Grav Field Flashcards
Define Newton’s law of gravitation
Two points masses attract each other with a force that is directly proportional to the product of their point masses and inversely proportional to the square of the distance between them
Grav force formula
GMm/r^2
Define Gravitational field
a region of space in which a mass experiences a force due to the presence of another mass
Define gravitational field strength at a point in the gravitational field
The gravitational force per unit mass acting on a small test mass placed at that point
Gravitational field strength formula
(GM)/r^2
Define Gravitational potential energy
The work done by a test mass in bringing a mass from infinity to that point
Gravitational potential energy formula
U = -(GMm)/r
Define gravitational potential
The work done per unit mass by an external agent in bringing a test mass from infinity to that point without a change in kinetic energy.
Gravitational potential formula
-(GM)/r
Kepler’s third law
The square of the period of revolution of the planets is directly proportional to the cubes of the mean distances from the sun
Define gravitational force
The force acting on a mass that is placed in a gravitational field
Explain why for changes in vertical position of a point mass near the earth’s surface, gravitational field strength may be considered to be constant
Changes in height near the earth’s surface is much lesser than the radius of the earth,
so gravitational field lines are almost parallel and equally spaced to one another near the earth’s surface,
hence grav field strength is constant.
Explain why, at the surface of a planet, g field strength is numerically equal to the acceleration of free fall. (Relate to grav force)
At the surface of a planet, a mass will experience a grav force equal to weight mg, where g is the g field strength at the surface.
By N2L, resultant force acting on the mass = grav force so g = a
Explain what it means for a mass to feel ‘weightless’.
Weightless -> normal contact force is zero. In this situation, only force that provides the centripetal force is his gravitational force which is also equal in magnitude to the centripetal force.
By N2L, the acceleration of the mass is numerically equal to g at that point, hence apparent weight of astronaut is zero.
mg - N = ma, and mg = ma, so N = 0
Suggest quantitatively why it may be assumed that the sun is isolated in space from other stars.
Quantitatively, the g force of attraction between the sun and star causes a very small hence negligible attraction on the sun due to the sun’s large mass.
There are many other stars around the sun so the net grav force on the sun is 0.
Explain why the centripetal force on two stars in binary orbit has the same magnitude.
Grav force provides centripetal force. By N3L, grav force on each star is equal in magnitude and opposite in direction, so centripetal force will have the same magnitude.
Explain why binary stars must orbit with the same angular velocity.
Grav force provides centripetal force which acts along the line joining the centre of the stars. So stars must always be on opposite ends of the line through their common centre of the mass, and thus must orbit with the same angular velocity.
Why is grav potential near an isolated mass always negative?/a negative quantity?
Grav force is attractive in nature so the external agent has to exert a force equal and opposite such that the test mass does not experience a change in kinetic energy.
Since the external agent is opposite to the displacement of the test mass, the work done per unit mass by the external agent is negative
What is a geostationary orbit
- A circular orbit in the earth’s equatorial plane
- An orbital period of 24 hours
- The same direction of rotation as the earth from west to east.
One advantage and one disadvantage of the use of geostationary satellites
Advantage: provides continuous surveillance if the region under it
Disadvantage: unable to provide coverage for the polar regions
Explain why a geostationary satellite must be positioned directly above the equator.
This is to ensure the satellite rotates about the same axis as the earth. The line joining the object and the centre of the earth has to pass through the equator and rests along the plane perpendicular to the earth’s axis of rotation.
If the object lies above other latitudes besides the equator, it’s axis of rotation would not coincide with that of the earth’s. as such it would be above different latitudes as it rotated and will not be geostationary.
Using Newton’s laws of motion, explain why the two planets orbit about the center of mass of the double planet system.
Each planet orbits due to the gravitational force exerted by the other. As a system, there are no external forces exerted on them.
Thus by N1L, the center of mass must remain stationary. So the center of mass is the center of both planet’s orbit.
Derive grav field strength
ΣF = ma
(GMm/R²) = ma
a = GM/R
Derive Gravitational potential energy using terms
Integrate GMm/r²
Derive escape velocity.
E at Earth’s surface = E at infinity
(Ep + Ek) Earth’s surface = (Ep + Ek) at infinity
-(GMem)/Re + ½ m[v(esc)]² =0+0
½ m[v(esc)]² = GMe/Re
v(esc) = (2GMe/Re)½
Derive the formula for a mass of a planet in terms of r, G and T
ΣF = ma
GMem/R² = mrω²
GMem/R² = mr(2π/T)²
Me = 4πr³/GT²
Derive kinetic energy of a satelite
ΣF = ma
Gmm/r² = mv²/r
½mv² = GMm/2r
