# Find the radii of the two stars

• leonne
In summary, a spectroscopic binary star system with an orbital period of 3.15 years and maximum radial velocities of 5.2 km s^-1 and 21.6 km s^-1 for stars A and B, respectively, has a time difference of 0.45 days between first contact and minimum light, and a primary minimum length of 0.52 days. The primary minimum is only 54.8% as bright as the maximum brightness, while the secondary minimum is 88.1% as bright. Assuming circular orbits seen perfectly edge on, the ratio of the stellar masses is found using the formula m1=(4V1^2*r1)/G. The radii of the two stars can be
leonne

## Homework Statement

From the light and velocity curves of an eclipsing, double-lined spectroscopic binary
star system, it is determined that the orbital period is 3.15 yr, and the maximum radial
velocities of stars A and B are 5.2 km s^-1 and 21.6 km s^-1, respectively. Furthermore,
the time between first contact and minimum light is tb-ta = 0.45 days, while the length
of the primary minimum is tc -tb = 0.52 days. Relative to the maximum brightness,
the primary minimum is only 54.8% as bright, while the secondary minimum is 88.1%
as bright
You may assume the orbits are circular and seen perfectly edge on.

Find the ratio of the stellar masses (mA/mB), the sum of the masses (M =
mA + mB), and the individual masses (mA and mB).
(b) Find the radii of the two stars. Hint: Use the speed of one star relative to the
other and the eclipse timings given.

## Homework Equations

v1=(2pie a1)/p r=a(1-e^2)/(1+ecos@) m1=(4V1^2*r1)/G

[c]3. The Attempt at a Solution [/b]
so becasue its edge on that means inclination angle is 90degrees so that's the real velocity and e = 0 too so just use these formula to find masses right?
now for part B would i just the formula r=a(1-e^2)/(1+ecos@) to find the radii? checked in book showed this as radii but hint says to use something different i think

nvm i think i figured it out

## 1. How do you find the radii of two stars?

Finding the radii of two stars involves measuring the distance between the two stars and using the inverse square law to calculate their sizes. This can be done using telescopes and specialized instruments.

## 2. What is the inverse square law?

The inverse square law states that the intensity of radiation, in this case from the stars, is inversely proportional to the square of the distance between the source and the observer. This means that as the distance between the stars and the observer increases, the intensity of radiation decreases.

## 3. Are there any other methods for finding the radii of stars?

Yes, there are other methods such as using the stars' brightness, temperature, and spectral type to estimate their sizes. However, these methods may not be as accurate as measuring the distance between the stars directly.

## 4. What units are used to measure the radii of stars?

The radii of stars are typically measured in units of solar radii, which is the distance from the center of the sun to its outer edge. For example, a star with a radius of 2 solar radii would be twice the size of the sun.

## 5. Can the radii of stars change over time?

Yes, the radii of stars can change over time due to various factors such as nuclear reactions, mass loss, and interactions with other stars. This is especially true for younger stars that are still in the process of forming.

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