I have a drawing of a satellite orbiting the sun in an elliptical shape. The sun is closer to the right side of the ellipse.
As the satellite travels from the left side of the ellipse to the right, the speed increases and the angular momentum remains constant. Why?????
The satellite sweeps out equal areas in equal time (Kepler). As its distance from the sun gets smaller, its speed has to get bigger to sweep out the same area per hour.
There is no torque on the thing. Torque is rate of change of angular momentum. No torque ---> constant angular momentum.
To understand why the speed of the satellite increases while the angular momentum remains constant as it travels from the left side to the right side of the ellipse, we need to look at the relationship between angular momentum and the speed of an object in circular or elliptical motion.
Angular momentum is a property of a rotating object and is defined as the product of an object's moment of inertia and its angular velocity. Mathematically, it can be expressed as:
Angular Momentum (L) = Moment of Inertia (I) * Angular Velocity (ω)
In the case of a satellite orbiting the sun in an elliptical orbit, the moment of inertia remains constant throughout the orbit. Therefore, for the angular momentum to remain constant as well, the satellite would need to maintain the same angular velocity.
Now let's consider the speed of the satellite. In elliptical orbits, the speed of an object varies depending on its position in the orbit. As the satellite moves closer to the sun (moving from the left to the right side of the ellipse), it experiences a stronger gravitational pull from the sun, leading to an increase in speed due to the conservation of mechanical energy.
The conservation of mechanical energy states that the sum of the satellite's kinetic energy and potential energy remains constant as it moves along its orbit. As the satellite moves closer to the sun, its potential energy decreases. To conserve the total mechanical energy, the kinetic energy (which is directly related to the speed) of the satellite must increase.
In summary, the speed of the satellite increases as it moves from the left side of the ellipse to the right due to the stronger gravitational pull from the sun. However, the angular momentum remains constant since the moment of inertia and the angular velocity remain constant.