Gravitational Fields Flashcards
Gravitational fields
a region of space where a mass experiences a force due to the gravitational attraction of another mass
Equation for gravitational field
g = Fg / m
Describe the field lines of gravitational fields on a planet
- Field lines always toward the centre of the mass
- Gravitational force gets wearker as you get further away from the planet’s surface
Newton’s law of gravitation
any two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of their seperation
Equation of Newton’s law of gravitation
Fg = GMm / r^2
The inverse square law
when a mass is twice as far away from one another, the force due to gravity reduces by 1/4 ; 1/r^2 relation
Gravitational field strength
a point where gravitational force exerted per unit mass on a small object is placed at that point
Equation for gravitational field strength
g = GM / r^2
GPE
the energy an object possess due to its position in a gravitational field
GPE = mgh
Gravitational potential
the work done per unit mass in bringing a test mass from infinity to a defined point
Equation of gravitational potential
ϕ = -GM / r
Why does gravitational potential have a negative value?
Because potential near an isolated mass when r is infinity is defined as 0
Gravitational forces are always attractive so when r decreases, positive work is done by the mass when moving from infinity to that point
Mass closer to each other = grav. potential becomes more negative
Mass further from each other = grav. potential becomes more positive
Equation for GPE of two point masses
GPE = -GMm / r
Equation for change in GPE of two point masses m and M from r1 to r2:
△ ϕ = GM (1/r1 - 1/r2)
Circular orbits in gravitational frields
Fg = F circ
GMm / r^2 = mv^2/r
Therefore: v^2 = GM / r
