A-Level Notes > Bishop Vesey's Grammar School A-Level Notes > AQA PHYA4 - Fields and Further Mechanics Notes

Topic 2 Gravitation Notes

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Topic 2 Gravitation Revision

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Topic 2: Gravitation 1

Newton's law of gravitation a Newton's law of gravitation states that the gravitational force of attraction between two point masses is proportional to the product of the masses and inversely proportional to the square of the distance between the centre of the masses:

F=

Gm1 m2 r

2

where

G ,the gravitational constant =6.67 ¿ 10−12 N m2 kg−2 i In a radial field, ii In a uniform field, 2

F=

Gm1 m2 r2

F=mg

Gravitational field strength and potential a Gravitational field strength (vector) at a point in the gravitational field is the force per unit mass on a test mass:

g=

F m

i In a radial field, ii In a uniform field, b

GM r2

g=

V r

Gravitational potential (scalar) at a point in a gravitational field is the work done per unit mass on a test mass when it is moved from infinity to that point whereas gravitational potential difference is the work done per unit mass on a test mass when it is moved from one point to another point i In a radial field, ii In a uniform field,

c

g=

V=

−GM r

V =−gh

Gravitational potential energy: Gravitational potential energy is the work done in moving an object against the gravitational force of attraction from a reference point to its current location:

E p=m∆ V

i On the Earth, the reference point is the surface of the Earth where 1

E p=mgh This is only valid for short distances away from the Earth as g is not constant over large distances

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