1. Gravity field and steady-state Ocean Circulation Explorer
GOCE was equipped with three pairs of ultra-sensitive accelerometers arranged in three dimensions that responded to tiny variations in the 'gravitational tug' of Earth along its orbital path. Because of their different positions in the gravitational field they all experienced gravitational acceleration slightly differently. The three axes of the gradiometer allowed the simultaneous measurement of six independent, but complementary, components of the gravity field.
In order to measure gravity, there can be no interference from moving parts so the entire satellite was actually one extremely sensitive measuring device.

2. Gravitational Field Strength Maps
Gravity does not exert an equal force everywhere on Earth. Factors such as the rotation of the planet, the effects of mountains and density variations in Earth’s interior mean that this fundamental force is not quite the same all over.
Although invisible, gravity is a complex force of nature that has an immeasurable impact on our everyday lives. It is often assumed that the force of gravity on the surface of Earth has a constant value, but in fact the value of 'g' varies subtly from place to place.
These variations are due to a number of factors such as the rotation of Earth, the position of mountains and ocean trenches and variations in density of Earth's interior.

4. Geoid Map
ESA's GOCE mission has delivered the most accurate model of the 'geoid' ever produced. Red corresponds to points with higher gravity, and blue to points with lower gravity

5. Inverse Square Law

6. Newton’s Law of Universal Gravitation

7. von Jolly Experiment
Confirmed the Cavendish Experiment using a highly sensitive set-up

8. Newton’s Law of Universal Gravitation

10. Newton’s Law of Universal Gravitation

11. Newton’s Law of Universal Gravitation
Ex 2. Find an expression in terms of g for the gravitational field strength on a planet that has twice the mass of Earth and three times the radius. Then calculate the gravitational field strength, g’, on that planet.

12. Newton’s Law of Universal Gravitation
Ex. 3. Find g on Jupiter: mass = 1.90 x 1027 kg (318me) and
radius = 7.15 x 104 km (11.2re).
Mass Jupiter =318*mass earth
Radius of Jupiter= 11.2 earth radii

13. Newton’s Cannon & Escape Velocity
Defined a little more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity with a residual velocity of zero, with all speeds and velocities measured with respect to the field.