How the Earth can maintain its same angular momentum even after the Sun disappears

[Benjamin_harsh]

Homework Statement

How Earth maintain its same angular momentum even after sun disappears?

Relevant Equations

How Earth maintain its same angular momentum even after sun disappears?

In this video, around 2:28 He explains Earth maintain its same angular momentum even after sun disappears. I didn't get it.

How Earth maintain its same angular momentum even after sun disappears?

 

[Doc Al]

How Earth maintain its same angular momentum even after sun disappears?

They try to explain that in the video. Realize that a point mass moving in a straight line past some point has an angular momentum about that point that doesn't change. $\vec{L} = \vec{r} \times \vec{p}$ remains constant.

 

[Benjamin_harsh]

What is $\vec{r}$ & $\vec{p}$ ?

Are you telling Earth's angular momentum has nothing to do with Sun or moon?

 

[Doc Al]

What is $\vec{r}$ & $\vec{p}$ ?

$\vec{r}$ is the position vector of the particle as measured from the point in question; $\vec{p}$ is the particle's momentum.

Are you telling Earth's angular momentum has nothing to do with Sun or moon?

The sun provides the force keeping the Earth in orbit, but the Earth's angular momentum about the sun doesn't change as it moves.

 

[Benjamin_harsh]

The sun provides the force keeping the Earth in orbit, but the Earth's angular momentum about the sun doesn't change as it moves.

So Earth has two angular momentum: about its axis and about the sun?

I think Earth converts its angular momentum into Linear momentum after sun disappears.

 

[jbriggs444]

I think Earth converts its angular momentum into Linear momentum after sun disappears.

Angular momentum and linear momentum are both independently conserved. Since the units of measurement for the two have different dimensions, it follows that they cannot be converted to one another.

Angular momentum is conserved. It does not go away.
Linear momentum is conserved. It does not go away.

Now, with that said, making the Sun disappear violates conservation of momentum. So you cannot do that. You could explode the sun, perhaps splitting it in two and sending one half flying "north" relative to the plane of the ecliptic and the other half flying "south". That could be done while still conserving momentum, energy and angular momentum.

The gravitational pull from the resulting Sun fragments would gradually disappear and the trajectory of the Earth would converge on a straight line. But that straight line would not project back to the pre-existing position of the Sun. As a result, $\vec{r} \times \vec{p}$ would be non-zero, thereby conserving angular momentum.

 

[Doc Al]

So Earth has two angular momentum: about its axis and about the sun?

Sure. (It can have any number of angular momenta about any point you like.)

I think Earth converts its angular momentum into Linear momentum after sun disappears.

No. Linear and angular momentum are two very different things. One does not convert to the other. (They have different units!)

 

[kuruman]

Angular momentum is conserved because the Sun exerts no torque on the Earth as long as the Earth is orbiting and certainly it can exert no torque after it disappears. I interpret this question to be large scale analogue of the more common question where a puck, attached to a string tied to a peg, is rotating on a frictionless horizontal surface when suddenly the string is severed. I would agree, though, that "maintain the same angular momentum" is a bit nebulous if one does not specify the point about which this angular momentum is to be considered.