Equate the two forces (since centripetal force is supplied by gravity) and see what you get. (Note: r = d = distance between centres of mass).eku_girl83 said:Two gravitaionally bound stars with equal masses m, separated by a distance d, revolve about their cneter of mass in circular orbites. Show that the period is proportional to d^3/2 and find the proportionality constant.
I know that in this case, F = mv^2/r and that F=Gm^2/d^2.
But where do I go from here??
Thanks for any help!
Kepler's Third Law, also known as the Harmonic Law, states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. In simpler terms, it describes the relationship between a planet's distance from the sun and its orbital period.
Kepler's Third Law is derived from the application of Newton's Law of Universal Gravitation and the laws of motion. By equating the centripetal force of a planet's orbit to the gravitational force between the planet and the sun, the relationship between the orbital period and semi-major axis can be mathematically derived.
Kepler's Third Law is important because it allows us to calculate the orbital periods of planets based on their distance from the sun. This law also played a crucial role in the development of the laws of planetary motion and our understanding of the solar system.
Yes, Kepler's Third Law can be applied to any two objects that orbit around a central point, such as moons orbiting planets or satellites orbiting Earth. However, it is most commonly used for planets orbiting the sun.
There are some exceptions to Kepler's Third Law, such as in the case of binary star systems where two stars orbit around each other. In these cases, the masses of the two objects must be taken into account in the calculations, and the law may not hold true in its original form.