




In these questions, where necessary, use the following: 


G=6.7×10^{11}Nm^{2}kg^{2} 


mass of earth M=6.0×10^{24}kg 


radius of earth R=6400km 



1. 

Calculate the magnitude of the earth’s gravitational field
strength at a point 1500km above the
surface of the earth. 



2. 

Calculate the gravitational potential at a point on the earth’s
surface. 



3. 

The acceleration due to gravity at the
surface of the moon is about 1.6ms^{2}. 


The diameter of the moon is about 3460km. 


Use these figures to calculate the average density of the moon. 



4. 

A spaceship is moving directly away from the earth. 


When it is just outside the earth’s atmosphere, it is moving at
5kms^{1}. 


If the rocket motors are stopped at this point, how far away
from the centre of the earth will the spaceship be when it starts
to "fall" back towards the earth? 


N.B. the height of the earth’s atmosphere is very small compared
with the radius of the earth. 



5. 

Assume the earth to be a sphere of uniformly distributed
mass. 


Let g_{1} be the gravitational field strength at a point
2000km above the earth’s surface and
let g_{2} be the gravitational field strength at a point 2000km
below the earth’s surface. 


Calculate the ratio g_{1}/g_{2}. 



6. 

A person can jump (vertically) 2.5m
on the earth. 


How high could the same person jump on a planet which has
twice the average density of the earth and three times
the radius of the earth? 



7. 

A planet has half the radius of the earth and the
acceleration due to gravity on the planet is found to be twice
the acceleration due to gravity on the earth. 


If the average density of the earth is
ρ, calculate the average density of the other planet (in
terms of ρ). 



8. 

A planet of mass m_{1}=6×10^{24}kg
has a satellite (moon) of mass m_{2}=4×10^{23}kg
orbiting at a distance r=3×10^{5}km. 


Calculate 

a) 
the value of g at 5×10^{4}km
from the centre of the planet 

b) 
the distance from the centre of the planet at which
g=zero. 