gravitational fields

Equation for gravitational force (g)

-GM/r²

Gravitational field strength (F)/m

Equation for gravitational field strength (F)

-GMm/r²

gm

How to calculate the distance of an object when the resultant forces=0

1. GMm/x²=GMm/x²

2. Remove all constants, flip equations round and cross multiply

3. Square root EVERYTHING

4. Put x on one side and factorise to get x

Equation of centripetal force

Mv²/r

If an object moves closer to its orbiting object, what happens to the time and speed

V is directly proportional to 1/r

T² is directly proportional to r³

What is keplers 3rd law time constant

T²=4pi²/GM x r³

Equation for orbital speed

V²=GM/r

Where the mass is whatever the object is orbiting around

Mass is equal to

Density x volume

Volume of a sphere=4/3 pi r³

Is the angular speed for a geostationary and synchronous orbit the same or different?

The same with the time period of how many minutes in a day

How to calculate the height from a surface

1. Calculate radius or in from keplers 3rd law equation

2. Radius of orbit - surfaces radius

Equations for gravitaional potential (V)

-GM/r

Change in Ep/m

Change in Wd/m

equation of Ep

M x change in gravitational potential

Equation of Wd or change in Wd

F x dist

Gravitational field strength x radius

M x change in gravitational potential

GMm (1/r1 - 1/r2)

Where m is the mass of object and M is mass of what it’s orbiting around

When an object moves from equipotential circles, what happens

Nothing happens as there is no Wd

When an object moves from field line to field line in the same equipotential circle,what happens

Work is done

Derive Etotal= ½ mv² +mV

1/2m(GM/r) +m(-GM/r)

Simplify

Etotal =-GMm/2r

If Wd=Ep, how do you find the gravitational field strength from this

F x change in r =change in gravitational potential x m

F/m = change in V/change in r

g=- change in V/change in r

Change in Ek is equal to

Change in Et is equal to

½ x change in Ep

-change in Ek or change in Ep/2

Equation for escape velocity

Square root 2GM/r

Square root 2V

Square root Wd gravitational force x r

Ceptripetal force is equal to

Gravitational force

How to calculate the Ek

Mv²/r = GMm/r²

Mv² v GMm/r

Times by ½ = GMm/2r

what direction does the gravitational field go at point X

Right angle/ perpendicular to the equipotential and towards increasing -ve potential

Draw out the Etotal graph = Ek + Ep

How to calculate percentage uncertainty from multiple readings

Calculate mean

Calculate change in mean = ½ range

Change in mean/ mean x 100