# Estimate time scale of expansion of a star

• Poirot
In summary, the task is to estimate the expansion time scale of a star experiencing a sudden increase in pressure to a new value. The given parameters are the average density (ρ) and the radius (R), and the equation provided is tdynamical ≈ √R3/GM. The attempt at a solution involves creating an equation of motion for an outer shell and equating it to the pressure, but the use of G is not applicable as gravity is to be ignored. The suggestion to use dimensional analysis is also mentioned.

## Homework Statement

A star experiences a sudden increase in pressure to a new value P'. Taking the average density as ρ and the radius R, estimate the time scale of expansion of the star. (Ignore gravity altogether).

## Homework Equations

The only thing I can see in my notes that may (or may not) be related to this is :
tdynamical ≈ √R3/GM

## The Attempt at a Solution

I'm not sure how to begin, I thought perhaps I could make an equation of motion for an outer shell and equate this to some kind of pressure but I don't know how/ am quite lost.

Any help would be much appreciated thanks.

Did you try dimensional analysis?

You cannot use G if you should ignore gravity.

## 1. What is the time scale of expansion of a star?

The time scale of expansion of a star is the duration of time it takes for a star to grow in size and become a red giant. This process can vary depending on the mass of the star, but typically ranges from a few million to a few billion years.

## 2. How is the time scale of expansion determined?

The time scale of expansion is determined by the mass of the star and its luminosity. More massive stars have shorter expansion timescales, as they have more fuel to burn and therefore evolve faster.

## 3. Can the time scale of expansion be accurately predicted?

While the time scale of expansion can be estimated based on a star's mass and luminosity, it is not an exact science. There are many factors that can affect a star's evolution, such as its composition, rotation, and interactions with other stars.

## 4. What happens to a star during its expansion phase?

During its expansion phase, a star's core begins to run out of hydrogen fuel and contracts. This causes the outer layers of the star to expand and cool, making the star appear larger and redder in color. Eventually, the star will run out of fuel and collapse, leading to its death.

## 5. How does the expansion of a star impact its surroundings?

As a star expands, it can have a significant impact on the surrounding space. The increased size and luminosity of the star can heat up and ionize nearby gas clouds, triggering the formation of new stars. The star's expansion can also cause it to lose mass, creating a stellar wind that can shape and influence the surrounding environment.