Calculate New Period of Star After Shrinking Diameter

In summary, the formula for calculating the new period of a star after shrinking its diameter is P1 = P0 * (R1/R0)^3/2. The new radius of a star can be determined by multiplying the original radius by the ratio of the new diameter to the original diameter, expressed as R1 = R0 * (D1/D0). The mass of a star does affect its new period, being directly proportional to the square root of its mass. The new period cannot be negative and other factors such as changes in internal structure, external forces, and interactions with a companion star can also affect it.
  • #1
joeypeter
5
0
The mass of a star is 1.170×1031 kg and it performs one rotation in 28.30 day. Find its new period (in days) if the diameter suddenly shrinks to 0.610 times its present size. Assume a uniform mass distribution before and after.

How do I even start this problem? Can anyone give me step by step how to do this?
 
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  • #2
Hi joeypeter! :smile:

We can give you one step:

Use conservation of angular momentum (what is it in this case?)
 
  • #3


To calculate the new period of the star after shrinking its diameter, we can use the equation for rotational period:

T = 2π√(I/mr^2)

Where:
T = period
I = moment of inertia
m = mass
r = radius

Step 1: Determine the initial moment of inertia (I)

Since the mass distribution is assumed to be uniform before and after shrinking, the moment of inertia can be calculated as:

I = (2/5)mr^2

Step 2: Calculate the initial radius (r)

The initial radius can be calculated using the mass and the given diameter:

r = d/2 = (0.610)(diameter)/2 = 0.305(diameter)

Step 3: Calculate the initial mass (m)

The initial mass is given in the problem as 1.170×1031 kg.

Step 4: Calculate the new moment of inertia (I')

Since the mass distribution is still assumed to be uniform after shrinking, the new moment of inertia can be calculated using the initial moment of inertia and the ratio of the new and initial radii:

I' = (2/5)m(0.305diameter)^2 = 0.0186mdiameter^2

Step 5: Calculate the new period (T')

Using the equation for rotational period, we can now calculate the new period:

T' = 2π√(I'/m(0.305diameter)^2)

= 2π√(0.0186mdiameter^2/m(0.305diameter)^2)

= 2π√(0.0186/0.305)

= 0.419 days

Therefore, the new period of the star after shrinking its diameter would be 0.419 days, or approximately 10 hours. This is a significant decrease from the initial period of 28.30 days. This calculation assumes that the star maintains its mass and rotational speed after shrinking its diameter, which may not be accurate in reality. Further research and observations would be needed to determine the exact effects of a shrinking diameter on a star's period.
 

What is the formula for calculating the new period of a star after shrinking its diameter?

The formula for calculating the new period of a star after shrinking its diameter is: P1 = P0 * (R1/R0)^3/2, where P1 is the new period, P0 is the original period, R1 is the new radius, and R0 is the original radius of the star.

How do you determine the new radius of a star after shrinking its diameter?

The new radius of a star can be determined by multiplying the original radius by the ratio of the new diameter to the original diameter. This can be expressed as: R1 = R0 * (D1/D0), where R1 is the new radius, R0 is the original radius, D1 is the new diameter, and D0 is the original diameter of the star.

Does the mass of a star affect its new period after shrinking its diameter?

Yes, the mass of a star does affect its new period after shrinking its diameter. This is because the period of a star is directly proportional to the square root of its mass. Therefore, a star with a greater mass will have a longer period, even if its diameter is smaller.

Can the new period of a star after shrinking its diameter be negative?

No, the new period of a star after shrinking its diameter cannot be negative. This is because the period of a star is a measure of time and cannot be negative. If the calculated value for the new period is negative, it may indicate an error in the calculation or an invalid input.

What other factors can affect the new period of a star after shrinking its diameter?

Aside from mass and diameter, other factors that can affect the new period of a star after shrinking its diameter include changes in the star's internal structure, such as changes in its core temperature or fusion rate. Other external factors, such as gravitational forces from nearby objects, can also influence a star's period. Additionally, if the star is part of a binary system, interactions with its companion star can also affect its period.

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