Resource Lesson
Advanced Satellites
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Newton's Law of Universal Gravitation states that
Every object in the universe attracts every other object in the universe with a force which is directly proportional to the product of their masses and is inversely proportional to the square of the distance between their centers.
This can be stated mathematically as
G
is a very small constant that was first experimentally determined by Henri Cavendish in 1798. Today it's accepted value is 6.672 x 10
^{-11}
Nm
^{2}
/kg
^{2}
. Since
G
is so very small, the gravitational attraction between small masses on the earth's surface is not noticeable compared with the gravitational attraction between either mass and the earth. Gravitation is only an attractive force unlike electromagnetic forces which can be both attractive and repulsive. Moreover, since the majority of the universe is neutral, it is gravity that holds it together.
The region around a massive object in which another object having mass would feel a gravitational force of attraction is called a
gravitational field
. The gravitational field's strength at a distance
r
from the center of an object of mass,
M
, can be calculated with the equation.
This field is a radial, inverse-square field, meaning that if one doubles the distance from the mass' center, the field strength becomes ¼ as large.
The units on
g
can be expressed as either N/kg or m/sec
^{2}
. On the surface of the earth, the value for
g
is often expressed as 9.8 m/sec
^{2}
and is known as the acceleration due to gravity. When expressed as 9.8 N/kg,
g
is referred to as the earth's gravitational field strength at its surface.
Satellites in Circular Orbits
When examining satellites in circular orbits, gravitation supplies the required centripetal force.
Using this relationship, it is possible to calculate the minimum velocity needed to maintain a satellite’s circular orbit around the earth when it is located at a height, h, above the earth’s surface.
Remember that this speed is constant, satellites in circular orbit are an example of uniform circular motion. If the satellite was in an elliptical orbit, its speed would change with its distance from the earth, and conservation of angular momentum would be required to calculate its instantaneous speed at any given position.
Binary Stars
In a
binary system
, two stars are orbiting each other. In our first example, both stars have the same mass,
M
. Setting the required centripetal force equal to the gravitational force between the two stars allows us to determine their orbital period.
In our second example, stars having different masses are
orbiting each other
- one star has mass
M
, while the other has mass,
2M
. Note that the center of mass is located one-third of the distance between the two stars, closer to the larger star. Setting the required centripetal force being exerted on the
2M
star equal to the gravitational force between the two stars allows us to determine their orbital period.
Related Documents
Lab:
Labs -
Gravitational Field Strength
Labs -
Kepler's 1st and 2nd Laws
Labs -
Lab: Triangle Measurements
Labs -
Mars' Lab
Resource Lesson:
RL -
Advanced Gravitational Forces
RL -
Gravitational Energy Wells
RL -
Gravitational Potential Energy
RL -
The Law of Universal Gravitation
RL -
Universal Gravitation and Satellites
RL -
Universal Gravitation and Weight
Review:
REV -
Review: Circular Motion and Universal Gravitation
Worksheet:
CP -
Gravitational Interactions
WS -
Advanced Properties of Freely Falling Bodies #3
WS -
Kepler's Laws: Worksheet #1
WS -
Kepler's Laws: Worksheet #2
WS -
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS -
Parallel Reading - The Atom
WS -
Standard Model: Particles and Forces
WS -
Universal Gravitation and Satellites
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