Title: InkPhysics / Gravitational fields
On every note of this deck, unless a note says otherwise:
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Front: SPOT THE ERROR
Say what is wrong with this claim: There's no gravity in space.
Back: Gravity follows an inverse square law and never reaches zero; at the ISS it is about 90% of surface g. Astronauts float because they and the station free-fall together.

Front: RECALL
State the defining property of a geostationary satellite.
Back: A geostationary satellite remains above the same point on the Earth's equator.

Front: RECALL
State the radius of the geostationary orbit.
Back: About 4.2 × 10^7 m from the Earth's centre, roughly 36 000 km above the surface.

Front: EQUATION · NOT ON THE DATA SHEET
Kepler's third law, from Newton:
T^2 = ?\(T^{2} = \, ?\)T^2 = ?
Back: T^2 = 4π^2GM r^3\(T^{2} = \frac{4\pi^{2}}{GM}\,r^{3}\)T^2 = (4π^2/GM) r^3

Front: RECALL
State how to find the change in potential from a g-r graph.
Back: The magnitude of ΔV is the area under the field strength against distance graph between the two distances.

Front: SPOT THE ERROR
Say what is wrong with this claim: Forces need contact.
Back: Gravitational, electric and magnetic forces act without contact. Each is described by a field: a region in which a body experiences a force without touching anything.

Front: RECALL
Explain why a planet moves fastest at perihelion.
Back: By Kepler's second law the Sun-planet line sweeps equal areas in equal times. Near the Sun that line is short, so the planet must swing through a wider angle to cover the same area, and it therefore travels fastest at its closest approach and slowest at its furthest.

Front: SPOT THE ERROR
Say what is wrong with this claim: A satellite needs its engines running to stay in orbit.
Back: An orbit is free fall: gravity alone provides the centripetal force, and with no drag nothing slows the satellite, so no engine thrust is needed to stay in orbit.

Front: RECALL
State how to find gravitational field strength from a V against r graph.
Back: g is the negative of the gradient of the graph of V against r.

Front: RECALL
State the equation for gravitational potential in a radial field.
Back: V = −GM/r, with r measured from the centre of the mass.

Front: DEFINITION
Define: Kepler's third law for circular orbits.
Back: The square of the orbital period is proportional to the cube of the orbital radius: T^2 ∝ r^3.

Front: RECALL
State Kepler's first two laws of planetary motion.
Back: First, every planet moves in an ellipse with the Sun at one focus, the other focus being empty. Second, the line joining a planet to the Sun sweeps out equal areas in equal times.

Front: RECALL
State the origins of the three force fields.
Back: Gravitational fields arise from mass, electric fields from static charge, and magnetic fields from moving charge.

Front: EQUATION · NOT ON THE DATA SHEET
Escape velocity:
v_esc = ?\(v_{esc} = \, ?\)v_esc = ?
Back: v_esc = √2GMr\(v_{esc} = \sqrt{\frac{2GM}{r}}\)v_esc = √(2GM/r)

Front: RECALL
State what field-line spacing shows.
Back: The closer together the field lines, the stronger the field.

Front: RECALL
State the effect of dropping to a lower orbit on a satellite.
Back: The satellite speeds up, even though its total energy decreases.

Front: DEFINITION
Define: Newton's law of gravitation.
Back: Two point masses attract with a force F = Gm_1m_2/r^2.

Front: RECALL
State the sign of gravitational potential.
Back: Gravitational potential is zero at infinity and negative everywhere else, because gravity is attractive.

Front: DEFINITION
Define: Escape velocity.
Back: The minimum launch speed at which an object escapes to infinity from a body's gravitational field without further propulsion.

Front: DEFINITION
Define: Force field.
Back: A region in which a body experiences a non-contact force.

Front: SPOT THE ERROR
Say what is wrong with this claim: It takes energy to move anywhere in a gravitational field.
Back: Only moving to a different potential costs or releases energy. Moving along an equipotential, at constant r, needs no work; work done equals mass times the change in potential.

Front: RECALL
State the appearance of a uniform field on a field-line diagram.
Back: Parallel, equally spaced field lines.

Front: DEFINITION
Define: Gravitational potential.
Back: The work done per unit mass to move a small test mass from infinity to that point.

Front: EQUATION · NOT ON THE DATA SHEET
Orbit condition: gravity as the centripetal force:
GMmr^2 = ?\(\frac{GMm}{r^{2}} = \, ?\)GMm/r^2 = ?
Back: GMmr^2 = mv^2r\(\frac{GMm}{r^{2}} = \frac{mv^{2}}{r}\)GMm/r^2 = mv^2/r

Front: DEFINITION
Define: Gravitational field strength.
Back: The force per unit mass on a small test mass placed in the field: g = F/m, in N kg^−1.

Front: DEFINITION
Define: Geostationary orbit.
Back: A circular orbit above the equator with a period of 24 hours, travelling in the direction of the Earth's spin.

Front: RECALL
State the effect on g of doubling the distance from the centre.
Back: g falls to one quarter, because g follows an inverse-square law.

Front: RECALL
State where r is measured from in the inverse square law.
Back: From the centre of the mass, never from its surface.