Give an equation for gravitational field strength close to Earth
g=F/m
Where do gravitational field lines point?
Towards the point mass.
What is Newton’s Law of Gravitation?
F=-GMm/r^2
gravitational force is proportional to field strength, and inversely proportional to the square of the distance from the point mass
Why does a negative sign appear in the algebraic expression of Newton’s Law of Gravitation?
A gravitational force is always attractive.
How might we determine overall gravitational force due to multiple point masses?
Consider x- and y- components of gravitational force for each then use Pythagoras to determine the resultant, and trigonometry for the direction
How does gravitational force vary as one moves from Earth to the Moon?
- Initially large and negative
- Decreases towards zero as we move away
- Smaller and positive as we approach the Moon as it has lower gravitational field strength
Give an algebraic expression for g, gravitational field strength, in radial terms.
g=f/m
Thus g=-Gm/r^2
How does gravitational force vary within a planet?
- Initially force increases from zero as we move toward the surface. At first forces are balanced in each direction as the point is surrounded; this becomes unbalanced as we move outward
- Until the radius is reached where this is a maximum
- Force decreases by an inverse square relationship as we move away from the surface
What is Kepler’s 1st law of planetary motion?
Planets orbit stars in an elliptical path with the Sun at one focus.
What can be said about the sum of the lengths joining each point in an object’s orbit to both foci it surrounds?
The sum will always be constant.
Why can we model an orbit as circular?
The orbit of a planet, albeit elliptical in reality, has low eccentricity.
What is Kepler’s 2n law of planetary motion?
A line joining the planet to the star sweeps out equal areas in equal amounts of times.
What is the consequence of Kepler’s 2nd law regarding speed?
A planet does not move at a constant speed as it orbits. It moves faster when. it is closer to the planet, and slower when it is at it’s furthest
What is Kepler’s third law of planetary motion?
T^2 is proportional to r^3
What relationship do we use to derive Kepler’s 3rd law?
Equating gravitational force and centripetal force required to maintain a circular path…
GMm/r^2 = mv^2/r
Define gravitational potential.
The work done per unit mass in bringing a small test mass from a distance of infinity to a given point
Why is gravitational potential always negative?
Gravity is an attractive force - work must be done to overcome it and escape the field
Give an equation for gravitational potential.
V = -Gm/r
How does potential dry as we move from Earth to the Moon?
- Initially very negative
- Tends toward zero as we leave Earth
- Decreases to a lesser extent as we approach Moon
For a graph of gravitational potential against distance, what does the gradient represent?
gravitational field strength, g
Define gravitational potential energy.
Work done moving a small test mass from infinity to that point.
What is the equation for gravitational potential energy?
E=-GMm/rH
How can we derive the equation for gravitational potential energy, and gravitational potential?
Potential energy - w=Fs
Potential - divide by mass (by definition)
