1. The Earth’s gravitational field

* Define weight as the force on an object due to a gravitational field
Weight is the force that is applied to an object due to its gravitational field. It is a vector quantity and measured in Newtons. * Explain that a change in gravitational potential energy is related to work done
The gravitational potential energy at a height is equal to the work done in raising it to that height.
Consider:
W = F x d
Therefore, W = Fg x d (where Fg is the weight of the object)
Fg = mg (as weight of the object = mass x acceleration due to gravity)
Therefore, W = mg x d
Therefore, W = m x g x h (h is the distance the object has been moved)

* 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

The GPE of an object of an object anywhere in a gravitational field is equivalent to the work done in moving the object from an infinite distance to that point. It can be shown mathematically using this following equation: .

This graph represents the potential energy of a planet.
This graph represents the potential energy of a planet.

When you lift an object against a gravitational field then work is being done on the object which is then transferred to energy and the objects GPE is also increased. When an object moves towards the source of the gravitational field like the centre of the Earth then energy is transferred into kinetic energy. The only way for something to have zero GPE then that object needs to be at an infinite distance away.

2. A successful rocket launch * Describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and vertical components
The trajectory of an object undergoing projectile motion will follow a parabolic path. The horizontal component will always be constant whilst the vertical component is changing all the time due to the effect of gravity.

* Describe Galileo’s analysis of projectile motion
Galileo found that all object of any mass fall at the same rate. This means the acceleration due to gravity is the same for all objects. This only works if air resistance can be ignored.
“Experiments based on dropping different objects proved inconclusive so Galileo developed a method of rolling balls down highly polished ramps in order to make his comparisons. This enabled him to slow down the motion enough to make more accurate observations of the motion.”

* Explain the terms of escape velocity in the terms of:
-Gravitational constant
-Mass and radius of planet
Escape velocity is the velocity required in order for something to escape an objects gravitational field. So during this rise the objects kinetic energy is transferred into gravitational potential energy. Escape velocity depends on the universal gravitaional constant, the mass and radius of a planet. For an object to escape Earths gravitational pull, speeds need to be approximately 40000kmh. It is impossible for humans to perform a launch like this because the G forces produced would easily kill any life form. And also the heat generated in our atmosphere would vaporise the projectile.

* Outline Newtons concept of escape velocity
Newton’s concept of escape velocity consisted of a hypothetical scenario where if a person climbed a very tall mountain and launched a projectile horizontally from its peak then the projectile will follow a parabolic path before it hits the ground. But if this projectile was launched fast enough then it wouldn’t touch the ground, it would travel right around the earth because as it is falling the earth is curving away. The projectile would then be in Earth’s orbit and be at a fixed height. If the projectile is launched even faster than it would travel in an elliptical orbit or even escape Earth’s gravitational field. This speed is also known as escape velocity.

* Identify why the term ‘g