# Distacne of planet

## Main Question or Discussion Point

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.

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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...)

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)

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, doesnt the laser have to be a high power one?

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

D H
Staff Emeritus
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.

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
Homework Helper
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
Staff Emeritus