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

Checkfate

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, [tex]g=\frac{Gm}{r^{2}}[/tex] and thus [tex]g\alpha\frac{m}{r^2}[/tex]

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

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

Saying [itex]g \propto m/r^2[/itex] is equivalent to saying that [itex]g = Gm/r^2[/itex] 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.

[tex]g_1 = \frac{GM_1}{r_1^2}[/tex]

[tex]g_2 = \frac{GM_2}{r_2^2}[/tex]

dividing, the constant falls out:

[tex]\frac{g_2}{g_1} = \frac{M_2}{M_1}\frac{r_1^2}{r_2^2}[/tex]

AM

Chi Meson

g is proportional to [tex]\frac{m}{r^2}[/tex]
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 [itex]g_{e/x}[/itex] refers to earth or planet x etc. Now you can say:

[tex]\frac{g_x}{g_e}=\frac{M_xr_e^2}{r_x^2M_e^2}[/tex]
[tex]g_x}=g_e\frac{M_xr_e^2}{r_x^2M_e^2}[/tex].


By the way, the "proprtional to" symbol isn't alpha. In tex it's "\propto"... heres the difference:

[tex]\alpha \ldots \propto[/tex]

The first is alpha, the second is proptional to.

Checkfate

Thanks alot guys! :)