Information about F = G Mm

F = GMm/r 2

g = F/m = GM/r 2

Mass of Earth = 6x10 24 kg

Radius of Earth = 6.4 x10 6 m

Calculate g on Earth

g = GM/r 2

= 6.67x10 -11 x 6x10 24 / (6.4 x 10 6 ) 2

= 9.8 Nkg -1

g is a vector g from planet g from star Total g = Vector sum Star planet

Gravitational PE These magnets have no energy when they are separated You do work when you push them together When they are close together potential energy is stored Let them go and the energy is released PE N S S N F F

These magnets have no energy when they are separated

You do work when you push them together

When they are close together potential energy is stored

Let them go and the energy is released

Gravitational PE The magnets have zero energy when they are apart. They slide together and have less energy (negative) A force must do work to pull them back to zero When objects attract each other they have negative potential energy - PE S N S N F F

The magnets have zero energy when they are apart.

They slide together and have less energy (negative)

A force must do work to pull them back to zero

When objects attract each other they have negative potential energy

Gravitational Potential Gravitational potential is always negative The potential at a point is the amount of energy needed to move 1 kg from infinity to that point V = -GM/r planet A distant object has zero PE Attracted by gravity Negative PE Back to zero energy Amount of work needed to remove object Zero energy

Gravitational potential is always negative

The potential at a point is the amount of energy needed to move 1 kg from infinity to that point

V = -GM/r

Gravitational Potential Energy planet 1 kg Attracted by gravity Negative PE Back to zero energy 2kg The potential at a point is the energy needed to move 1 kg from infinity to that point The potential energy of an object is the energy needed to move the object from infinity to that point PE = mV = -GMm/r V = -GMm/r Amount of work needed to remove 1kg Zero energy Amount of work needed to remove 2 kg

Escape velocity How fast must an object go so that it doesn’t come back? It must have enough KE to overcome the negative PE (-GMm/r) and get to zero energy 1/2mv 2 = GMm/r V 2 = 2GM/r V = (2GM/r) Calculate the escape velocity of Earth r= 6.4 x10 6 m m =6 x 10 24 kg v = (2GM/r) = (2 x 6.67 x 10 -11 x 6 x10 24 / 6.4 x10 6 ) = 11 000 ms -1 = 11kms -1 planet

How fast must an object go so that it doesn’t come back?

It must have enough KE to overcome the negative PE (-GMm/r) and get to zero energy

1/2mv 2 = GMm/r

V 2 = 2GM/r

V = (2GM/r)

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