1.1. To investigate the value of To investigate the value of gg on other on other planets in our solar system & to practice our planets in our solar system & to practice our graph drawing and other practical skillsgraph drawing and other practical skills

2.2. To recreate some of Newton’s work on To recreate some of Newton’s work on gravitation & to establish Newton’s law of gravitation & to establish Newton’s law of gravitationgravitation

3.3. To use Newton’s law to establish the To use Newton’s law to establish the gravitational force of attraction between two gravitational force of attraction between two objectsobjects

Book Reference : Pages 59-61Book Reference : Pages 59-61

Using the supplied planetary data complete the following:Using the supplied planetary data complete the following:

1.1.For each planet complete the table by calculating the value of For each planet complete the table by calculating the value of m/rm/r22

2.2.Next plot a good quality line graph for g against m/rNext plot a good quality line graph for g against m/r22

3.3.Find the Gradient of your graphFind the Gradient of your graph

Mass/kg Radius/m g N/kg m/r2

Mercury 3.18E+23 2.43E+06 3.59 5.39E+10

Venus 4.88E+24 6.06E+06 8.87 1.33E+11

Earth 5.98E+24 6.38E+06 9.81 1.47E+11

Mars 6.42E+23 3.37E+06 3.77 5.65E+10

Jupiter 1.90E+27 6.99E+07 25.95 3.89E+11

Saturn 5.68E+26 5.85E+07 11.08 1.66E+11

Uranus 8.68E+25 2.33E+07 11.08 1.60E+11

Neptune 1.03E+26 2.21E+07 14.07 2.11E+11

You should have a straight line graph. What does You should have a straight line graph. What does this tell us aboutthis tell us about

The relationship between g and the mass of The relationship between g and the mass of the planet?the planet?

The relationship between g and the radius of The relationship between g and the radius of the planet?the planet?

We introduce a constant of proportionalityWe introduce a constant of proportionality

F = GmF = Gm11mm22

rr22

Where Where FF is the gravitational force between is the gravitational force between the two objects, the two objects, mm11 & & mm22 are the masses of are the masses of the two objects & the two objects & rr is the separation is the separation between the centres of the masses (think between the centres of the masses (think point masses)point masses)

G is the universal constant of gravitation, G is the universal constant of gravitation, has a value of 6.67 x 10has a value of 6.67 x 10-11-11 Nm Nm22kgkg-2-2

Mass m1 Mass m2

Distance r

Force F Force F

The distance from the centre of the sun to the The distance from the centre of the sun to the centre of the Earth is 1.5x10centre of the Earth is 1.5x101111m & the masses of m & the masses of the Earth & sun respectively are 6.0x10the Earth & sun respectively are 6.0x102424kg & kg & 2.0x102.0x103030kgkg

a)a) The diameters of the Sun & Earth The diameters of the Sun & Earth respectively are 1.4x10respectively are 1.4x1099m & 1.3x10m & 1.3x1077m why m why is it reasonable to consider them both to be is it reasonable to consider them both to be point masses?point masses?

b)b) Calculate the force of gravitational Calculate the force of gravitational attraction between the Earth & the Sunattraction between the Earth & the Sun

The diameters of both are small compared to the The diameters of both are small compared to the separation. Distance between any part of the sun separation. Distance between any part of the sun and Earth is the same within 1%and Earth is the same within 1%

F = GmF = Gm11mm22 /r /r22

F = 6.67x10F = 6.67x10-11-11 x 6.0x10 x 6.0x102424 x 2.0x10 x 2.0x103030 /(1.5x10 /(1.5x101111))22

F = 3.6x10F = 3.6x102222N N

Take care with separation between the two Take care with separation between the two masses... (r).... Consider distances between the masses... (r).... Consider distances between the centres and surfaces.centres and surfaces.

r is the distance between their centresr is the distance between their centres