Fg =
Calculate the force of gravity that the earth
exerts on you. What is this value the same
as? What does this mean?
Calculate the force of gravity between two 75 kg
students if their centers of mass are 0.95 m apart.
A satellite weighs 9000 N on Earth’s surface. How
much does it weigh if its mass is tripled and its
orbital radius is doubled?
A satellite of the Earth, such as the moon, is constantly
falling. But it does not fall towards the Earth, rather it falls
around the Earth. Just as if you were in an elevator that was
falling towards the Earth, you would feel weightless if you
were on an artificial satellite falling around the Earth.
Consider the Moon:
A 4500 kg Earth satellite has an orbital radius of
8.50x107 m. At what speed does it travel?
Gravitational Fields
Scientists had difficulty explaining how two
objects that are not in contact can exert a
force on one another. In order to help
conceptualize how this can occur, we had
invented the idea of FIELDS.
A field is defined as an area of influence.
To help imagine how these fields work, consider a
campfire. It seems as though the fire is emitting a
heat field.
As you approach the fire the field strength increases.
As you increase the size of the fire the field strength
Just like this so-called heat field, gravitational fields
surround any mass. Just like any other value, fields
can be described as either vector or scalar.
While heat is measured by temperature
(a scalar) its field is also scalar.
Gravitational fields are force fields and as
such are vectors.
Vector fields, like vector
quantities, are
represented by arrows.
In this case, the density
of the arrows represent
the magnitude of the
field strength…
We are already quite familiar with gravitational field strength
by its other name acceleration due to gravity.
Fg = mg
Where g
= acceleration due to gravity
= gravitational field strength
= 10 m/s2 near Earth’s surface
This formula works fine if we stay put on Earth,
but it falls way short once we leave Terra Firma,
because the Earth’s gravitational field changes
depending on how far you are from Earth’s
surface. However, we can derive a more useful
What is the gravitational field strength on the surface of
the Moon?
mmoon = 7.35x1022 kg
rmoon = 1.74x106 m
A satellite orbits the Earth at a radius of 2.20x107 m.
What is its orbital period?
Inertial vs. gravitational mass
• Gravitational mass indicates how much an
object responds to a gravitational field
• Inertial mass indicates how an object
accelerates in response to a net force.
• These two masses are always the same but
they are calculated differently.
Inertial vs. gravitational mass
• Gravitational mass is measured and compared with a
scale (a spring scale or balance) – whatever
compresses more springs, experiences more
gravitational force and so has more gravitational
• Inertia mass is measured by giving two objects the
same net force for the same amount of time,
whichever has more speed at the end of the time has
more inertial mass.
Fundamental forces: Gravity vs.
• All of the everyday forces that result from
contact between two objects are
fundamentally electrical.
• The electron shells in the outmost atomic
layers interact causing friction, normal forces,
tensions, etc.
• The electrical force between two particles is
generally much much stronger than the
gravitational force between them
Why is gravity such a dominant force
• First is the massive scale of the earth in both
circumference and mass.
• The more important issue is that masses
always causes a gravitational field that attracts
other masses. Electrical forces both attract
and repel.
• So stuff on earth is generally electrically
neutral leaving gravity as the dominant force