Gravitational Fields Newtons Law of Gravitation The gravitational

Gravitational Fields Newton’s Law of Gravitation: The gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. G is the universal gravitational constant – its experimental value is 6. 67 x 10 -11. Its units are Nm 2 kg-2. There is a minus sign to show that it is an attractive force. This law applies for point masses (when we imagine that the mass off the object originates from one point) or spherical masses. The Earth has a radial gravitational field. The field lines get further apart as you go further from the Earth’s surface – this represents how the field is weaker the further out you go. All of the field lines meet at the centre of the Earth, showing how it behaves as a point mass to any object beyond its surface. On the scale of a building, the earth’s gravitational strength is said to be uniform. The field lines are parallel and equally spread. Think about your weight if you go upstairs – it does not get significantly less, so the gravitational field strength must be the same.

Gravitational Fields Gravitational Field Strength, g, at a point, is the gravitational force exerted per unit mass at that point. F is the gravitational force on the object and m is the mass of the object. The units are NKg-1 (equivalent to ms-2). From this, we can determine the gravitational field strength due to an isolated point mass, m: Substitute this into this… to get… The field strength obeys an inverse square law: increasing the distance by a factor of 2 means the force is ¼ of the original value.

Gravitational Fields Orbiting under Gravity: Rearranging this gives: Orbital Periods: Johannes Kepler came up with an empirical law , known as Kepler’s Third Law, which linked the time period of an orbit to its radius: After Isaac Newton formulated his law of Gravitation, it was possible to explain the relationship The square of the orbital period of a satellite in a system is proportional to the cube of the mean radius of its orbit. Equating these two equations force, we get:

Gravitational Fields T 2 Geostationary Orbits r 3 A geostationary orbit is one in which the satellite is positioned so that as it orbits, the Earth rotates a the same rate. The satellite remains above a fixed point on the Earth’s surface. A geostationary satellite orbits at around 36, 000 km above the Earth’s surface. Geostationary satellites are used for telecommunications and weather forecasting.