15.1 Gravitational Fields Flashcards
Gravitational Field
A region of space where a mass experiences a force due to the gravitational attraction of another mass
Newton’s Law of Gravitation
Any 2 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 separation
Newton’s Law of Gravitation Formula
F=GMm/r^2
Relation of force to distance
F ∝ 1/r^2 (inverse square law) so if you move 2x the distance from original, you only experience 1/4 of the force
Gravitational Constant
6.67x10^-11 Nm^2kg^-2
Gravitational Field Strength (per unit mass)
The gravitational force exerted per unit mass on a small object placed at a point
Gravitational Field strength due to mass at a distance of r from the center
g=F/m so g=GM/r^2
Gravitational potential (at a point)
The work done at a point per unit mass in bringing a mass from infinity to the point
Formula of gravitational potential
Φ(phi) = -GM/r
Why is gravitational potential always negative?
As mass is brought closer to another mass, GPE decreases, and since GPE is zero at infinity, it follows that, anywhere else, GPE and potential are less than zero
Formula for speed at which a satellite must travel at to stay in a circular orbit (centripetal force for orbit)
v^2 = GM/r
Formula for centripetal force
F=mv^2/r
Formula for orbital period
T^2=(4π^2/GM)r^3
Remember mv
Relation of orbital period and radius
T^2 ∝ r^3
Geostationary orbit
Orbit where the satellite remains above a fixed point on the Earth’s equator
