18, Gravitational Fields Flashcards
Give the equation for gravitational field strength in a uniform field.
g = F/m (field strength = force / mass).
Explain the equation F = - GMm/r^2.
Force = - the gravitational constant * the product of masses of the two objects / radial distance between the centres of the objects^2, this is Newton’s law of gravitation, the negative shows the force is in the opposite direction to the radius.
How is gravitational field strength in a radial field derived?
Take F = - GMm/r^2 and divide by the mass to give g = - GM/r^2.
State Kepler’s first law.
The orbit of an object is an ellipse with the object being orbited being one of the two focal points.
State Kepler’s second law.
A line segment joining the orbiting mass and the mass being orbited sweeps out equal area’s in equal time intervals.
State Kepler’s third law.
The square of the orbital period is directly proportional to the average distance from the two masses.
Explain the equation T^2 = 4pi^2 r^3/GM
Time period^2 = 4pi^2 * radius^3 / (G * mass object being orbited) this comes from equating centripetal force (circular motion) to gravitational force and subbing v = 2pi/T, this is Kepler’s 3rd law with the proportionality constant.
How do you derive the velocity of a stable orbit at a set distance away?
Set F = mv^2/r from circular motion to F = GMm/r^2 and solve for v.
Give some uses of satellites.
Communications, military, research (e.g. telescopes, observing earth), weather and GPS.
What is a polar orbit?
An orbit which is perpendicular to the equator, these orbits give a complete view of earth as it rotates.
What is a geostationary satellite?
A satellite which orbits above the equator at a set distance such that it’s angular velocity is the same as the earths (i.e. has an orbital period of 24h).
Definition of gravitational potential?
Gravitational potential at a point is defined as the work done per unit mass to move an object through the field from infinity (unit J/kg).
Give an example where an object has non-zero potential energy but has no acceleration.
When an object is between two masses such that the gravitational forces are zero.
Equation for energy in terms of potential?
E = mV_g (energy = mass * gravitational potential).
How do you find the velocity required to change orbit and escape velocity?
Set ΔKE = mΔV_g so (v1^2-v2^2)/2 = -GM(1/r1-1/r2). For the escape velocity the GPE is equal to the KE needed so KE = mV_g and v = sqrt(2GM/r).
