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

[tex]g_{e}\propto \frac{M_e}{r_e^2}[/itex]

and

[tex]g_{x}\propto \frac{M_x}{r_x^2}[/itex]

where $g_{e/x}$ refers to Earth or planet x etc. Now you can say:

$$\frac{g_x}{g_e}=\frac{M_xr_e^2}{r_x^2M_e^2}$$
$$g_x}=g_e\frac{M_xr_e^2}{r_x^2M_e^2}$$.By the way, the "proprtional to" symbol isn't alpha. In tex it's "\propto"... here's the difference:

$$\alpha \ldots \propto$$

The first is alpha, the second is proptional to.

 

[Checkfate]

Thanks a lot guys! :)