C18 - Gravitational Fields Flashcards
What’s a gravitational field?
A region in space where any mass will experience a force of attraction.
All masses have a gravitational field around them.
What is field strength, g?
The force per unit mass experienced by a mass at that point in a gravitational field.
Calculated by g = F/m
Field strength at any point = acceleration of free fall at that point.
What formula expresses Newton’s law of gravitation?
F = - (GMm)/r^2
What do gravitational field lines / lines of force show?
The gravitational field around an object.
They don’t cross and have arrows to show the field direction.
How do gravitational field patterns / field lines appear around a planet (sphere)?
Near the surface, they are close together, showing a uniform field.
Ultimately it shows a radial field where gravitational field strength decreases as radius increases.
What does the graph of g against r (gravitational field vs radius) look like?
A curve (like 1/x graph where x>0)
Values of g are negative.
As radius increases, g decreases until reaching zero at infinity.
What does the graph of g against 1/r^2 (gravitational field vs 1/radius squared) look like?
A (negative) straight line through the origin with a gradient equal to -GM.
What’s Kepler’s first law?
The orbit of a planet is an ellipse where one focus of the ellipse is the sun.
What’s Kepler’s second law?
A line segment from the planet to the sun sweeps out equal areas during equal amounts of time.
What’s Kepler’s third law?
The period of a planet’s orbit squared is proportional to its average distance from the sun cubed.
T^2 proportional to r^3
T^2 / r^3 = constant
How can Kepler’s third law be proven?
Centripetal force = gravitational force on planet
mv2/r = GMm/r2
v2 = (2pi*r/T)2/
4pi2r2/T2 = GM/r
T2 proportional to r3
What are geostationary satellites?
Satellites placed in orbit above the equator.
They must be in orbit above the Earth’s equator, rotate in the same direction as the Earth’s rotation and have an orbital period of 24 hours.
What’s the symbol to gravitational potential?
Vg in J/Kg
Where is gravitational potential at its maximum?
At infinity (where its value is 0J/Kg) - a distance so far from the object producing the gravitational field that the gravitational field strength is zero.
This means all values of gravitational potential are negative.
What is gravitational potential?
The gravitational potential energy per unit mass.
