# Finding the Schwarzchild radius of a star of solar mass 30

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!

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

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