Gravitational Fields Flashcards
How are these two gravitational fields similar? How are they different?
Both are uniform (constant field strength)
Closer field lines represent stronger field
How are radial and uniform fields different?
Radial fields have a decreasing field strength
(Field lines increasing in separation)
Uniform fields have a constant field strength
(Field lines constant\ separation)
In gravitational fields when can you use the equation EP = mgh?
Over small distances
When radial fields are approximately uniform
And g is approximately constant
Why can’t SUVATs be used for radial gravitational fields?
SUVATs need a constant acceleration
Radial fields have a variable field strength and so a variable acceleration
What are equipotentials and how are they related to field lines?
An equipotential has the same potential along that line
(So no work is done moving along the equipotential)
They are always perpendicular to field lines
What is Newton’s Universal Law of Gravitation?
Force acting between two bodies is:
- Directly proportional to the product of their masses (F∝m1m2)
- Inversely proportional to the square of their separation (F∝1/r2)
Define gravitational field strength and state its units
The force acting per unit mass on an object in a gravitational field
[NKg-1] or [ms-2]
In the gravitational field strength equation what does M represent?
The mass of the object creating the field
If the Earth is exerting a force on the rocket of 5000N,
What force is the rocket exerting on the Earth?
5000N also. An equal and opposite force from Newton’s 3rd Law
(Which has little effect on the Earth because it has so much more mass)
How do you calculate the resultant gravitational field strength at a point between two bodies?
- Calculate the field strength for each body in turn (ignoring the other one)
- Calculate the difference between the field strengths (g is a vector)
How do you you calculate the field strength (or force) neutral point between two bodies in a gravitational field?
What is the definition of and the equation for absolute potential energy in a gravitational field?
The work done moving an object from infinity to that point in the field
Why is gravitational potential energy always negative?
- Gravitational potential energy is 0 at infinite distance
- And decreases inwards as you move towards object creating field
- (So must go negative)
What is gravitational potential?
The work done per unit mass moving an object from infinity to that point in a field
In this equation for gravitational potential what object is represented by mass M?
The mass of the object creating the field
Which astronaut has a greater loss in gravitational potential energy?
Neither. Potential energy (and potential) are scalar quantities so are unaffected by the path
Both decrease by 1440MJ
What is the mistake here?
In the second stage the mass of the satellite must be used
(Not the Earth’s mass again)
If a gravitational fields question uses the word ‘height’ what must you do?
Height is the distance above the surface
So you must add on the radius of the planet/star/object
Why can’t two objects have a neutral point for gravitational potential? (or GPE)
Gravitational potential from both is negative
So they combine
To increase the magnitude of the potential
In gravitational fields What does a force-separation graph look like?
And what else does the graph tell you?
The area under the curve is the change in potential energy moving between the two separations
In gravitational fields What does a field strength-separation graph look like?
And what else does the graph tell you?
The area under the curve is the change in potential moving between the two separations
In gravitational fields What does a potential-separation graph look like?
And what else does the graph tell you?
The gradient of a tangent is the field strength at that point
In gravitational fields What does a potential energy-separation graph look like?
And what else does the graph tell you?
The gradient of a tangent is the magnitude of the force at that point
What is the equation for gravitational field strength within a planet?
(r ≤ R)
This part of the graph is linear as g ∝ r
How do you derive the equation for gravitational field strength inside a planet?
- Use general equation for density (M/V)
- With V as the volume of a sphere (4/3πr3)
- Sub into general equation for field strength
How do you derive Kepler’s 3rd Law? (r3 ∝ T2)
- Equate centripetal force to force due to gravity
- Substitute in angular speed formula (from circular motion)
- Rearrange
How do you derive the formula for the velocity of a satellite orbiting a planet or star?
- Equate centripetal force to force due to gravity
- Rearrange
Which planet has the greatest orbital velocity and why?
Mercury
It is closest to Sun so smallest r
How do you derive the formula for the escape velocity of a planet or star?
In these 3 equations what does the mass refer to?
The mass of the object creating the field
Why does a satellite not need to be above the escape velocity to reach low Earth orbit?
- Escape velocity only applies to objects without engines (that can’t increase their KE)
- Satellite isn’t escaping the field (so doesn’t need as much KE)
How do you calculate the Kinetic Energy of a satellite orbiting a planet?
Substitute orbital velocity into equation for kinetic energy
How do you calculate the total energy of an orbiting satellite?
Add the kinetic and potential energy together… (v is orbital velocity) Include the negative
What is the difference between a geosynchronous and geostationary orbit?
Both have orbital periods of 24 hours (the same as the Earth)
How are geostationary and polar satellites different?
Geostationary satellites orbit above the same point of the equator and have an orbital period of 24 hours
Polar satellites orbit over the North and South pole with an orbital period of much less (around 2 hours)
What are polar satellites used for?
- Communication for high latitude regions (close to the poles)
- Espionage (spying)
- Meteorology (weather)
What are Geostationary satellites used for?
- Satellite television
- Mobile Phone Communications
- GPS
