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I am currently trying to determine the Schwarzchild radius of a star with solar mass 30. I am calculating it both with respect to solar mass, and w.r.t kilograms, however I am getting conflicting answers. (of a factor of 10)

$$ 1 \text{ solar mass} \sim 1.9891 \cdot 10^{31}\,\text{kg} $$ so I calulated

$$ 30\,\text{SM}\sim 5.97 \cdot 10^{32}\,\text{kg} $$

Using the formula for the Sch Radius:

$$ R_s =\frac{2GM}{c^2} $$

I determined that you can calculate this using both the solar mass, and the kg mass to confirm.

Using given proportionality constants for $2G/c^2$:

$$ = 2.95\,\text{km/solar mass}\\ = 1.48 \cdot 10^{-27}\,\text{m/kg} $$

Using the formula above, I have obtained:

$$ \text{using solar mass: }R_s=88.5\,\text{km}\\ \text{using kg: } R_s=883\,\text{km} $$

If someone could work this out and help me clarify I would be very grateful!

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    $\begingroup$ You will need to show us the details of the two calculations for us to comment usefully. $\endgroup$
    – John Rennie
    Commented Jan 9, 2014 at 13:46
  • $\begingroup$ WolframAlpha confirms the 88 km number $\endgroup$
    – user23660
    Commented Jan 9, 2014 at 14:17

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Your method is correct, but you've got lost in the numbers. This is a good opportunity to use some neat web tools.

Google: 30 solar masses

Answer: 30 solar masses = 5.9673 × $10^{31}$ kg

So you have miscalculated your solar masses in kg.

Secondly, there is a neat WolframAlpha tool:

Given Mass = 30 solar masses

Answer: 88.59 km

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  • $\begingroup$ Fantastic! Thank you so much! This has been frustrating me for a long time! I really appreciate your help! :) $\endgroup$
    – Sarah Jayne
    Commented Jan 9, 2014 at 14:19

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