Kepler’s Laws of Planetary Motion
1. All planets move in elliptical orbits with the sun at a focus.
2. The radius vector from the sun to the planet sweeps equal area in equal time.
3. The square of the time period of a plant is proportional to the cube of the semimajor axis of the ellipse.
(Chapter: Gravitation)
1. All planets move in elliptical orbits with the sun at a focus.
Circular path is a special case of an ellipse when the major and minor axes are equal. For a circular apth, the planet should have velocity perpendicular to the line joining it with the sun and the magnitude has to be
v = √(GM/a)
If these conditions arenot satisfied, the planet moves in an ellipse.
2. The radius vector from the sun to the planet sweeps equal area in equal time.
For a circular orbit, as the speed of the particle remains constant, it will sweep equal area in equal time.
3. The square of the time period of a plant is proportional to the cube of the semimajor axis of the ellipse.
For circular orbits this law is proved.
Past JEE Questions
According to Kepler’s second law, the radius vector to a plant form the sun sweeps out equal areas in equal intervals of time. This law is a consequence of the conservation of -----------------.
(JEE 1985)
Answer: Angular momentum
Showing posts with label Gravitation. Show all posts
Showing posts with label Gravitation. Show all posts
Wednesday, August 27, 2008
Wednesday, May 7, 2008
Concept Review - Chapter 11 Gravitation
Universal law of gravitation
F = GMm/r²
Universal constant of gravitation (G)
G = 6.67*10^-11 N-m² /kg²
Gravitational potential energy
Gravitational potential
Gravitational potential at a point is equal to the change in potential energy per unit mass, as the mass is brought from the reference point to the given point.
Gravitational field
It is assumed that a body say A, creates a gravitational field in the space around it. The field has its own existence and has energy and momentum. When another body B is placed in gravitational field of a body, this field exerts a force on it. The direction and intensity of the field is defined in terms of the force it exerts on a body placed in it.
The intensity of gravitational field vector E at a point is defined by the equation
vector E = force vector F/mass
where F is the force vector exerted by the field on a body of mass m placed in the field. The intensity of gravitational field is abbreviated as gravitational field. Its SI unit is N/kg.
By the way they are defined, intensity of gravitational field and acceleration due to gravity have equal magnitudes and directions, but they are two separate physical quantities.
Acceleration due to gravity (g)
Variation in the value of g
Kepler's laws
Time period of a planet
Escape velocity
gravitational binding energy
Black holes
Inertial and gravitational mass
Geostationery satellite
F = GMm/r²
Universal constant of gravitation (G)
G = 6.67*10^-11 N-m² /kg²
Gravitational potential energy
Gravitational potential
Gravitational potential at a point is equal to the change in potential energy per unit mass, as the mass is brought from the reference point to the given point.
Gravitational field
It is assumed that a body say A, creates a gravitational field in the space around it. The field has its own existence and has energy and momentum. When another body B is placed in gravitational field of a body, this field exerts a force on it. The direction and intensity of the field is defined in terms of the force it exerts on a body placed in it.
The intensity of gravitational field vector E at a point is defined by the equation
vector E = force vector F/mass
where F is the force vector exerted by the field on a body of mass m placed in the field. The intensity of gravitational field is abbreviated as gravitational field. Its SI unit is N/kg.
By the way they are defined, intensity of gravitational field and acceleration due to gravity have equal magnitudes and directions, but they are two separate physical quantities.
Acceleration due to gravity (g)
Variation in the value of g
Kepler's laws
Time period of a planet
Escape velocity
gravitational binding energy
Black holes
Inertial and gravitational mass
Geostationery satellite
Tuesday, October 23, 2007
Study guide H C Verma JEE Physics Ch. 11 GRAVITATION
JEE syllabus
Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Motion of planets and satellites in circular orbits; Escape velocity.
---------
Sections in H C Verma
1. Historical Introduction
2. Measurement of Gravitational Constant G
3. Gravitational Potential Energy
4. Gravitational Potential
5. Calculation of Gravitational Potential
6. Gravitational Field
7. Relation between Gravitational Potential and Field
8. Calculation of Gravitational Field
9. Variation in the Value of G
10.Planets and Satellites
11.Kepler's laws
12.Weightlessness in a Satellite
13. Escape Velocity
14. Gravitational Binding Energy
15. Blackholes
16. Inertial and Gravitational Mass
17. Possible Changes in the Law of Gravitation
---------
Study Plan
Day 1
1. Historical Introduction
Ex. 11.1
Day 2
2. Measurement of Gravitational Constant G
3. Gravitational Potential Energy
Ex. 11.2
4. Gravitational Potential
Day 3
5. Calculation of Gravitational Potential
Ex. 11.3
Worked Out Examples: 1,2
Day 4
6. Gravitational Field
Ex. 11.4
7. Relation between Gravitational Potential and Field
Ex. 11.5
WOE 3,4
Day 5
8. Calculation of Gravitational Field
Ex. 11.6, and 7
WOE 5,6
Day 6
9. Variation in the Value of G
Ex. 11.8
10.Planets and Satellites
11.9
11.Kepler's laws
12.Weightlessness in a Satellite
Day 7
13. Escape Velocity
Ex. 11.10
14. Gravitational Binding Energy
15. Blackholes
Day 8
16. Inertial and Gravitational Mass
17. Possible Changes in the Law of Gravitation
WOE 7 to 9
Day 9
WOE 10 to 13
Exercises 1 to 5
Day 10
Exercises 6 to 15
Day 11
Exercises 16 to 20
Day 12
Exercises 21 to 25
Day 13
Exercises 26 to 30
Day 14
Exercises 31 to 35
Day 15
Exercises 36 to 39
Day 16
Objective I
Day 17
Objectve II
Questions for Short Answer 1 to 5
Day 18
Questions for Short Answer 6 to 10
Day 19
Questions for Short Answer 11 to 15
Day 20
Questions for Short Answer 16 to 19
------------------
Law of gravitation
Eq (11.1) oin H C Verma
F = GMm/r²
The above equation is known as the universal law of gravitation
G = 6.67*10^-11 N-m² /kg²
Gravitational potential and field
Gravitational potential at a point is equal to the change in potential energy per unit mass, as the mass is brought from the reference point to the given point.
Gravitational field: It is assumed that a body say A, creates a gravitational field in the space around it. The field has its own existence and has energy and momentum. When another body B is placed in gravitational field of a body, this field exerts a force on it. The direction and intensity of the field is defined in terms of the force it exerts on a body placed in it.
The intensity of gravitational field vector E at a point is defined by the equation
vector E = force vector F/mass
where F is the force vector exerted by the field on a body of mass m placed in the field. The intensity of gravitational field is abbreviated as gravitational field. Its SI unit is N/kg.
By the way they are defined, intensity of gravitational field and acceleration due to gravity have equal magnitudes and directions, but they are two separate physical quantities.
Obtaining gravitational potential from gravitational field: If intensity of gravitational field E is defined in term of r the distance from the body exerting the gravitational force, its potential can be obtained by integrating e with respect to r ( ∫Edr).
If the potential is known, then its partial derivatives with respect to x, y, and z can be taken and they can be combined to get E, the intensity of gravitation field.
E = iEx + jEy + kEz
http://plasma4.sr.unh.edu/ng/phys407/phys407-7-27-05.pdf
Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Motion of planets and satellites in circular orbits; Escape velocity.
---------
Sections in H C Verma
1. Historical Introduction
2. Measurement of Gravitational Constant G
3. Gravitational Potential Energy
4. Gravitational Potential
5. Calculation of Gravitational Potential
6. Gravitational Field
7. Relation between Gravitational Potential and Field
8. Calculation of Gravitational Field
9. Variation in the Value of G
10.Planets and Satellites
11.Kepler's laws
12.Weightlessness in a Satellite
13. Escape Velocity
14. Gravitational Binding Energy
15. Blackholes
16. Inertial and Gravitational Mass
17. Possible Changes in the Law of Gravitation
---------
Study Plan
Day 1
1. Historical Introduction
Ex. 11.1
Day 2
2. Measurement of Gravitational Constant G
3. Gravitational Potential Energy
Ex. 11.2
4. Gravitational Potential
Day 3
5. Calculation of Gravitational Potential
Ex. 11.3
Worked Out Examples: 1,2
Day 4
6. Gravitational Field
Ex. 11.4
7. Relation between Gravitational Potential and Field
Ex. 11.5
WOE 3,4
Day 5
8. Calculation of Gravitational Field
Ex. 11.6, and 7
WOE 5,6
Day 6
9. Variation in the Value of G
Ex. 11.8
10.Planets and Satellites
11.9
11.Kepler's laws
12.Weightlessness in a Satellite
Day 7
13. Escape Velocity
Ex. 11.10
14. Gravitational Binding Energy
15. Blackholes
Day 8
16. Inertial and Gravitational Mass
17. Possible Changes in the Law of Gravitation
WOE 7 to 9
Day 9
WOE 10 to 13
Exercises 1 to 5
Day 10
Exercises 6 to 15
Day 11
Exercises 16 to 20
Day 12
Exercises 21 to 25
Day 13
Exercises 26 to 30
Day 14
Exercises 31 to 35
Day 15
Exercises 36 to 39
Day 16
Objective I
Day 17
Objectve II
Questions for Short Answer 1 to 5
Day 18
Questions for Short Answer 6 to 10
Day 19
Questions for Short Answer 11 to 15
Day 20
Questions for Short Answer 16 to 19
------------------
Law of gravitation
Eq (11.1) oin H C Verma
F = GMm/r²
The above equation is known as the universal law of gravitation
G = 6.67*10^-11 N-m² /kg²
Gravitational potential and field
Gravitational potential at a point is equal to the change in potential energy per unit mass, as the mass is brought from the reference point to the given point.
Gravitational field: It is assumed that a body say A, creates a gravitational field in the space around it. The field has its own existence and has energy and momentum. When another body B is placed in gravitational field of a body, this field exerts a force on it. The direction and intensity of the field is defined in terms of the force it exerts on a body placed in it.
The intensity of gravitational field vector E at a point is defined by the equation
vector E = force vector F/mass
where F is the force vector exerted by the field on a body of mass m placed in the field. The intensity of gravitational field is abbreviated as gravitational field. Its SI unit is N/kg.
By the way they are defined, intensity of gravitational field and acceleration due to gravity have equal magnitudes and directions, but they are two separate physical quantities.
Obtaining gravitational potential from gravitational field: If intensity of gravitational field E is defined in term of r the distance from the body exerting the gravitational force, its potential can be obtained by integrating e with respect to r ( ∫Edr).
If the potential is known, then its partial derivatives with respect to x, y, and z can be taken and they can be combined to get E, the intensity of gravitation field.
E = iEx + jEy + kEz
http://plasma4.sr.unh.edu/ng/phys407/phys407-7-27-05.pdf
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