The motion of a particle in the central force

[GeoStudy]

Homework Statement

I just need a hint. So we are given:

F = -kr

We are asked:

Show that:

(a) The orbit is an ellipse with the force center at the center of the ellipse.

Homework Equations

I guess we break it up into its components:

The Attempt at a Solution

m d²x/dt² = -kx => x = Acos(ωt + β_x)

m d²y/dt² = -ky => y= Bsin(ωt + β_y)

where β_x = β_y = 0

 

[haruspex]

Homework Statement

I just need a hint. So we are given:

F = -kr

We are asked:

Show that:

(a) The orbit is an ellipse with the force center at the center of the ellipse.

Homework Equations

I guess we break it up into its components:

The Attempt at a Solution

m d²x/dt² = -kx => x = Acos(ωt + β_x)

m d²y/dt² = -ky => y= Bsin(ωt + β_y)

where β_x = β_y = 0

Yes, except why assume the phase constants are zero?