Universal Law of Gravitation - Topic 6.2
Bite-sized Universal Law of Gravitation Study Notes for IB Physics HL/SL
Table of Contents
Key points
- Any two objects with mass exert the same gravitational force upon each other.
- Attractive force that causes the acceleration in uniform circular motion.
- The factors that contribute to the force are the Universal Gravitational Constant, the two masses, and the radius (distance) between the center of each mass.
- Point masses are ideal objects that have no size, but have mass.
- Practical objects follow the same gravitational law.
Newton’s Law of Gravitation explains and models the gravitational interactions between two objects.
- Any two objects with mass exert an equal and opposite gravitational force upon each other (Newton’s Third Law).
- Gravitational forces causes the acceleration in uniform circular motion, as well as acceleration due to gravity, g.
- This law explains how planets orbit stars (circular motion).
- Gravitational forces causes the acceleration in uniform circular motion, as well as acceleration due to gravity, g.
- This law is modeled with point masses, or ideal objects that have mass, but no size.
- However, distance matters. Whenever calculating gravitational forces, be sure to account for the radius of each object.
Formula Booklet
This is the formula booklet equation for calculating the magnitude of gravitational force that objects exert upon each other.
- G is the universal gravitational constant (6.667e-11).
- The two masses are multiplied by each other.
- The radius, r, is calculated as the distance between the center of the two objects.
- Force has an inverse square relationship with distance.
Key points
- Gravity operates via gravitational fields.
- Every object with mass has its own gravitational field.
- The gravitational field strength at a certain point is the gravitational force per unit mass experienced by a point mass at that certain point.
- Gravitational field strength is equivalent to acceleration due to gravity.
Gravitational Field Strength is defined as the gravitational force per unit mass experienced by a point mass at a certain point.
- Every object with mass creates a gravitational field by bending space-time to carry out the attractive force of gravity.
- Gravitational Field Strength is a vector quantity whose direction is given by the direction of the force that a point mass would experience at that certain point.
- Direction in the example is toward the center of the earth, as its mass would attract a point mass within its gravitational field
- It is not uniform – it gets weaker as the distance increases.
- Distance between the red lines increases.
- Gravitational field strength is radial around a single point or spherical mass, like the Earth.
Formula Booklet
The formula booklet equation for the gravitational field strength is based on its definition.
- The gravitational force per unit mass leads to the fraction F/m.
- Substituting the equation for the force of gravity and cancelling leads to the second equation.
- Only the mass of one object is needed – the one that is creating the observed force.
Key points
- Two objects with a great difference in mass orbit each other due to the gravitational force and acceleration that they exert upon each other.
- The smaller object orbits the larger.
- Gravitational force provides centripetal force for orbital motion.
- Kepler’s Third Law dictates the period of planets’ orbits around the sun.
Orbital Motion is a type of circular motion that two bodies of significantly different masses engage in.
- Smaller planets orbit larger stars, and moons orbit planets.
- To maintain a constant orbit, frictional forces are at a minimum compared to the gravitational force.
- The gravitational force creates a centripetal force for the circular motion of the orbit.
Not in Formula Booklet but important
For this section, there are two relevant equations, neither of which are included in the formula booklet:
- The first equation is used to find orbital velocity.
- Found by setting the expression for centripetal force equal to the expression for gravitational force, then simplifying.
- The second equation is Kepler’s Third Law.
- Derived by taking the square of the linear velocity expression (in circular motion), and setting that equal to the square of the velocity, as defined by the first expression.
- This law shows that the period of planets orbiting around a star is proportional to 3/2 of the orbital radius.
This is a summary of the concepts and equations above.
Not in Formula Booklet but important
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