9.2 Space – Physics Module 1 1. The Earth has a gravitational field that exerts a force on objects both on it and around it

* Define weight as the force on an object due to gravitational field * Any object with mass has its own gravitational field. * Any two objects in the universe exert a force on each other. * This force is always attracting and depends on the masses of the objects and the separation distance of the objects.

F = G.M1.M2 d2
F=Force
G=Universal Gravitational Constant (6.67x10-11)
M1= Mass 1
M2= Mass 2 d= separation distance of the objects

* Weight is the force on an object due to the gravitational field. It is a vector quantity and the measurement unit is the Newtons (N) * Mass is the amount of matter in a body, whereas Weight is the force due to gravity acting on a mass. * Mass will not change where the acceleration due to gravity is different, but the weight will change.
F = mg
F = Force m = mass, g = acceleration due to gravity.
This formula is derived from Newton’s Second Law of Motion, F=ma

* Explain that a change in gravitational potential energy is related to work done * Gravitational Potential Energy (Ep) is the energy that is stored in a body of mass due to its position within a gravitational field. * Gravitation is a force of attraction. * If an object moved from a point in the Earth’s gravitational field to a point further away from the centre of the earth, work must be done on this object.
The object moves against the field, hence gaining (Ep) * If an object is moves closer to the centre of the Earth, some of its (Ep) is changed into Kinetic Energy; therefore work is done by the object rather than on the object.
The work done (W) on an object when a force causes it to move is given by:
W=F x s
F=force acting on the object
S=distance the object moves

* When an object is raised to a height (h) above the ground, then its gravitational potential energy becomes
Ep = W=F x s
F=mg (as the force needed must be at least equal to the weight force of the object) s=h (height is the distance moved)

THEREFORE: Ep=mgh
Where: Ep = Gravitational potential energy, measured in J
M= mass of object, measured in kg g= Gravitational acceleration measure in ms-2 h= height above the ground, measured in m

* Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field
Ep = -G m1m2 r * Gravitational Potential Energy (Ep) is the energy that is stored in a body of mass due to its position within a gravitational field.

* The gravitational potential energy of an object at some point within a gravitational field is equivalent to the work done in moving the object from an infinite distance to that point.

* When lifting an object against a gravitational field, e.g. launching a rocket, work is done on the object, that is, energy is transferred to the object.

* The object’s gravitational potential energy, Ep, increases as a result.

* When an object moves toward the source of the gravitational field, such as when dropping a stone, energy due to position in a field is transformed into kinetic energy (the stone speeds up).

* Hence the position of lowest Ep in the gravitational field surrounding a planet is at the surface of the planet.

* An object only has zero Ep when it is no longer within the gravitational field, that is, a very large distance away. (Mathematically, distance must be infinite.)

* It leads to the following expression for the gravitational potential energy of a mass m1 at a distance r from a mass m2 in the gravitational field due to m2:

* Gravitational potential energy is the work required to bring an object from infinity to that point. Since gravity does work on the object the potential energy is negative.

Ep = -G m1m2 r
Where: Ep =