Compare the average density of a newly formed star of mass 20 M⊙( radius ≈10 R⊙) and 0.1 M⊙ (ra

step 1 Welcome to this lesson. In this lesson we find the density of a star given that we have a mass w

Compare the average density of a newly formed star of mass...

Compare the average density of a newly formed star of mass $20 M_{\odot}\left(\text { radius } \approx 10 R_{\odot}\right)$ and $0.1 M_{\odot}$ (radius $\approx 0.1 R_{\odot}$ ) to the Sun's density. You should find that the higher-mass star has a lower density. Relate these relative densities to the formation processes that determine the upper and lower mass limits for stars.

Key Concepts

Average Density

Average density in stars is determined by the ratio of the star’s mass to its volume, where the volume scales with the cube of the radius. This concept is important because even when a star is more massive, if its radius increases sufficiently, its average density can be lower. This relationship helps in understanding the physical characteristics of stars during and after their formation.

Mass-Radius Relationship

The mass-radius relationship in stars is a crucial aspect of stellar structure that shows how a star's radius does not increase linearly with its mass. In young or newly formed stars, higher mass does not necessarily mean a higher density because the increase in radius can outpace the increase in mass. This relationship underpins why some massive stars can be less dense overall compared to their lower-mass counterparts.

Star Formation Processes

The processes involved in star formation, particularly the collapse of molecular clouds under gravity, play a key role in determining the initial conditions of a star including its mass and radius. Factors such as turbulence, magnetic fields, and radiation feedback affect the manner in which a cloud fragments and collapses, influencing the mass of the forming star and hence its mean density.

Stellar Mass Limits

The formation of stars is subject to both lower and upper mass limits that are dictated by different physical mechanisms. The lower mass limit is set by the minimum mass required for a protostar to ignite sustained nuclear fusion, while the upper mass limit is influenced by radiative feedback, which can inhibit further accretion of material. These limits are intimately related to the density and structural properties of stars as they form, with density playing a role in how effectively a cooling cloud can fragment and collapse into stars of various masses.

Transcript

00:02 Welcome to this lesson.

00:04 In this lesson we find the density of a star given that we have a mass which is 2 times 10 to the power 36 kilograms.

00:14 And we have the radius of the star which is spherical in shape.

00:20 That would be radius of 7 .0 times 10 to the power 5 kilometers.

00:25 So here let's convert the mass to grams.

00:29 And we'll convert the radius to centimeters.

00:33 So 2 times 10 to the power 36 kilograms is equal to 2 times 10 to the power 36 times 10 to the power 3 again for the kilo.

00:46 This is grams.

00:48 And the mass is finally equals to 2 times 10 to the power 39 grams.

00:57 Now the radius was given as 7 .0 times 10 to the power 5 kilometers which we can convert to centimeters as so.

01:09 So here the kilometers converting to centimeters we have 10 to the power 5 centimeters which now becomes radius as 7 .0 times 10 to the power 10 centimeters.

01:24 So here we need to find the volume of the sphere which is equals to 4 on 3 pi r cube.

01:40 So here given that r is equals to 7 .0 times 10 to the power 10 centimeters we have 4 on 3 pi.

01:51 Then this is 7 times 10 to the power 10 centimeters.

01:58 This is the power 3 and that is equals to here we have 1, 3, 7, 2 on 3.

02:08 Then 5 times 10 to the power 30 cubic centimeters.

02:17 So this is the volume.

02:21 Then we move to the density which is equals to the mass over volume...

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