Physics / Physik exam preparation and summary - Kepler’s Laws, Gravity,
Gravitational Fields, Gravitational Potential, Orbital Motion & Electric Forces
1. Kepler’s Laws of Planetary Motion
1.1 Key Terms
1.2 Three Laws Explained
1.3 Calculations and Examples
2. Gravity
2.1 Key Terms
2.2 Characteristics and Equations
3. Gravitational Field Model
3.1 Field Concepts
3.2 Uniform vs. Radial Field Lines
4. Gravitational Force
4.1 Properties of the gravitational force
4.2 Force Calculations
5. Gravitational Field Strength
5.1 Uniform & Radial Field Strength
5.2 Field Strength Calculations
6. Gravitational Potential & Potential Energy
6.1 Definitions & Key Characteristics
6.2 Calculations (Uniform & Radial Fields)
7. Newton’s Law of Gravitation
7.1 Inverse Square Law Explained
7.2 Equation Overview & Example Problems
8. Planetary Velocities & Orbital Motion
8.1 Orbital + Newton’s Cannon Experiment
8.2 Orbital Velocity Calculations
9. Electric Forces
9.1 Coulomb’s Law & Charge Interactions
9.2 Electric Force Calculations
1
,1. Kepler’s law of planetary motion
1. Key words for Kepler’s law of planetary motion:
1. Au= Astronomical unit, the average distance between Earth and the Sun. Around 150 million km.
2. Planet= A body in orbit around a star that has cleared its orbit and whose gravity makes it
roughly spherical.
3. Ellipse= A regular oval shape, made around two central points.
4. Orbits= The curved path of a celestial object around a star, planet or moon.
2. The properties of Kepler’s law of planetary motion:
-Definition:
Kepler's laws of planetary motion describe the movements (motion) of planets in the solar system
in astronomy and classical physics.
-State the three laws of planetary motion:
1. First law (Elliptical orbits):
The first of Kepler´s three laws of planetary motion states that planets move in elliptical orbits with
the sun as a focus.
2. Second law (Constant area carved out per unit time):
Based on the second law a planet covers the same area of space in the same amount of time no
matter where it is in its orbit. Accordingly, planets that are closer to the sun move at higher speeds
due to stronger gravitational forces, but also cover a smaller area since they are orbiting very close
to it. Meanwhile, planets that are farther from the sun's gravitational forces and therefore move
more slowly still cover the same area, as their total distance travelled is much greater.
3. Third law (Planet distance3 is proportional to year2):
Kepler´s third law describes how a planet's orbital period is proportional to the size of its orbit.
This implies that the period for a planet to orbit around the sun increases proportionally to the
radius of its orbit as it becomes bigger.
2
,3. Calculations for the third law of Kepler’s law of planetary motion:
1. Important equations:
1. Orbital period T (measured in years) = The orbital period is the time it takes for an object to
make one complete orbit around another object and arrive back to the same point in its orbit.
2. Planet distance r (measured in astronomical unit/au) = The average distance between Earth and
another planet.
3. Constant (k) = The constant is the variable that never changes. In our solar system it is 1.
2. Calculations:
1. (Orbital period) T2 = k x r3
2. (Planet distance) r3 = T2/1
3. (Constant) k = T2/r3
3. Examples:
Employ Kepler´s third law to find the planetary distance from the sun if an orbit takes 20 years.
Also calculate the length of a year if it orbits at 3 AU.
1. Calculation:
202 = 1 x r3 I:1
400 = r3 I√
r = 7,37 Au
2. Calculation:
T2 = 1 x 33
T2 = 27 I√
T = 5,2 years
3
,2. Gravity
1. The structure of gravity
-Definition:
Gravity is defined as the force that attracts a body towards the center of the earth, or towards any
other physical body having mass. In addition, the force of gravity keeps all of the planets in orbit
around the sun.
-The characteristics of gravity:
-Gravity acts as the force that pulls things toward the core of a planet as well as other objects
-Anything that has mass also has gravity
-Objects with more mass have more gravity while objects with lower mass have weaker gravity
-Gravity also gets weaker with distance, which is why the closer objects are to each other, the
stronger their gravitational pull is
-You exert the same gravitational force on Earth that it does on you. But because Earth is so much
more massive than you, your force does not have an effect on our planet
-Difference between gravity and gravitation:
Gravity is force of attraction acting between an object and the earth's surface. The earth has a
pulling force towards itself, thereby attracting an object towards itself. Meanwhile, the
gravitational force is the universal force of attraction between two bodies with a mass placed at
some distance in the universe. According to Newton's law of universal gravitation, the force of
attraction between any two bodies is directly proportional to their masses and inversely
proportional to the square of the distance between them.
-Important points:
-While gravitation is the force of attraction between two bodies in the universe, gravity is the force
of attraction between some objects and the Earth's surface in particular
-The force of gravitation is directly proportional to the masses of both the objects as well as is
inversely proportional to the distance between the objects
-The gravitational force can be either attractive or repulsive but the force of gravity is only
attractive in nature
4
, 2. Calculations for gravity
1. Important equations:
1. Weight W (measured in N) = Weight is the force exerted on mass by gravity. It is not constant
and changes from place to place.
2. Mass m (measured in kg) = Mass is how much matter an objects contains. It is not a constant for
a body and does not change with location
3. Gravity g (measured in N/kg or m/s2) = Gravity is defined as the force that attracts a body toward
the center of the Earth or any other physical body with mass. On Earth, the average gravitational
pull is 9,807 m/s².
2. Examples:
A 1,62 x 105 N shuttle leaves the moon what is its weight on Mercury?
1. Calculation:
W=mxg
1,62 x 105 = 1,62 x m I: 1,62
m = 100000 kg
2. Calculation:
W=mxg
W = 100000 x 3,7
W = 37000 N
5
Gravitational Fields, Gravitational Potential, Orbital Motion & Electric Forces
1. Kepler’s Laws of Planetary Motion
1.1 Key Terms
1.2 Three Laws Explained
1.3 Calculations and Examples
2. Gravity
2.1 Key Terms
2.2 Characteristics and Equations
3. Gravitational Field Model
3.1 Field Concepts
3.2 Uniform vs. Radial Field Lines
4. Gravitational Force
4.1 Properties of the gravitational force
4.2 Force Calculations
5. Gravitational Field Strength
5.1 Uniform & Radial Field Strength
5.2 Field Strength Calculations
6. Gravitational Potential & Potential Energy
6.1 Definitions & Key Characteristics
6.2 Calculations (Uniform & Radial Fields)
7. Newton’s Law of Gravitation
7.1 Inverse Square Law Explained
7.2 Equation Overview & Example Problems
8. Planetary Velocities & Orbital Motion
8.1 Orbital + Newton’s Cannon Experiment
8.2 Orbital Velocity Calculations
9. Electric Forces
9.1 Coulomb’s Law & Charge Interactions
9.2 Electric Force Calculations
1
,1. Kepler’s law of planetary motion
1. Key words for Kepler’s law of planetary motion:
1. Au= Astronomical unit, the average distance between Earth and the Sun. Around 150 million km.
2. Planet= A body in orbit around a star that has cleared its orbit and whose gravity makes it
roughly spherical.
3. Ellipse= A regular oval shape, made around two central points.
4. Orbits= The curved path of a celestial object around a star, planet or moon.
2. The properties of Kepler’s law of planetary motion:
-Definition:
Kepler's laws of planetary motion describe the movements (motion) of planets in the solar system
in astronomy and classical physics.
-State the three laws of planetary motion:
1. First law (Elliptical orbits):
The first of Kepler´s three laws of planetary motion states that planets move in elliptical orbits with
the sun as a focus.
2. Second law (Constant area carved out per unit time):
Based on the second law a planet covers the same area of space in the same amount of time no
matter where it is in its orbit. Accordingly, planets that are closer to the sun move at higher speeds
due to stronger gravitational forces, but also cover a smaller area since they are orbiting very close
to it. Meanwhile, planets that are farther from the sun's gravitational forces and therefore move
more slowly still cover the same area, as their total distance travelled is much greater.
3. Third law (Planet distance3 is proportional to year2):
Kepler´s third law describes how a planet's orbital period is proportional to the size of its orbit.
This implies that the period for a planet to orbit around the sun increases proportionally to the
radius of its orbit as it becomes bigger.
2
,3. Calculations for the third law of Kepler’s law of planetary motion:
1. Important equations:
1. Orbital period T (measured in years) = The orbital period is the time it takes for an object to
make one complete orbit around another object and arrive back to the same point in its orbit.
2. Planet distance r (measured in astronomical unit/au) = The average distance between Earth and
another planet.
3. Constant (k) = The constant is the variable that never changes. In our solar system it is 1.
2. Calculations:
1. (Orbital period) T2 = k x r3
2. (Planet distance) r3 = T2/1
3. (Constant) k = T2/r3
3. Examples:
Employ Kepler´s third law to find the planetary distance from the sun if an orbit takes 20 years.
Also calculate the length of a year if it orbits at 3 AU.
1. Calculation:
202 = 1 x r3 I:1
400 = r3 I√
r = 7,37 Au
2. Calculation:
T2 = 1 x 33
T2 = 27 I√
T = 5,2 years
3
,2. Gravity
1. The structure of gravity
-Definition:
Gravity is defined as the force that attracts a body towards the center of the earth, or towards any
other physical body having mass. In addition, the force of gravity keeps all of the planets in orbit
around the sun.
-The characteristics of gravity:
-Gravity acts as the force that pulls things toward the core of a planet as well as other objects
-Anything that has mass also has gravity
-Objects with more mass have more gravity while objects with lower mass have weaker gravity
-Gravity also gets weaker with distance, which is why the closer objects are to each other, the
stronger their gravitational pull is
-You exert the same gravitational force on Earth that it does on you. But because Earth is so much
more massive than you, your force does not have an effect on our planet
-Difference between gravity and gravitation:
Gravity is force of attraction acting between an object and the earth's surface. The earth has a
pulling force towards itself, thereby attracting an object towards itself. Meanwhile, the
gravitational force is the universal force of attraction between two bodies with a mass placed at
some distance in the universe. According to Newton's law of universal gravitation, the force of
attraction between any two bodies is directly proportional to their masses and inversely
proportional to the square of the distance between them.
-Important points:
-While gravitation is the force of attraction between two bodies in the universe, gravity is the force
of attraction between some objects and the Earth's surface in particular
-The force of gravitation is directly proportional to the masses of both the objects as well as is
inversely proportional to the distance between the objects
-The gravitational force can be either attractive or repulsive but the force of gravity is only
attractive in nature
4
, 2. Calculations for gravity
1. Important equations:
1. Weight W (measured in N) = Weight is the force exerted on mass by gravity. It is not constant
and changes from place to place.
2. Mass m (measured in kg) = Mass is how much matter an objects contains. It is not a constant for
a body and does not change with location
3. Gravity g (measured in N/kg or m/s2) = Gravity is defined as the force that attracts a body toward
the center of the Earth or any other physical body with mass. On Earth, the average gravitational
pull is 9,807 m/s².
2. Examples:
A 1,62 x 105 N shuttle leaves the moon what is its weight on Mercury?
1. Calculation:
W=mxg
1,62 x 105 = 1,62 x m I: 1,62
m = 100000 kg
2. Calculation:
W=mxg
W = 100000 x 3,7
W = 37000 N
5
