Gravitational Fields Flashcards
What does Newton’s Law of Gravitation state?
The gravitational force between two point masses is proportional to their masses and is inversely proportional to the square of the separation of their centres
State the defining equation for Newton’s Law of Gravitation.
F = -GMm/r²
What does ‘G’ represent?
Gravitational Constant. Equal to 6.67x10⁻¹¹ Nm ²kg⁻²
What is always true about the gravitational force between two masses?
It is always an attractive force
What is a gravitational field?
A region in which any object with mass experiences a non-contact force
What is gravitational field strength?
The force per unit mass felt by the object
What is the unit for gravitational field strength?
N kg⁻¹
State the equation for gravitational field strength.
g = Gm/r²
g = F/m
What is the gravitational potential at a point?
The energy transferred per unit mass when moving an object from infinity to that point
State the equation for gravitational potential energy.
GPE = mass x gravitational field strength x height
= -GMm/r
What is an equipotential?
A plane in which all points have the same potential
What is true when a mass moves along an equipotential?
No work is done
What does the area under a force-separation graph represent?
(Gravitational Fields)
Energy
What is gravity?
Gravity is the universal attractive force which acts between all matter
What can field lines tell you about a field?
The direction of the arrows show the direction of the field. The strength of the field is represented by the density of the field lines
What is gravitational potential?
The potential energy per unit mass, at any point in the field. Zero potential is defined at infinity, hence at a point close to a mass, the potential of an object would be negative
How do you calculate the work done by moving a mass in a field?
Work Done = Mass x Change in Gravitational Potential
What is gravitational potential difference?
The difference in gravitational potentials between two points in a gravitational field
How much work is done per unit distance when you move along an equipotential?
No work is done when moving across equipotentials, as the potential at each point is the same
Why is gravitational potential a negative value?
Work needs to be done to move an object from inside the field to outside the field. Since outside the field, the potential is defined as zero, then the potential inside the field must be zero.
How is the orbital period related to the radius of a circular orbit?
T² ∝ R³ (kepler’s third law)
Compare the PE and KE of a lower orbit to a higher one.
A lower orbit (smaller m) has less potential energy and more kinetic energy than a higher orbit which has a greater r
What is the period of a geosynchronous orbit?
24 hours - Geosynchronous orbits have a period of one day
What type of matter is affected by a gravitational field?
Any object or matter with mass will experience an attractive force
What is a point mass?
A point mass is a theoretical object that has a mass but no dimensions. This means that all of its mass acts at a single point
What is the relationship between the field strength and the field lines that represent it?
The closer the lines are together, the stronger the gravitational field strength and vice versa
Describe similarities between electric and gravitational fields.
- forces both follow an inverse square law
- use field lines to be represented and can both be uniform or radial ( Gravitational never fully radial but for example near to the Earth’s surface its pretty much uniform)
- Similar equations to find force exerted and field strength
What are differences between gravitational and electric fields?
- In gravitational fields, the force exerted is always attractive while in electric fields it can be attractive or repulsive
- Electric fields act on charge, while gravitational fields act on mass (all objects)
How can you derive kepler’s third law using equations, this is for an object orbiting a mass?
Centripetal force = mv²/r
Gravitational force = GMm/r²
Equate them and so v²= GM/r
But v = 2πr/T
v² =4π²r²/T² = GM/r
T² = 4π²/ GM x r³
