B
on their masses and the square of the distance
between them. Written mathematically, this is:
F = GxM¹xM²
r²
where G is the Gravitational Constant, M1 and
M2 are the masses of the two bodies and r is the
distance between their centres. This mathematical
expression of the Universal Law of Gravitation
provided a means for determining Earth’s mass.
The force, F, with which a mass M1 is attracted
to Earth is easily measured. Hence, the mass of the
Earth, M2, can be calculated provided r and G are
known. The term r is simply the radius of the Earth,
which was known, so only the value of G was needed
to calculate the mass of the Earth. Nevil Maskelyne,
the British Astronomer Royal, attempted to determine
G in the mid 1700s by measuring the sideways
deflection of a pendulum of known mass caused by
a mountain. The distance from the centre of mass of
the mountain to the pendulum and the mass of the
mountain had to be estimated, so needless to say,
the results were not very accurate. Instead, Henry
Cavendish, a wealthy recluse with a deep interest in
apparatus used to weigh the earth
large spheres
can be rotated
supporting arm
suspending wire
beam
rotation caused by
gravitational
attraction between
spheres
5 cm sphere
20 cm sphere
glass
window
pointer
scale
16
the earth and its environment
box
A sketch of the apparatus used by Henry
Cavendish to determine the value of the
Gravitational Constant, which enabled
him to measure Earth’s mass.
www.africaninspace.com / HBD
efore discussing this question, we need to
resolve some terminology. First, the weight of
an object is really the force with which it is attracted
to the Earth by gravity. Secondly, the amount of
material making up an object is called its mass. For
example, the mass of the Apollo astronauts was the
same on Earth as on the Moon, but their weight on
the Moon was about one sixth because of its weaker
gravitational attraction. An astronaut will experience
weightlessness (zero weight) when in orbit, but his
or her mass will remain unchanged. Hence, when
we talk of Earth’s weight, we really mean its mass.
A way of measuring the Earth’s mass was
formulated by Sir Isaac Newton in 1666, based
on his discovery of the mathematical laws that
describe gravity. Legend has it that Newton was
relaxing in the shade beneath an apple tree when
an apple fell on him. This got him thinking – why
do objects fall to Earth? He reasoned that there
must be a force of attraction between them.
Newton realized that this force – gravity – must
be a fundamental property of all matter, including
Earth. He went on to work out that the force
of attraction between any two bodies depends
chemistry and physics, measured the value of G
under controlled laboratory conditions. He achieved
this in 1798, using apparatus built some years
earlier by the Rev John Mitchell, who unfortunately
died before he himself could obtain any results.
The apparatus consisted of a 100 cm long wire
secured at one end, which supported a horizontal
beam. Attached to each end of the beam were lead
spheres about 5 cm in diameter. Suspended by the
wire, the beam was perfectly balanced, and was
encased in a box to isolate it from air movements.
A similar arrangement was constructed outside the
box. Two lead spheres about 20 cm in diameter
were suspended from an arm in such a way that
they could be brought into close proximity to the
spheres inside the box by rotating the supporting
arm. Gravitational attraction between the spheres
would cause the beam inside the box to rotate,
creating a twisting force in the wire, which opposed
the attraction between the spheres. A window in
the side of the box permitted Cavendish to see and
measure how much the beam was deflected. The
entire apparatus was placed in a sealed room to
keep the temperature uniform and Cavendish made
the measurements from outside the room using
a telescope, so that his own mass and body heat
would not affect the measurements.
Cavendish determined the twisting strength of
the wire by measuring the period of oscillation
of the beam. Using the wire’s twisting strength
and the measured deflection of the beam, he was
able to calculate the force of attraction between
the spheres, which is the term F in the Universal
Law of Gravitation equation. M1 and M2 were
the known masses of the spheres, and r was the
distance between the spheres. As G was then the
only unknown remaining, he could thus calculate
its value. Once G was known, he was able to
calculate the Earth’s mass.
This turned out to be 6x1024 kg, or if written in
full, 6 followed by 24 zeros. This very large number
is rather meaningless to us. Cavendish was actually
more interested in calculating the density of the
Earth (mass/volume), which he determined to be
5.48 g/cm3. This is close to the value generally
accepted today (5.519 g/cm3). As common rocks
have a density of about 2.9 g/cm3, Earth’s higher
density indicates the presence of a dense core.
Once the mass of the Earth and G were
known, it became possible to measure the
masses and densities of the Sun and all the
other planets, again using Newton’s Universal
Law of Gravitation. For example, the density
of Jupiter is 1.34 g/cm3, so it clearly differs in
composition from Earth.
Astronauts such as Mark Shuttleworth (above), experience
weightlessness when in orbit. On the Moon (below) astronauts
weigh about a sixth of their normal weight because of the
Moon’s weak gravitational attraction.
NASA
How was the Earth
first weighed?
17