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Robittybob1
Post  Post subject: Algebra problem help requested  |  Posted: Wed May 25, 2016 5:53 am

Joined: Thu Jan 29, 2015 4:11 pm
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This problem relates to finding the speed and height of a satellite where the effects from gravitational time dilation and dynamic (velocity) dependent time dilation will cancel each other.

"The function is $ \displaystyle h=\frac{R}{\frac{r_s}{R} \frac{c^2}{v^2}-1}$. The effect happens for any speed $ \displaystyle 0<v<c \sqrt{\frac{r_s}{R}}$. For $ \displaystyle v \to c \sqrt {\frac{r_s}{R}$ we have $ \displaystyle h \to \infty$.
$ \displaystyle R$ is the radius of the planet and $ \displaystyle r_s$ is its respective Schwarzschild radius. $ \displaystyle v$ is the orbiting speed of the satellite."

Are those two formulas interchangeable?
Can you algebraically move between these two?
$ \displaystyle 1-r_s/R=1-r_s/(R+h)-(v/c)^2$ and $ \displaystyle h=\frac{R}{\frac{r_s}{R} \frac{c^2}{v^2}-1}$

Can anyone show me the steps I need to take to convert one equation into the other please? Or if that can't be done, how do I solve the first one for "h" which is the height of the satellite above the Earth's surface.

Even if you could give me one clue at a time so I have to do it myself.


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Robittybob1
Post  Post subject: Re: Algebra problem help requested  |  Posted: Thu May 26, 2016 6:47 am

Joined: Thu Jan 29, 2015 4:11 pm
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$ \displaystyle 1-r_s/R=1-r_s/(R+h)-(v/c)^2$ rearranged to solve for "a" (a = h + R) is giving identical values to the other formula.
$ \displaystyle h(v)=\frac{R}{\frac{r_s}{R}\frac{c^2}{v^2}-1}$
But I'd love to know how to rearrange one formula to result in the form of the other. Is there anyone good at algebra here?

{Note: Wait till the Latex appears. On my computer it takes about 30 seconds for the latex formulas to show up on the post.]


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plusminusgravity
Post  Post subject: Re: Algebra problem help requested  |  Posted: Thu May 26, 2016 7:16 pm
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Joined: Thu May 26, 2016 5:24 pm
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My girlfriends son is getting home schooled and I had to help
him with some algebra and it was was to hard for me.

So I did some searching online and I found this really
cool algebra help site.

It doesn't benefit me in anyway if you visit the site
I just wanted to give it to you because it saved
the day for me: Tiger Algebra

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“Mediocrity is self-inflicted and genius is self-bestowed.” ― Walter Russell


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Robittybob1
Post  Post subject: Re: Algebra problem help requested  |  Posted: Thu May 26, 2016 9:52 pm

Joined: Thu Jan 29, 2015 4:11 pm
Posts: 183

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Robittybob1 wrote:
$ \displaystyle 1-r_s/R=1-r_s/(R+h)-(v/c)^2$ rearranged to solve for "a" (a = h + R) is giving identical values to the other formula.
$ \displaystyle h(v)=\frac{R}{\frac{r_s}{R}\frac{c^2}{v^2}-1}$
But I'd love to know how to rearrange one formula to result in the form of the other. Is there anyone good at algebra here?

{Note: Wait till the Latex appears. On my computer it takes about 30 seconds for the latex formulas to show up on the post.]


Why does the latex stay in the Latex editor mode after submission and not display the formulas properly?


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iNow
Post  Post subject: Re: Algebra problem help requested  |  Posted: Thu May 26, 2016 10:04 pm
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Robittybob1 wrote:
Why does the latex stay in the Latex editor mode after submission and not display the formulas properly?

I'm not yet sure, but have created a thread in the mod forum requesting Skinwalker take a look next time he logs in (don't feel the need is critical enough to contact him at his personal account and appreciate your patience and understanding)

my best guess is that the most likely scenario is an upgrade in the background borked the code we inserted to make it work and something on our end needs to be changed

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iNow

"[Time] is one of those concepts that is profoundly resistant to a simple definition." ~C. Sagan


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Robittybob1
Post  Post subject: Re: Algebra problem help requested  |  Posted: Fri May 27, 2016 12:02 am

Joined: Thu Jan 29, 2015 4:11 pm
Posts: 183

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iNow wrote:
Robittybob1 wrote:
Why does the latex stay in the Latex editor mode after submission and not display the formulas properly?

I'm not yet sure, but have created a thread in the mod forum requesting Skinwalker take a look next time he logs in (don't feel the need is critical enough to contact him at his personal account and appreciate your patience and understanding)

my best guess is that the most likely scenario is an upgrade in the background borked the code we inserted to make it work and something on our end needs to be changed


Thanks for responding to the note. [This forum has some really good attributes but if it ever did go stronger in the math and physics threads the Latex features would be a limiting factor. I have no knowledge on how to fix it.]


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iNow
Post  Post subject: Re: Algebra problem help requested  |  Posted: Sat Jun 11, 2016 11:22 pm
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Joined: Thu Aug 04, 2011 11:40 pm
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Location: Austin, Texas

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Robittybob1 wrote:
Why does the latex stay in the Latex editor mode after submission and not display the formulas properly?

Thanks to Skinwalker this has been fixed

_________________
iNow

"[Time] is one of those concepts that is profoundly resistant to a simple definition." ~C. Sagan


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Robittybob1
Post  Post subject: Re: Algebra problem help requested  |  Posted: Sun Jun 12, 2016 4:52 am

Joined: Thu Jan 29, 2015 4:11 pm
Posts: 183

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iNow wrote:
Robittybob1 wrote:
Why does the latex stay in the Latex editor mode after submission and not display the formulas properly?

Thanks to Skinwalker this has been fixed

Thanks to all. It is not every day we need the latex but next time.


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