Gravitational Fields

Gravitational Fields Basics

  • Gravitational fields define the space around a mass where another mass would experience a force.

  • The gravitational field strength (g) is the force experienced by a unit mass due to a gravitational field. Its SI unit is N/kg.

  • Gravity is a type of non-contact or field force that acts between masses.

  • Isaac Newton’s law of gravitation states that any two masses attract each other with a force that is directly proportional to their product and inversely proportional to the square of their separation, which in equation form, is represented by F = G (m1 * m2) / r^2. Here, F is the force between the masses, G is the gravitational constant, m1 and m2 are the two masses and r is the distance between the centres of the two masses.

  • The gravitational potential (V) at a point in a gravitational field is the work done per unit mass in bringing a small test mass from infinity to that point.

  • The gravitational potential energy of an object at a point in the gravitational field is the work done in bringing it from infinity to that point.

Gravitational Fields and Field Lines

  • Gravitational field lines are the paths that a small mass would take if it was free to move in the field.

  • The shape of a gravitational field can be visualised with the help of these lines.

  • Field lines around a single mass are radial and point inwards.

  • The strength of the field is represented by the density of these field lines.

Gravitational Fields and Kepler’s Laws

  • Kepler’s first law (The Law of Ellipses) states that each planet moves in an elliptical orbit with the Sun at one of the foci.

  • Kepler’s second law (Area Law) states that the line from the sun to any planet sweeps out equal areas in equal time intervals, implying planets move faster when they are closer to the sun.

  • Kepler’s third law (Harmonic Law) is represented by the equation T^2 = k r^3, where T is the orbital period, r is the average distance from the Sun, and k is a constant of proportionality. This law implies that the square of the period of orbit is proportional to the cube of the radius.

  • These laws provide a detailed understanding of planetary motion and reinforce the concept of Gravitational fields.

Escape Velocity

  • Escape velocity is the minimum velocity an object must have in order to escape the gravitational field of a planet or other body.

  • The escape velocity from the Earth’s surface is approximately 11.2 km/s.

  • The formula to calculate escape velocity is given by Ve = √(2Gm/r), where G is the gravitational constant, m is the mass of the body being escaped, and r is the distance from the centre of the body.

Satellites

  • A satellite is an object in space that orbits or revolves around another object.

  • Geostationary satellites follow an equatorial orbit and rotate with the same period as Earth, making them appear to be stationary when viewed from Earth.

  • Polar satellites have orbits that pass above or near the Earth’s poles.