View Full Version : Mass of Earth

Galaxian

2012-Oct-25, 07:39 AM

A student doubting his professors decided to estimate the mass of the earth by himself,astronomically.

He has following data:

(a) Radius of earth = 6400 km.

(b) speed of light.

(c) true orbital period of Moon = 27.3 days.

(d) signals sent by Apollo astronauts reached earth in 1.3 sec.

Help him estimate the mass of the Earth.

I don't know the answer. Help me .

Jens

2012-Oct-25, 08:31 AM

I don't know the answer either, but from the information, you can find the distance from the earth to the moon, and its orbital period.

Van Rijn

2012-Oct-25, 09:18 AM

Is this a class question? A hint: Can you think of a relationship between mass and orbits?

Galaxian

2012-Oct-25, 09:23 AM

This is not a class question.

Hornblower

2012-Oct-25, 10:23 AM

In addition to what is given so far, he would need to know the value of the gravitational constant, or a means of determining it, such as the Cavendish experiment.

What does he doubt, and why?

Jeff Root

2012-Oct-25, 12:34 PM

Assuming that what the student doubts is the mass of

the Earth, then the most important information missing

from the question is Newton's law of gravity. If it is

instead Newton's law of gravity that the student doubts,

then it will be considerably more difficult to estimate

the Earth's mass.

Newton's law of gravity needs the value of the gravitational

constant which Hornblower pointed out, the orbital period

of the Moon, as given, and the distance between Earth and

Moon, which of course can be calculated from the speed of

light (which I suppose you can look up or have already

memorized) and the given time for signals to travel that

distance.

The only way I see the radius of the Earth being used is to

add to the distance you calculate from the signal travel time,

to get the distance between the center of the Earth and the

near surface of the Moon. The Moon's orbit is sufficiently

eccentric, though, that Earth's radius doesn't matter much,

in comparison. But you wouldn't know that if you had no

idea what Earth's radius is, so it is still important.

In fact, I suspect that the given figure for the signal travel

time is not an actual measurement between Earth's surface

and the Moon's surface, but a rough figure calculated from

the mean center-to-center distance. I get 1.28 seconds

travel time for that distance.

Another bit of information you need in order to apply

Newton's law of gravity is that the Moon's mass is much

less than that of the Earth. If you can also estimate the

mass of the Moon you can use it to get a more accurate

and precise value for the mass of the Earth.

-- Jeff, in Minneapolis

NEOWatcher

2012-Oct-25, 12:50 PM

The only way I see the radius of the Earth being

used is to add to the distance you calculate from the signal

travel time, to get the distance between the center of the

Earth and the near surface of the Moon.

If you only have the surface gravity, then you need it to compute the gravitational gradient. No?

ngc3314

2012-Oct-25, 12:59 PM

Either the surface gravity and radius of the Earth, or the Moon's orbital period and radius, will get you there via Kepler's third law (or at least Newton's form including the constants).

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