
I am doing a planet report and I am wondering how
scientists know the weights of the planets. Do
they calculate it?

Question Date: 20020424   Answer 1:
You can measure the mass of something that orbits
a larger body by how far away they are, and how
long they take to make one complete
orbit. Johannes Kepler, in the 1500's,
predicted that the orbital sizes and periods of
the planets should have a very definite proportion
 that is: If we call T = time to make
one orbit
around the sun, and R = radius of the
orbit, then
(R^{3})/(T^{2}) for all the
planets = a constant,
which includes the mass of the sun. So, to
measure the mass of a planet, you can measure the
periods and radii of the orbits of all the moons
that orbit around it , graph
R^{3}/T^{2} for all the
moons, and calculate the mass of the planet. This
is one way to do it.
Another way is by
measuring the shape and the gravitational field,
and then you can calculate the mass.
  Answer 2:
This is a good question. What astronomers actually
calculate is the mass of all the planets, not
their weight. The mass tells you how much matter
there is in the planet but the weight tells you
how heavy something is on the Earth. The
difference is that, on the moon, you are much
lighter than on the Earth, but you still have the
same mass (because you have the same amount of
matter in you!).
Anyway, the way to
calculate the masses of the planets is using
Newton's law of gravity The law of gravity
is an
equation that tells you how strong objects pull on
each other due to gravity, and it depends on the
masses of the two objects and on their distance
apart. Using this law of gravity, you can
calculate exactly where the planet should be and
how fast it should be going at any time, and all
of that information turns out to depend on the
mass of the sun and the mass of the planet. By
studying the exact orbit of the planets and sun in
the solar system, you can calculate all of the
masses of the planets.
  Answer 3:
Yes. The masses of the planets are calculated
most accurately from Newton's law of gravity,
a = (G*M)/(r^{2}), which can be used
to calculate how
much gravitational acceleration (a) a planet of
mass M will produce on objects at distance
r away.
One can solve for M once the other numbers are
known. G is a universal number which
determined
here on Earth by measuring the attraction of
objects of known mass at a known spacing r,
then
solving for G. (The law of gravity applies to all
objects, no matter how small we just don't notice
the gravity of everyday objects, because it is so
weak). The measurement is done with a Cavendish
balance, which is surprisingly sensitive I used
one once, but got too close to the device and the
experiment was ruined because of the gravitational
pull of my head.
A planet's mass can in
principle be calculated by observing how its
gravity causes small wobbles in the orbits of
other planets. In fact, college student John
Couch Adams realized that small wobbles in
Uranus's orbit could be nicely explained by the
presence of an undiscovered planet. Astronomers
looked where Adams told them to, and found Neptune
(which other astronomers, including Galileo, had
seen but dismissed as just another faint star).
Since a planet's gravity is stronger near the
planet, a more accurate determination of its mass
involves observing the orbits of its moons. All
planets except Mercury and Venus have moons, but
those two planets have been visited by space
probes, along with all other planets except Pluto.
Probes provide the most accurate measurement of
the mass because the probe's motion can be
measured to high accuracy by recording the times
at which its radio pulses arrive on Earth. The
probe's distance from Earth determines how long it
takes the signal to reach us, and with
highaccuracy clocks we can measure, within
meters, how much the probe was gravitationally
deflected by the planet.
  Answer 4:
The short answer to your question is that yes,
scientists calculate the mass of planets. Before
describing it to you in detail, I should point out
that in physics, the terms "mass" and "weight"
have significantly different meanings. Mass is a
measure of how much matter there is in an object.
For any object, this number is the same anywhere
in the universe. Weight, on the other hand, has
to do with the attractive force between different
objects. Every object with mass attracts every
other body with mass according to Isaac Newton's
equation F = G * M * m /
(r^{2}) rwhere M is
the mass of one object, m is the mass of a
different object, d is the distance between
them,
and G is the "gravitational constant."
First off, we can see that as the mass of the
objects increases, their product will increase and
give bigger forces. However, G is a very, very
small number (Side note: although G is extremely
small, it is possible to measure it in a
laboratory, as was originally done by Cavendish
just before 1800). The other key part is that
the attractive force (gravity) decreases as the
inverse square of the distance between the
objects. That means, if the distance between the
two objects doubles, the force drops by 4; if it
triples, the force drops by 9; if it's quadrupled,
the force drops by 16, and so on.
So how do
we use this to measure the mass of the planets?
For this, there are basically two options  you
either 1. Need to be on the planet, or 2.
Get some information about an object orbiting the
planet. Let's talk about each one.
1. Calculating the mass of a planet while on that
planet. It turns out that in the above
equation, the group of terms G*M / (r^{2})
is what
scientists think of as the acceleration due to
gravity (taking M as the mass of the planet).
This is something that can be experimentally
measured. For example, on Earth, the value is
about 10 m / s^{2}. That means if I drop
an object
on earth (any object such that there is negligible
air resistance), after 1 second, it will be
falling at about 10 m / s; after 2 seconds it'll
be about 20 m /s ; after 3 seconds it'll be about
30 m /s, and so on. So, if you drop an object on
another planet, you could first measure how fast
it accelerates towards the planet. Since you know
what G is, and r would be the
radius of the
planet, you could then calculate M, or the
mass of
the planet!
2. Calculating the mass of a
planet from earth
Since we can't fly to the
different planets to use method 1, we are forced
to come up with the mass of planets a different
way. To do this, you need to have some
information about an object that is orbiting it.
Without going into details, it turns out that
starting from the first equation above, you can
describe an object (say, a moon) orbiting a
another object (say, a planet) by the
equation
M = 4 * pi^{2} * r^{3} /
T^{(} 2G)
Here, M is the mass of
the planet, pi is
3.14..., r is the distance between the
center of
the moon and the center of the planet, T is the
period (the time it takes the moon to make one
full orbit around the planet), and G is
again the
gravitational constant. The interesting part
about this equation is that you do not need to
know the mass of the orbiting moon to get the mass
of the planet! If we see an object orbiting a
planet, then all we need to do is figure out how
far apart they are, and how long one orbit takes,
and we can calculate the mass of that planet!
  Answer 5:
The weight of the planet can be computed through
several methods:
1) For our planet, the volume of
the planet has been measured for several hundred
years assuming it is a perfect sphere. Also the
average density is known form measurements at the
surface and in the depth of the earth. Once you
have the 2 it is easy to compute the approximate
weight of the earth.
2) For other planets it is
more complex. Lately, radar waves are used to
measure the density of the planet. The shape and
dimensions of the planet are also measured using
radar waves and astronomical observations. Once
the shape, dimensions and density are known, it is
trivial to get the weight.
3) Another technique is
to use Newton's law which predicts the trajectory
in space of a planet gravitating around another
one. The trajectory can be measured precisely
using astronomical techniques. The weight of one
of the planet (eg. The earth) is known and using
Newton's gravity law, and the known trajectory of
the other planet (eg the moon) , its weight is
deduced. I am sure there are many other techniques
which I do not know.
  Answer 6:
Well, the best way to do it is to measure the
orbit of something around the planet, like a
satellite. If the satellite is small enough
compared to that of the planet, the path it
travels around the planet will depend on the mass
of only the planet. Many of the planets have
moons orbiting around them. All you have to do is
watch the moon travel around the planet and figure
out how far it is from the planet as it orbits and
how long it takes to make one circuit around the
planet. You also, of course, need to know the
distance to the planet. That can be measured by
observing the planet's orbit around the Sun and by
using parallax methods (observing the planet
"shifting" in the sky compared to the background
stars when observing from different locations on
Earth). In reality, it's a bit more complicated
than I've said, but this is the basic idea.
  Answer 7:
Like much of astronomy, the masses of the planets
are known by a set of linked assumptions about the
universe. We know the mass of the earth since we
can measure the gravitation constant (using a
known mass). Since we also know the force of
gravity on the surface of the earth, we can find
its mass. Then, since we know the period of the
revolution of the earth about the sun (1 year), we
can find the mass of the sun as well. Finally, we
know the periods of the planet orbits by
observations from the earth  so we can use the
known solar mass to find the planet's masses. (The
assumption is that newton's law of gravity
applies
everywhere...) If you think this is a long chain
of reasoning, you should see how one finds the
distance to far away galaxies and galaxy
clusters...
  Answer 8:
You probably know that massive objects, such as
planets, attract each other. This effect is
called gravity. Newton first understood the
mathematical equations that describe this
attraction. Kepler later extended Newton's
theories and derived an equation know as Kepler's
law. This equation relates the distance between a
planet and its moon to the period of the moon?s
orbit, and the planet?s mass. Therefore, if you
know the distance to the moon, and how long it
takes the moon to travel around the earth, you
can use Kepler's law to 'weigh' the earth.
  Answer 9:
The weight of planets is not easy to calculate,
but we can get an idea with some simple geometry.
If you know how big they are (i.e. treating them as
a sphere, with a radius) then you can work out
their volume (I think the rule is something like
Volume = 4*pi*radius^{2})
Once you
have the
volume, you have to make some assumptions about
what sort of rock or gas the planet is composed
of, and how dense this material is.
For
instance, the radius of the Earth is about 6370
km. This is a volume of about 5,000,000,000 cubic
kilometers. Most of the earth below 40 km deep is
composed of an olivine rock called peridotite
which has a density of about 3300 to 3500 kg per
cubic meter. Therefore if we multiply this figure
by 1000 to put it in cubic kilometers and multiply
it by the volume of the Earth, we get a awesomely
huge figure! This is only a low estimate though, as
rocks become more dense as you go deeper into a
planet (and the Earth is composed of different
rock types with different densities, especially
towards the core).
We don't know much about
what sort of rocks are on Mars or Venus,
hopefully this will become clearer over the next
decade as we send more probe missions there.
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