Newton's Laws and the Detection of Planets Around Nearby Stars

Here is the data, obtained with a precision of 11 meters/sec that shows the radial velocity variation, indicating the presence of a small companion, in this case, a Jupiter size object.

Planetary Detection Applet

Angular Momentum

Angular momentum is the tendency for objects in rotation or orbit to stay that way.

Rotational Kinematics is very analagous to Linear Kinematics:

Linear Mechanics	Rotational Kinematics
Velocity	Angular Velocity
Mass	Moment of Inertia
Acceleration	Angular Acceleration
Linear Momentum	Angular Momentum

Angular velocity (w = number of rotations per second. One rotation is 360 degrees or 2p radians.

The total distance travelled in one rotation is:

2p R where R is the radius of the circle.

The orbital period, P, would be 2p R/V but P is just the inverse of the angular velocity w

So the linear velocity would be 2pR w or 2pR/P

Take the Earth:

• R = 6000 km
• Period = 24 hours

Linear velocity at the surface is then:

2p(6000)/24 hours or around 1500 km/hr.

The earth-moon system is an interesting case of conservation of angular momentum.

The total angular momentum of the system is the sum of the rotational angular momentum of the earth and the moon and the orbital angular momentum of the moon.

The tidal force exerted by the moon on the earth is causing the rotation period of the earth to slow down. This loss in angular momentum of the system is not allowed and the only way in which the angular momentum can be constant is if the orbital angular momentum is increased.

This requires that the moon is getting farther away from the earth.

Orbital angular momentum = mass x orbital velocity x radius of orbit.

The orbital velocity of the moon depends only on its distance from the earth and the mass of the earth. As the radius increases the orbital velocity decreases but only as the square root of r. Thus increasing the radius increases the total orbital angular momentum.