Author Topic: Finding the size of an orbit (question) (Read 757 times) Tweet Share

n.f · « **on:** May 29, 2010, 01:37:34 pm »

Question:
Determine the size of the Moon's orbit around the Earth from the following
Radius of Earth = $6.4*10^6 m$
Gravitational field strength at Earth's surface = $9.8 N kg^-1$
Period of the Moon's rotation around the Earth = $27.3 days$

Help would be greatlyappreciated

Blakhitman · « **Reply #1 on:** May 29, 2010, 02:13:12 pm »

I would find Mass of earth using g, r and G via the formula $g=\frac{GM}{R^{2}}$

then find distance of orbit of Moon using $\frac{R^{3}}{T^{2}}=\frac{GM}{4\pi ^{2}}$ where M=mass of earth and T=period of moon's orbit which is $2.36 X10^{6}$

m@tty · « **Reply #2 on:** May 29, 2010, 02:21:49 pm »

First find the value they used for the mass of earth

$g=\frac{GM}{r^2}$

At $r=6.4\times 10^6 m$ $g=9.8 Nkg^{-1}$ and $G=6.67\times 10^{-11}$ .

$M=\frac{gr^2}{G}=\frac{9.8\times (6.4\times 10^6)^2}{6.67 \times 10^{-11}}=6.02\times 10^{24} kg$ .

Now circular(almost) motion with the moon.

$a=\frac{v^2}{r}$ and $v=\frac{2\pi r}{T}$ .

Sub for v: $a=\frac{4\pi^2 r }{T^2}=\frac{GM}{r^2}$ .

$\implies r^3=\frac{GMT^2}{4\pi^2}$ .

$T=27.3\times24\times60\times60=2358720 \ seconds$

$r^3=\frac{6.67\times10^{-11}\times 6.02\times 10^{24} \times (2358720)^2}{4\pi^2}=5.66\times10^25$ .

$\implies r= \left(5.66\times10^{25}\right)^{\frac{1}{3}}=383877822 =3.84\times10^8 \ m$ .

n.f · « **Reply #3 on:** May 29, 2010, 02:51:17 pm »

Thank you both very much

lachymm · « **Reply #4 on:** May 30, 2010, 03:23:53 pm »

That $r^3$ formula i didnt know about, thanks

superflya · « **Reply #5 on:** May 30, 2010, 03:27:47 pm »

Quote from: lachymm on May 30, 2010, 03:23:53 pm

That $r^3$ formula i didnt know about, thanks

its just keplers, it may look unfamiliar coz he rearranged it

Blakhitman · « **Reply #6 on:** May 30, 2010, 03:41:20 pm »

Look at matty's post, shows how it's derived.

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Author Topic: Finding the size of an orbit (question) (Read 757 times) Tweet Share

n.f

Finding the size of an orbit (question)

Blakhitman

Re: Finding the size of an orbit (question)

m@tty

Re: Finding the size of an orbit (question)

n.f

Re: Finding the size of an orbit (question)

lachymm

Re: Finding the size of an orbit (question)

superflya

Re: Finding the size of an orbit (question)

Blakhitman

Re: Finding the size of an orbit (question)

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