3. The solar system is held together by

gravity

Shortcut to Gravitation - Encarta 99 Encyclopedia.LNK

Describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it

Present information and use available evidence to discuss the factors

affecting the strength of the gravitational force

A gravitational field is a field within which any mass will experience a gravitational force.

The gravitational field around a planet has a radial pattern similar to the electric field around a negative point charge. The field lines are in the direction towards the centre of the planet and the closer field lines represent the stronger gravitational field. The presence of another mass (such as a moon) effects the field lines in a way which is similar to the presence of another negative charge. (see Jacaranda p.5 for a diagram)

The strength of the gravitational forcedepends on the mass of the central object,the mass of the object experiencing theforce, and on the distance between thetwo objects. A larger mass of either objectincreases the gravitational force and increasing the distance decreases the gravitational force.

A gravitational field is a field surrounding a massive object, within which any other mass will experience a gravitational force. This force is a force of attraction - the greater the mass, the greater the gravitational attracting force.

The gravitational field around a planet has a radial pattern similar to the electric field around a negative point charge. The field lines are in the direction towards the centre of the planet and the closer field lines represent the stronger gravitational field. The presence of another mass (such as a moon) effects the field lines in a way which is similar to the presence of another negative charge. (see Jacaranda p.5 for a diagram)

The strength of the gravitational force depends on the mass of the central object, the mass of the object experiencing the force, and on the distance between the two objects. A larger mass of either object increases the gravitational force and increasing the distance decreases the gravitational force.

Describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it

Use available evidence to discuss the factors affecting the strength of the gravitational force

Define Newton's Law of Universal Gravitation

221

d

mmGF

( the law)

(NOT the law)

Solve problems and analyse information using 2

21

d

mmGF

Jacaranda Chapter 4

221

d

mmGF

Solve problems and analyse information using 2

21

d

mmGF

Try Jacaranda p.57 onwards

Define Newton's Law of Universal Gravitation

where F = gravitational force between two objectsG = universal gravitational constant = 6.67 x 10-11

m1= mass of object 1m2= mass of object 2d = distance between the two centres of mass

Discuss the importance ofNewton‘s Law of Universal

Gravitation in understandingand calculating the motion

of satellites

r

vmrmGm SSE

2

2 r

mvmg

2

2vrGmE

vrGmE

remember r = rE+ altitude

So high altitude (e.g. geostationary) orbits are lower velocity

and low altitude (e.g. low Earth) orbits are higher velocity

Newton’s Law of Universal gravitation allows us to calculate the gravitational force experienced by a satellite at any altitude. We understand that this gravitational force is the centripetal force that keeps the satellite in its orbital motion. We can

equate the two expressions for force to calculate the orbital velocity of the satellite. We therefore know all quantities (e.g. angular velocity, period

etc.) that relate to the uniform circular motion of the satellite.

r

vmrmGm SSE

2

2 r

mvmg

2

2vrGmE

vrGmE

remember r = rE+ altitude

So high altitude (e.g. geostationary) orbits are lower velocity

and low altitude (e.g. low Earth) orbits are higher velocity

Discuss the importance ofNewton‘s Law of UniversalGravitation in understandingand calculating the motionof satellites

Identify that a slingshot effect can be provided by planets for space probes

Planetary swing-by to pick up speed by gaining K.E. from the planet (which consequently loses a bit of speed)

Interaction behaves as an elastic collision

Vi vi

Conservation of momentum and conservation of kinetic energy gives

vf = vi + 2ViVf

N.B. this is the maximum result and will be less if not head-on interaction 10 1 satellite approaches planet at

relative velocity of 11 so it will bounce off at 11 relative to planet

2111 relative to the planet is 21 relative to the sun

The slingshot effect is a planetary swing-by to pick up speed by gaining K.E. from the planet (which consequently loses a bit of speed)

The interaction behaves as an elastic collision

Vi vi

Conservation of momentum and conservation of kinetic energy gives

vf = vi + 2ViVf

N.B. this is the maximum result and will be less if it is not a head-on interaction 10 1

E.g. The satellite (moving at 1 relative to the sun) approaches the planet at a relative velocity of 11 so it will bounce off at a velocity of 11 relative to planet

21

11 relative to the planet is 21 relative to the sun!

Identify that a slingshot effect can be provided by planets for space probes