Calculating Satellite Orbital Radius from Period

[Format]

I need to find the orbital radius of a satilite, while only knowing its orbital period.


i tried..

a = 4π²r/T²
Fnet = Fg
a = Gm/r²

Gm/r² = 4π²r/T²
r = cuberoot(T²Gm/4π²)

didnt work out..

 

[dextercioby]

What??What are u saying by "didn't work out" ?Your formula is okay for a circular orbit...

Daniel.

 

[Format]

Hmm..i keep getting 3.19x10^7

but the answer is 6.95x10^6

 

[christinono]

Try this:
From the period, find the speed (simple calculation). Then, use this formula to find the radius:

$$v=\sqrt{\frac{Gm_E}{r}}$$

 

[Format]

hmm, in order to find the speed don't you need the radius?

like v = 2πr/T ?

 

[Gokul43201]

Hmm..i keep getting 3.19x10^7

but the answer is 6.95x10^6

I see nothing wrong with your approach. Why don't you post the numbers given (actually just the value of T), so we can check the calculation ?

 

[christinono]

Oh yeah. Just give me a second to think about this...

 

[Format]

i guess that would help lol..

A satilite has an orbital period of T = 5760 s. What is the average orbital radius of its orbit?

 

[dextercioby]

Hmm..i keep getting 3.19x10^7

but the answer is 6.95x10^6

Please post the initial text of the problem...

Daniel.

 

[Gokul43201]

I get 6.95 * 10^6 m.

You must have made a calculation error. Show us your working, and we'll show you what's wrong.

 

[christinono]

I need to find the orbital radius of a satilite, while only knowing its orbital period.


i tried..

a = 4π²r/T²
Fnet = Fg
a = Gm/r²

Gm/r² = 4π²r/T²
r = cuberoot(T²Gm/4π²)

didnt work out..

I did exactly that and got 6.95 x 10^6 m. Maybe you punched in the numbers wrong...

 

[Format]

well isn't this anoying..
k i put the cube root of..

( (5760²)(6.67x10^(-11)(5.98x10^24) ) / 4π²

 

[Format]

wait...i see a missing bracket, one sec lol

damn didnt make a difference...wut am i doing wrong?

 

[dextercioby]

Without using the calculator i could show that the result is
$$6\cdot 10^{6} <r<7\cdot 10^{6}$$



So how about pluggng in the numbers properly...

Daniel.

 

[christinono]

well isn't this anoying..
k i put the cube root of..

( (5760²)(6.67x10^(-11)(5.98x10^24) ) / 4π²

yeah, you're missing a bracket.

 

[Format]

ive done this like 10 times now and added the brackets...still gettin 3.2x10^7 lol

 

[christinono]

OK, show me exactly what you typed into you calculator.

 

[Gokul43201]

Here, hope this helps :

http://www.google.com/search?hl=en&...98)x(10^24)++/+(4*pi*pi))^(1/3)+=&btnG=Search

 

[dextercioby]

Okay:U need to take 3-rd order root from:
$$\frac{(5.76)^{2}\cdot 1000^{2}\cdot 6.67\cdot 10^{-11}\cdot 5.98\cdot 10^{-24}}{4\pi^{2}} \simeq 300\cdot 10^{18}$$

Daniel.

 

[Format]

ok i got it to work haha, thanks for the help guys

 

[tony873004]

$$r = (t / (2pi)) ^ {2 / 3} * (G * M) ^ {1 / 3}$$
r = 6942704.95871195 meters