

 

[D H]

Forget about orbits for a bit. Answers (a) and (c) are very basic.

- Regarding answer (a), what is momentum -- how is it defined?
- Regarding answer (c), what does Newton's second law have to say about dp/dt?

 

[Fredley_Banyo]

Momentum is defined as mass*velocity and is a vector. dp/dt is the rate of change of momentum and there is both a perpendicular component to the motion, which is the gravitational force and also one parallel which deals with the direction, which is constantly changing.

 

[D H]

What does it mean for something to be parallel to the trajectory? Again, forget orbits. Think in very basic, very general terms.

What is Newton's second law? (Hint: It is not F=ma.)

 

[Fredley_Banyo]

It says that the total vector sum of forces acting on a system is equal to the rate of change of its momentum (dp/dt)

 

[D H]

OK! Now look at answers (c) in light of what you just said.

 

[Fredley_Banyo]

So that is saying that the net force is pointing towards the center of the orbit.

 

[D H]

Correct.

 

[Fredley_Banyo]

I finally figured it out. For the circular orbit it is all five and for the elliptical it is a,c and d. Thank you for your help.

 

[D H]

Very good.

Oh yes, and welcome to PhysicsForums, Fredley.