Answer Happy

O Earth's orbit around the Sun Figure 3. Graphical representation of Earth orbiting the Sun due to the force of gravity. Newton's law of gravity describes the gravitational force between two bodies. If a mass M is positioned at the origin, and a mass m is at a position vector r = (xi + y + zk) which is a distance r - Ir away. then the gravitational force between them is defined by MMG F P r2 where is a unit vector in the direction of r, G is the gravitational constant, and the force acts towards mass M at the origin a) [5 marks] Define the ij,k components of this force as a function of x,y and z. b) [13 marks) Find the curl of the force field F. Hence, deduce what the state of Earth's movement must have been at its creation knowing it now spins around its geographical axis. C) [7 marks] With the help of some mathematical derivation(s), briefly discuss why your findings for the curl imply the existence of a gravitational potential function such that F = V. Use this to explain in your own words why the gravitational vector field is conservative. d) [15 marks) Find the gravitational potential function . Hence, find the work done by the gravitational field when the Earth moves from point A on its elliptical orbit the furthest away from the Sun (1.52 X 10 km away) to a point B closest to the Sun (1.47 x 10 km away). Use the values for the mass of the Earth m= 5.97 X 1024 kg, the mass of the Sun M = 1.99 % 1030 kg and G 6.67 X 10-11 Nm/kg? (Figure 3)