Gravitational Fields Flashcards
Describe Newton’s law of gravitation.
The force between two masses is:
Always attractive,
Directly proportional to the product of the masses,
Inversely proportional to the square of the distance between them.
Give the equation for the force between two masses.
F = GMm / r2
Define gravitational field strength in words.
Force per unit mass on an object due to a gravitational field.
Give the equation that defines gravitational field strength.
g = F / m
Give two units for gravitational field strength.
N kg-1
m s-2
Is gravitational field strength scalar or vector? What significance does this have when combining field strengths?
Vector quantity.
Direction must be considered when combining.
What do gravitational field lines show?
The direction of the force,
that a mass would feel in a gravitational field.
Sketch a radial gravitational field and describe the key features.
Field lines meet in the centre.
Field strength decreases with distance.
Shown by field lines getting further apart.
Give the equation for gravitational field strength in a radial field.
g = GM / r2
Sketch a uniform gravitational field and describe the key features.
Field strength is constant.
Shown by equally spaced parallel lines.
The surface of a planet can be approximated as a uniform field.
Define gravitational potential at a point in a gravitational field.
Work done per unit mass
To move an object from infinity to that point.
Give the equation for gravitational potential in a radial field.
V = -GM / r
Why is gravitational potential negative?
Gravitational potential is defined as zero at infinity.
And work needs to be done on an object to move it to infinity.
Give the equation for calculating work done moving an object in a gravitational field (i.e. change in GPE).
ΔW = mΔV
What are gravitational equipotentials?
Lines or surfaces connecting points of equal gravitational potential
(Usually shown at equal intervals of gravitational potential.)
How much work is done moving an object along an equipotential?
Zero as there is no change in gravitational potential.
What do you know about the direction of equipotentials relative to field lines?
Equipotentials and field lines are always perpendicular.
Explain the spacing of the equipotentials in a radial field.
Get further apart as distance from mass increases.
For a given energy per unit mass, an object can be moved further, as field strength decreases.
Explain the spacing of the equipotentials in a uniform field.
- Equally spaced as distance from mass increases. - For a given energy per unit mass, an object can be moved an equal distance, as field strength is constant.
Give the equation that relates gravitational potential V and gravitational field strength g.
g = -ΔV / Δr
Complete: gravitational field strength can also be referred to as…
Gravitational potential gradient.
What does the magnitude of the gradient of a graph of gravitational potential V against distance r represent?
Gravitational field strength (g).
If equipotentials are closer together, what does this tell you?
Greater rate of change of gravitational potential V with distance r (i.e. greater ΔV/ Δr).
Which means a greater gravitational field strength g.
What does the area under a graph of gravitational field strength g against distance r represent?
Gravitational potential difference ΔV.
Is gravitational potential scalar or vector? What significance does this have when combining potential?
Scalar quantity.
Direction does not need to be considered.
At a point between the Earth and Moon, the overall gravitational potential is at a maximum. What do you know about the gravitational field strength at this point?
It is zero.
The gradient = - g and at a turning point this is zero.
Show that the linear speed v of a satellite is inversely proportional to the square root of its orbital radius r.
Equate centripetal force and gravitational force.
Show that the square of the orbital period T of a satellite is proportional to the cube of the orbital radius r (i.e. Kepler’s 3rd law).
Equate centripetal force and gravitational force.
If the radius r of a satellite’s orbit increases, what happens to its linear speed v and orbital period T?
Linear speed decreases.
Time period increases.
What do you know about the total energy of a satellite?
Total energy = kinetic energy + gravitational potential energy
Total energy is constant at all points in the orbit.
Define escape velocity.
The minimum speed an unpowered object needs,
In order to leave the gravitational field,
And not fall back due to gravitational attraction.
Derive an equation for escape velocity.
Consider energy change: initial Ek converted to Ep.
1/2 mv2 = mΔV
Describe the key features of geostationary satellites.
Always above the same point on Earth.
In the plane of the equator (moving west to east)
Orbital period = 24 hours.
(Said to be in a ‘synchronous’ orbit with the Earth.)
(36 000 km from surface of Earth – can show this.)
Explain why geostationary satellites are useful in telecommunication signals.
The satellite is stationary relative to the Earth’s surface.
So transmitters and receivers stay aligned with the satellite and do not need to be adjusted.
Describe the key features of low orbiting satellites.
Orbit between 180 and 2000 km above the Earth.
Cheaper to launch and require less powerful transmitters.
Multiple satellites needed to maintain constant coverage.
Often lie in a plane that includes the poles so they can scan over the whole surface.
Explain why low orbit satellites are useful in imaging (e.g. spying and weather).
Close enough to Earth’s surface to see a high level of detail.
