Gravity and Light

[lildreamer]

question to our amateur and professional audience: <br />at what point does the "gravity of an object" prevent light from leaving it.? ie light does not leave a "black hole" but at what point 10G's 1000G's 10x106G's what is the value. <div class="Discussion_UserSignature"> </div>

 

[neutron_star6]

Kind of ironic how I was just about to post this very same topic. I would like to know as well as I am also curious. But Im also curious about the velocity of a black hole. But you will probably answer that question from just the first question.

 

[Maddad]

The escape velocity of the black hole at the event horizon is equal to the speed of light, 300,000,000 meters per second. The gravity on Earth is about 11,000 meters per second, so the gravity at the surface of a black hole would be about 27,000 gravities.

 

[lildreamer]

cool - thanks for the info maddad.<br /> <div class="Discussion_UserSignature"> </div>

 

[Maddad]

Yanno somthing lildreamer? I think I accidentally lied to you. It's the escape velocity on Earth that's 11,000 meters per second, not the gravity. But the ratio remains the same - 300 million divided by 11 thousand.

 

[Saiph]

actually maddad, I think you're still off. <br /><br />That ration gives: ~27000<br /><br />Seems really low to me, so I looked into it:<br /><br />The equations don't quite add up. Vescape isn't in direct proportion to gravity. There are a few factors you have to deal with to get it to come out right.<br /><br />Vesc= sqrt(2*G*M/R)<br /><br />V^2=2*G*M/R<br /><br />(V^2)/2 = G*M/R<br /><br />(V^2)*R/(2*m) = G*M*m/R^2<br /><br />(V^2)*R/(2*m) = Fgravity<br /><br />So, setting it up in a ratio:<br /><br />(Vb^2)*Rb/(2*m) = Fgravity(BH) <br /><br />(Ve^2)*Re/(2*m) = Fgravity(e) <br /><br />Fgravity(BH)/Fgravity(e)= (Vb^2)*Rb / ((Ve^2)*Re)<br /><br />Rb= ~20 Kilometers<br />Re= ~6000 kilometers<br /><br />Ve = 11 km/s<br />Vb = 300,000 km/s <br /><br />So F(bh)/F(e) = 9x10^10*20/121*6000<br /> = 1.8x10^12/ 726,000<br /> =~ 2.5 million<br /><br />So Fgravity(bh) =~ 2.5 million * Fgravity(earth)<br /><br /><br />The big key difference is, of course, the Vesc is squared when in proportion to gravity, not a linear relationship. <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

 

[Maddad]

Thanks for the tip Saiph. I'm in school right now; no time to learn anything *L* I'll look at your post later. You must be right; something in the back of my mind was buggin' me that the number was too low.