Find Distance Between Earth & Moon: Apply Circular Motion & Gravitation

[pakontam]

hey, how to find the distance of two planets, say, Earth and moon? i know it can done by apply equations of circular motion and gravitation, but it seems to me that there's always a piece of information missing.

like, mass of Earth M :
mg = GMm/r^2
M = gr^2/G
u still need r to find M.

if u know what i mean.

thanks.

 

[Hobnob]

The distance to the Moon, as well as its radius, can be found by various triangulation methods. A simple example: At a certain time, you measure the position of the Moon from an observatory in Britain. At the same time, someone else measures the position from Germany. You know the distance between the two observatories, and this gives you a triangle with two known base angles, so you can work out the height by trigonometry.

(I'm leaving out a lot of details...)

 

[Sourabh N]

Another way is to aim a laser towards moon and measure the time it takes to hit the moon and come back. (Hartle has given some quantitative description of this method in the book, Gravity)

 

[pakontam]

hobnob: that's simple, though never thought of it. obviously that's highly inaccurate, or is it? any famous experiment using this method?

sourabh: seems that I've heard of that. but, doesn't the laser have to be a high power one?

 

[Sourabh N]

yes. In fact it sends around 10^20 photons per second, only to detect one reflected photon every few seconds!

 

[D H]

hey, how to find the distance of two planets, say, Earth and moon? i know it can done by apply equations of circular motion and gravitation, but it seems to me that there's always a piece of information missing.

like, mass of Earth M :
mg = GMm/r^2
M = gr^2/G
u still need r to find M.

if u know what i mean.

thanks.

The radius of the Earth can be measured. It's a fairly well known quantity. What is hard to measure is G. It is one of the least-well known physical constants in terms of accuracy.

The distance to the Moon, as well as its radius, can be found by various triangulation methods.

that's simple, though never thought of it. obviously that's highly inaccurate, or is it? any famous experiment using this method?

Ptolemy estimated the distance to the Moon to be 27.3 Earth diameters (c.f. 30.13 Earth diameters). That's an error of 36,000 km -- not bad for an ancient. Using the laser techniques sourabh described, we now know the distance to the Moon in terms of millimeters.

 

[dnp33]

the triangulation method would be very inaccurate but they measure very small angles.
for example, most astronomical measurments are done in arcseconds, where 1 arcsec = 0.000277777778 degrees.
calculations in arcsec's are done to small numbers. from what I've seen in my limited astronomy background (very limited) into at least the thousandths of arcsec's which would make for an accurate distance from here to the moon.

PS the moon is definitely not a planet.

 

[mgb_phys]

the triangulation method would be very inaccurate but they measure very small angles.

You can get it to 5-10% if your baseline is > 1000km using regular surveying theodolites.
It's a simple lab practical, you just need some friends in another country to do it with you.

Ptolomy did the same thing, but rather cleverly instead of trekking half-way around the Earth he just observed the moon at two times, letting the Earth's rotation give him a baseline.

 

[D H]

the triangulation method would be very inaccurate but they measure very small angles.
for example, most astronomical measurments are done in arcseconds, where 1 arcsec = 0.000277777778 degrees.

Astronomy has improved a lot since you last read up on it. Hubble, for example, needs to be able to maintain attitude to within 7 milliarcseconds. Very long baseline interferometry can regularly achieve accuracies of 0.15 milliarcseconds, and can get in the microarcsecond range when orbiting and Earth-based radio telescopes are combined to make for an extremely long baseline.

It is this extreme accuracy that has led to a rather quick succession of distinctly different definitions of a celestial reference frame: the Mean of 1950 frame based on the FK4 catalog (1963), the J2000 frame based on the Fk5 catalog (1988), and the ICRF based on quasars (2003).

 

[dnp33]

alright well since a microacrsec is 10^-6 arcsecs, and i said thousandths which would be 10^-3, i was pretty close.
but thank you for the correction.