6.2 Gravitation Flashcards
What is Newton’s law of gravitation?
Two point masses m1 and m2 separated by a distance r attract each other with a force whose magnitude if F=GmM/r^2 where the force is directed along the line joining the two masses. The formula can be used for two uniform spherical masses in which case r is their centre to centre separation.
What is the concept of a field?
A mass M is the source of a gravitational field around it. Other masses respond to this field by experiencing a gravitational force. To feel the gravitational field you must have mass. In the case of gravity a gravitational field exists in a region of space around a mass and exerts a force on any other mass that is present in that region of space. The field is a property of the mass creating the field and of the distance from it.
What is the gravitational field strength?
The gravitational force per unit mass exerted on small point mass m (g = F/m F = mg).
What is the formula for the gravitational field strength if the gravitational field created y a spherical mass M a point mass m placed a distance r from th centre of M experiencing a force F = (GMm)/r^2.
g = F/m = ((GMm)/r^2)/m = GM/r^2
This formula only applies if M is a point mass or a spherical mass.
What happens to gravitational field patters close to the surface of a planet?
The surface looks flat and the gravitational field lines are approximately parallel lines.
When a particle of mass m is orbiting a larger body of mass M in a circular orbit of radio r what if the force that provides the centripetal force on the particle?
The only force on the particle is the force of gravitation F=GmM/r^2 and so this force provides the centripetal force on the particle.
Therefore mv^2/r = GMm/r^2 cancelling the mass and factor of r leads to
v = sqr root of GM/r
This gives the speed in a circular orbit of radius r. Squaring v=2pir/T we deduce that (4pi^2r^2)/(T^2) = GM/r —> T^2 =
(4pi^2)/(GM) x r^3 —–> T = 2pi/sqr root (GM) x r^2/3.
This shows that the period of a planet going around the sun is proportional to the 3/2 power of tis orbital radius.
