Gravitational Fields Flashcards

1
Q

What does Newton’s law of gravitation state ?

A

Any object with a mass will attract another mass with a force inversely proportional to the square of the distance between them and directly proportional to the product of the two masses

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2
Q

What would happens to the force when the distance between the masses doubles ?

A

The force would decrease by a factor of 4

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3
Q

What is the equation produced of the attractive force as a result of the masses ?

A

F=GMm/ r^2

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4
Q

What is the gravitational constant ?

A

6.67*10^-11

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5
Q

What is the units of the gravitational constant ?

A

Nm^2kg^-2

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6
Q

How do you work out the gravitational field strength ?

A

GM/r^2 = g or f/m

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7
Q

When you substitute g into the equation for the force of attraction produced by the masses what does it tell us about g ?

A

G is the acceleration (F=ma=mg)

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8
Q

How can you define gravitational field strength?

A

The gravitational force exerted per unit mass on a point within the field.

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9
Q

What direction would the gravitational field strength lines be drawn ?

A

In the same direction as the gravitational force (towards the centre of the mass

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10
Q

What do gravitational field lines represent?

A

The direction of force experienced by a mass placed in a field.

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11
Q

What is a radial field ?

A

A field that exists between point masses and around uniform spheres

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12
Q

Why does the field lines considered to be uniform on earth ?

A

Towards the surface they appear to be parallel to each other

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13
Q

What are uniform field ?

A

A field where the value of the field strength is the same at all points . The field lines will be equally spaced and parallel to each other.

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14
Q

What is gravitational potential energy ?

A

Gpe is what is stored when work is done against the gravitational field to move an object in the opposite direction

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15
Q

What is the gravitational potential energy in a uniform field ?

A

Ep = mgh - for small distances

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16
Q

What is the gravitational potential energy in a non- uniform field ?

A

We take the Ep at r = ♾️ as 0 so have negative values for Ep.

Ep= - GMm/ r (sub GM/r^2 as g in mgh )

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17
Q

What stays consistent with both uniform and non-uniform fields ?

A

The Ep increases along with the height.

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18
Q

What is gravitational potential ?

A

The gravitational potential energy given to a unit mass in moving a point from infinity to a point within the field

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19
Q

How can you work out the gravitational potential?

A

-GM/r as it remains the same for any object at a distance r

Or Ep/m

20
Q

What is the gravitational potential of a point within a gravitational field equal to ?

A

The work done per kilogram of mass in bringing the mass from infinity to the point

21
Q

What is the gravitational potential at infinity ?

22
Q

What quantity is gravitational potential?

23
Q

What is constant when a mass moves along the equipotential line ?

A

The gravitational potential energy as well as the gravitational potential as no work is done when something moves at right angles to the field

24
Q

What angles are equipotential surfaces to the gravitational field?

A

Right angles

25
What happens to v when r increases when plotting v against r ?
V decreases to produces a ln graph starting from the radius of the object
26
What does the gradient of a v against r graph give ?
-g ( gravitational field strength) As change in v / change in r means u divide v by r giving you the field strength.
27
How can you work out g at a certain distance by using a v against r graph ?
By drawing a tangent at that distance and calculating its gradient *-1
28
What does the area under a g against r graph give ?
The gravitational potential as g*r gives us v
29
At small distances where the field is uniform , what is the Ep of the surface ?
0 Ep
30
At large distances where the field is non uniform why are the values negative/ decrease closer to the surface ?
Ep is 0 when r( distance ) is at infinity
31
What is gravitational potential difference ?
The work done in moving a unit mass between two points between v1-v2
32
What equation links the orbital speed to the radius?
As we move in circular motion the centripetal force is provided by the gravitational force By equating the centripetal force and the gravitational force and rearrange for v you get V = root ( GM/ r )
33
What is the orbital period ?
The time taken for m to complete one orbit around M is T
34
If the distance r increases by a factor a what happens to the orbital speed ?
Decreases by root a
35
What is the equation for the kinetic energy of an orbiting satellite?
mv^2 / 2 substituting root ( GM/ r ) as v GMm/ 2r
36
What is the equation for the time period of an orbiting object ?
Using the orbital speed (2pir / t )equation substitute the velocity as root Gm/r and rearrange making t^2 the subject T^2 = 4pi^2 r^3 / Gm
37
What is the equation for orbital speed ?
Distance over time - 2pir / t
38
What is escape velocity?
The minimum velocity to escape a gravitational field of another object
39
Equation for escape velocity ?
For a rocket with mass mr Total energy at launch = Ek +Ep (0.5mr v^2 ) + (- GM mr / r ) To escape the field it must have zero velocity So at infinity - the Ek and Ep are both 0 Therefore the sum of the Ep and Ek at the start must be 0 so 0.5mr*v^2 = GMm/ r Vr = root ( 2GM/ r )
40
What is synchronic orbits ?
When the orbital period of a satellite it equal to the rotational period of the object that is orbiting
41
What are the two types of satellites?
Geo stationary and low orbit satellites
42
What are geostationary satellites?
They follow a geosynchronous orbit : They have the orbital period of 24 hours orbiting directly above the equator at a certain height staying above the same position on earth
43
What is a low orbit satellite?
They have lower orbits than geostationary satellites so travel much faster meaning the orbital period is much smaller. This requires less powerful transmitters and can potentially orbit across the entire earths surface
44
How can you work out the height of a geostationary object ?
Rearranging the time period equation to get r
45
Uses of geostationary satellites?
- sending to and telephone signals As they are always above that particular place - weather forecast for a particular area as it above the same point
46
Uses of low orbit satellites?
- military applications - scientific study’s on unreachable areas - communications