Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape velocity with the...

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. In 1909, he formulated his first two laws based on the observations of his forebears, Nikolaus Copernicus and Tycho Brahe. However, in 1918, he published his third law of planetary motion, which gives a precise mathematical relationship between a planet's average distance from the Sun and the amount of time it takes to revolve around the Sun. It...

Vector calculus provides mathematical tools for analyzing physical fields that vary throughout space. One important application is the study of gravitational interactions between celestial bodies. Consider the Earth positioned at the origin and a satellite located at a point in three-dimensional space. The Earth exerts a gravitational force on the satellite, and this force can be described by components acting along the coordinate directions. Together, these components form a vector field that...

Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s.
Their closest cousins are neutron stars, which are composed almost entirely of neutrons packed against each other, making them extremely dense. A neutron star has the same mass as the Sun but its diameter is only a few kilometers. Therefore, the escape velocity from their surface is close to the speed of light.
Not until the 1960s, when the first neutron...

Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...

Since all objects on the Earth's surface move through a circle every 24 hours, there must be a net centripetal force on each object, directed towards the center of that circle. The points of the north and south poles are the only exception to this rule.
For an object on the Earth's equator, the net centripetal force that accounts for its rotation is the Earth's pull towards its center, or the weight minus the normal force that prevents it from piercing into the Earth's surface. This force,...