1. 6.2: Newton’s Law of Gravitation
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Assessment Statements –  Due Thursday
(don’t forget about – 6.1.6, also!)

2. Gravitational field strength
Exists in the space around all objects with mass
Is responsible for applying the gravitational force on an object with mass that is placed in the field
Field lines are drawn to show the direction and magnitude of the gravitational field in space
Lines are always drawn towards the center of mass of the object generating the field
Field lines are known to come in contact with the mass’ surface perpendicularly (normal to the surface)
The strength of the field is indicated by the spacing of the field lines—lines that are more closely spaced indicate a stronger field; lines that are spaced further apart indicate a weaker field.

3. Gravitational field strength
By definition, the gravitational field strength at some point a distance from the center of mass of the object generating the field is:
The force, per unit mass, felt (experienced) by a small point mass placed at that point (in the gravitational field)
𝒈= 𝑭 𝒎
Does this look like anything you’ve seen before in this class?

4. Gravitational field strength
Units = N· kg-1
g  vector quantity, in the same direction as the gravitational force at that point
(Because it’s a vector quantity, we determine the net gravitational field strength at a point in space due to 2 or more objects through vector addition)
(fun connection: gravitational field strength is mathematically equivalent to the acceleration a mass experiencing a gravitational force will feel at that point in the gravitational field)

5. Gravitational Force
There must be two masses present to experience a gravitational force
The magnitude of the gravitational force felt by Object A because of the presence of Object B is equal in magnitude to the gravitational force felt by Object B because of the presence of Object A:
(an “action-reaction” force pair)

6. Newton’s Law of gravitation
developed around 1674, building off ideas formed through earlier astronomers: Kepler, Brahe, Copernicus, and Galileo
“Every material particle in the Universe attracts every other material particle with a force that is directly proportional to the product of the masses of the particles and that is inversely proportional to the square of the distance between them.”
Principia, Sir Isaac Newton

7. Newton’s Law of gravitation
𝑭=𝑮 𝑴𝒎 𝒓 𝟐
F = gravitational force, in N, between masses M and m.
M = mass #1 (typically the larger of the two masses), in kg
m = mass #2 (typically the smaller of the two masses), in kg
r = separation distance, in m, between the centers of mass for M and m
G = universal gravitational constant = 6.67 x N· m2· kg -2

8. Sample problem
What is the gravitational force acting on the International Space Station?
MEarth = 5.97 x 1024 kg
MISS = x 105 kg
Altitude of the ISS = 400. km
Radius of the Earth = 6367 km

9. Gravitational field strength (again)
If:
𝑭=𝑮 𝑴𝒎 𝒓 𝟐
and
𝒈= 𝑭 𝒎
then…what is another way we can quantify the gravitational field strength?

10. gravitational field strength
The strength of the gravitational field of a spherical mass, M, a distance, r, away from its center can be quantified with the following expression:
𝒈=𝑮 𝑴 𝒓 𝟐

12. Sample problem #2
Determine the acceleration due to gravity at the surface of a planet that is 10 times more massive than the earth and has a radius 20 times larger.