Correct use of is proportional to symbol (alpha)

[Checkfate]

Correct use of "is proportional to" symbol (alpha)

Hello, I am facing a problem that can be solved quite easily using the proportional symbol ( I think ), so I would like to try to use it! Only problem is.. I don't know exactly how to use it correctly...

The question is :An astronaut weighs 882N on Earth, determing the weight of the astronaut on Planet X, which has a mass 95.3 times that of Earth and a radius 8.9 times that of Earth.

So, g=\frac{Gm}{r^{2}} and thus g\alpha\frac{m}{r^2}

So I wrote down
g\alpha\frac{m}{r^2}
g\alpha\frac{95.3}{79.21}

But of course this false... g is not proportional to 95.3/79.21.. lol. Can someone show me how to correctly show my work? Thanks. This would allow me to simply use this ratio to calculate his new weight.

 

[J77]

Remember that G is the gravitational constant, ie. it always takes the value 6.67ishe-11

This constant turns the proportionality into an equality.

 

[Andrew Mason]

Hello, I am facing a problem that can be solved quite easily using the proportional symbol ( I think ), so I would like to try to use it! Only problem is.. I don't know exactly how to use it correctly...

The question is :An astronaut weighs 882N on Earth, determing the weight of the astronaut on Planet X, which has a mass 95.3 times that of Earth and a radius 8.9 times that of Earth.

So, g=\frac{Gm}{r^{2}} and thus g\alpha\frac{m}{r^2}

So I wrote down
g\alpha\frac{m}{r^2}
g\alpha\frac{95.3}{79.21}

But of course this false... g is not proportional to 95.3/79.21.. lol. Can someone show me how to correctly show my work? Thanks. This would allow me to simply use this ratio to calculate his new weight.

Saying g \propto m/r^2 is equivalent to saying that g = Gm/r^2 where G is a constant (the proportionality constant) ie. g is a linear function of m and r². If you want to perform mathematical operations you have to use the equality sign and the constant.

g_1 = \frac{GM_1}{r_1^2}

g_2 = \frac{GM_2}{r_2^2}

dividing, the constant falls out:

\frac{g_2}{g_1} = \frac{M_2}{M_1}\frac{r_1^2}{r_2^2}

AM

 

[Chi Meson]

Hello, I am facing a problem that can be solved quite easily using the proportional symbol ( I think ), so I would like to try to use it! Only problem is.. I don't know exactly how to use it correctly...

The question is :An astronaut weighs 882N on Earth, determing the weight of the astronaut on Planet X, which has a mass 95.3 times that of Earth and a radius 8.9 times that of Earth.

So, g=\frac{Gm}{r^{2}} and thus g\alpha\frac{m}{r^2}

So I wrote down
g\alpha\frac{m}{r^2}
g\alpha\frac{95.3}{79.21}

But of course this false... g is not proportional to 95.3/79.21.. lol. Can someone show me how to correctly show my work? Thanks. This would allow me to simply use this ratio to calculate his new weight.

g is proportional to \frac{m}{r^2}
but when cramming in the values you did, you get a comparison to Earth's "g." Multiply (95.3/79.21) by 9.81, and you get the "g" of the other planet.

 

[jpr0]

If you want to use the proportionality sign, then say

g_{e}\propto \frac{M_e}{r_e^2}[/itex]<br /> <br /> and<br /> <br /> g_{x}\propto \frac{M_x}{r_x^2}[/itex]&lt;br /&gt; &lt;br /&gt; where g_{e/x} refers to Earth or planet x etc. Now you can say: &lt;br /&gt; &lt;br /&gt; \frac{g_x}{g_e}=\frac{M_xr_e^2}{r_x^2M_e^2}&lt;br /&gt; g_x}=g_e\frac{M_xr_e^2}{r_x^2M_e^2}.By the way, the &amp;quot;proprtional to&amp;quot; symbol isn&amp;#039;t alpha. In tex it&amp;#039;s &amp;quot;\propto&amp;quot;... here&amp;#039;s the difference:&lt;br /&gt; &lt;br /&gt; \alpha \ldots \propto&lt;br /&gt; &lt;br /&gt; The first is alpha, the second is proptional to.

 

[Checkfate]

Thanks a lot guys! :)