Gravitational Fields

• Gravitational fields are due to objects having mass, causing any two objects with mass to experience an attractive force.
• Spheres are often modeled as having all of their mass concentrated in a point mass at the center of the sphere.
• Gravitational field lines follow the direction that a test mass will experience a force at, towards the center of the planet.
• The gravitational field strength is represented by the density of the field lines, with the formula for gravitational field strength being G = -g * (mass/r^2).
• Newton's law of universal gravitation states that the gravitational force between any two objects is equal to -g * (mass/r^2), where g is the gravitational field strength and r is the distance between the two objects.
• The net force acting on an object with constant mass is equal to -g * (mass/r^2), as per the second law of motion.
• Gravitational acceleration, symbolized as 'g', is the formula for the gravitational field strength.
• Gravitational fields can be approximated as being uniform close to the surface of the earth, represented by parallel lines that always enter the surface at 90 degrees and are equidistant.
• Kepler's first law states that the orbit of a planet is an ellipse with the sun at one of the foci.
• Kepler's second law states that a line segment joining the sun and the planet will sweep out equal areas in equal times.
• The centripetal force is equal to mv squared divided by r.
• t 1 squared over r 1 cubed can be particularly useful for problems in which the quantities are proportional.
• Whenever an object is moving in a circle, the speed v will be equal to the circumference of the circle which is 2 pi r divided by the period of rotation.
• The gravitational force is acting towards the center of rotation of the planet, meaning that the centripetal force is equal to the gravitational force.
• The height of a geostationary orbit can be calculated using Kepler's third law.
• The height of a geostationary satellite above the surface of the earth can be calculated using Kepler's third law.
• d is equal to some constant k multiplied by r cubed.
• The speed v squared is equal to 4 pi squared r squared divided by t squared.
• The radius of the earth is 6,400 kilometers and the mass of the earth is approximately 6.0 times 10 to the power of 24 kilograms.
• The magnitude of the gravitational force is equal to g m m divided by r squared.
• Kepler's third law states that t squared is equal to 4 pi squared divided by gm multiplied by d by r cubed.
• Geostationary orbits have an orbital period of 24 hours and are an equatorial orbit just above the equator, remaining fixed in the sky to an observer on earth or to a satellite dish pointing at a specific location in the sky.
• t squared divided by r cubed will be equal to some constant k.
• Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of its orbital distance, represented by the equation T^2 ∝ R^3.
• Both gravitational potential energy and gravitational potential are negative and increase with distance.
• For the Earth, the mass of the Earth is 6.0 times 10^24 kilograms and the radius of the Earth is 6400 kilometers, so the escape velocity is the square root of 2 times gravitational fields constant divided by the mass of the Earth, represented by the equation v = sqrt(2) gm/r.
• Gravitational potential is the work required to bring a unit mass from infinity to the point.
• The distance from the center of the Earth to the surface is the radius of the Earth, which is 6400 kilometers.
• The distance from a geostationary satellite to the center of the Earth is approximately 4.23 times 10^7 meters.
• The formula for kinetic energy is ½ mv^2.
• Escape velocity is the square root of 2 times gravitational fields constant divided by the mass of the object, represented by the equation v = sqrt(2) gm/r.
• Gravitational potential is the energy per unit mass, and is equal to the energy per unit mass.
• Gravitational force is given by Newton's law of universal gravitation, represented by the equation f = -gmm/r^2.
• Gravitational potential energy is expressed as -gm/r, where r is the distance from the center of the Earth.
• Escape velocity is the velocity that if reached, an object will leave the gravitational field.
• The formula for gravitational potential energy is uh gm m/r^2.
• Escape velocity is found by setting gravitational potential energy equal to the kinetic energy, represented by the equation gpe = ke.
• The height of a geostationary orbit is 3.6 times 10^7 meters.