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

• Benjamin_harsh
In summary, the conversation discusses the concept of angular momentum and how it is conserved even after the sun disappears. The Earth maintains its same angular momentum regardless of the presence of the sun or moon. Angular momentum and linear momentum are two different things and cannot be converted to one another. The sun provides the force to keep the Earth in orbit, but it does not affect its angular momentum. The conversation also touches upon the violation of conservation of momentum if the sun were to suddenly disappear.
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?

Benjamin_harsh said:
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.

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

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

Benjamin_harsh said:
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.
Benjamin_harsh said:
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.

Doc Al said:
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.

Benjamin_harsh said:
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.

Benjamin_harsh said:
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.)
Benjamin_harsh said:
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!)

Benjamin_harsh
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.

## What is angular momentum?

Angular momentum is a measure of an object's rotational motion. It is calculated by multiplying the object's moment of inertia (a measure of its resistance to rotation) by its angular velocity (the rate at which it is rotating).

## How does the Earth maintain its angular momentum?

The Earth maintains its angular momentum due to the conservation of angular momentum principle. This principle states that the total angular momentum of a system remains constant unless acted upon by an external torque. Since there are no external torques acting on the Earth-Sun system, the Earth's angular momentum remains constant.

## What happens to the Earth's angular momentum when the Sun disappears?

When the Sun disappears, the Earth's angular momentum will remain constant. This is because, according to the conservation of angular momentum principle, the total angular momentum of a system remains constant. Therefore, even though the source of the Earth's angular momentum (the Sun) is no longer present, its angular momentum will remain unchanged.

## Will the Earth's orbit change when the Sun disappears?

No, the Earth's orbit will not change when the Sun disappears. This is because the Earth's angular momentum, which determines its orbit, will remain constant. Therefore, the Earth will continue to orbit around the point where the Sun used to be, maintaining its same orbital path.

## What will happen to the Earth when the Sun disappears?

When the Sun disappears, the Earth will continue to exist and maintain its orbit around the point where the Sun used to be. However, without the Sun's heat and light, the Earth will become uninhabitable and eventually freeze over. The Earth will also lose its tidal forces, causing changes in ocean currents and potentially altering its rotation and axis tilt over time.

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