If mass distorts the curvature of space time which produces gravity and since it is a attractive force,it must attract smaller masses to the larger ones but instead the smaller mass assumes a stable round the larger mass.

What force is responsible for the orbit, Explain in detail along with mathematical expressions.

1 answer

The force responsible for the orbit of a smaller mass around a larger one is the gravitational force. According to Newton's law of universal gravitation, the gravitational force between two masses is given by:

F = G * (m1 * m2) / r^2

where F is the gravitational force between the two masses, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.

In the case of a smaller mass orbiting a larger one, such as a planet orbiting a star, the gravitational force provides the centripetal force necessary for the circular motion.

The centripetal force required for circular motion can be calculated using the formula:

F = (m * v^2) / r

where F is the centripetal force, m is the mass of the smaller object, v is its orbital velocity, and r is the radius of its orbit.

For a circular orbit, the gravitational force acts as the centripetal force, so we can equate the two expressions:

F = G * (m1 * m2) / r^2 = (m * v^2) / r

Rearranging the equation, we can solve for the orbital velocity v:

v^2 = (G * (m1 * m2)) / r

Taking the square root, we find the expression for the orbital velocity:

v = sqrt((G * (m1 * m2)) / r)

This equation explains the relationship between the masses of the two objects, the radius of the orbit, and the orbital velocity required for a stable circular orbit. It demonstrates that the gravitational force acting between the two masses provides the necessary centripetal force to keep the smaller object in a stable orbit around the larger object.

For elliptical or non-circular orbits, the equation would be slightly different. Instead of using the radius of the orbit, the distance between the centers of the two objects at a given point in the orbit should be used. The concept remains the same though, with the gravitational force providing the necessary centripetal force for the orbital motion.