Ryaners

## Homework Equations

Mass-radius relation: $$R \propto M^{-\frac{1}{3}}$$

## The Attempt at a Solution

So I've tried the following:
$$R_{D} \propto M_{D}^{-\frac{1}{3}} \Rightarrow \frac {R_{D}} {R_{sun}} = \frac{M_{D}^{-\frac{1}{3}}} {M_{sun}^{-\frac{1}{3}}} \Rightarrow R_{D} = \frac{M_{D}^{-\frac{1}{3}}} {M_{sun}^{-\frac{1}{3}}} R_{sun}$$
$$\Rightarrow R_{D} = \left( {\frac {1.3 M_{sun}} {M_{sun}}} \right) ^{-\frac{1}{3}} R_{sun} = \left( 1.3 \right) ^{-\frac{1}{3}} R_{sun}$$

This gives me an answer of about ##0.916~{R_{sun}}## , which is incorrect. Where am I going wrong here?

Thanks in advance for any help.

Homework Helper
Gold Member
Start with ##M_{Sun}^{1/3}R_{Sun}=M_{D}^{1/3}R_{D}## and replace ##M_D=1.3M_{Sun}##. The algebra is less confusing when you eliminate the proportionality constant.

Ryaners
Start with ##M_{Sun}^{1/3}R_{Sun}=M_{D}^{1/3}R_{D}## and replace ##M_D=1.3M_{Sun}##. The algebra is less confusing when you eliminate the proportionality constant.

That's a fair point - though I get the same result:

$$\left( M_{sun} \right) ^\frac {1}{3} R_{sun} = \left( M_{D} \right) ^{\frac {1}{3}} R_D$$
$$\Rightarrow R_D = \left( \frac {M_{sun}} {M_D} \right) ^{\frac{1}{3}} R_{sun}$$
$$\Rightarrow R_D = \left( \frac {1}{1.3} \right) ^{\frac {1}{3}} R_{sun} = \left( 1.3 \right) ^{-\frac {1}{3}} R_{sun}$$

Homework Helper
Gold Member
At this point you need to question why you think that the answer is incorrect. What you think is the correct answer may be a misprint or a miscalculated answer by whoever gave it to you. The only other thing I can think of is the starting equation which is approximate and may have to be refined.

Homework Helper
At this point you need to question why you think that the answer is incorrect. What you think is the correct answer may be a misprint or a miscalculated answer by whoever gave it to you. The only other thing I can think of is the starting equation which is approximate and may have to be refined.

Perhaps the problem is that the sun is not a white dwarf?

gneill
Homework Helper
Gold Member
Perhaps the problem is that the sun is not a white dwarf?
Perhaps, but the problem clearly states that you should use "the mass-radius relation for white dwarfs."

I am sorry, but my resources regarding this question have been exhausted. I took a single astrophysics course several decades ago and I have reached the point where I can no longer help you. Perhaps someone else may be able to step in.