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Templates

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Calculation templates

Welcome to the Physics library, here we have calculations and content for general physics concepts all the way through to topic areas like fluid mechanics and Astrophysics!

Statics

Dynamics

Thermodynamics and Fluid Dynamics

Acoustics and Optics

Relativity and Quantum Mechanics

Astrophysics

Physics Calculations

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Orbital Mechanics Calculator

Kepler's First Law Calculator

Kepler's Third Law Calculator

Y-coordinate of Keplerian Orbit

Gravitational Force Calculator

View detailed explanations and execute astrophysics calculations.

Physics - Astrophysics

Orbital velocity and period are an integral part of space mission design that is affected by key parameters such as the apogee and perigee of the spacecraft's orbit. This orbital mechanics calculator can help you the orbital velocity and period of a spacecraft in any circular or elliptical orbit around the Earth.

Orbital Velocity (Apogee)

Orbital Velocity (Perigee)

Orbital Period

Eccentricity

Perigee and apogee are terms used in orbital mechanics to describe the closest and farthest points, respectively, between an object and the primary body it orbits. Perigee represents the point of closest proximity, while apogee denotes the farthest distance in the object's orbit.

 of the spacecraft in orbit is found using:

The orbital velocity of the spacecraft at any point in the orbit is found using:

The orbital period in hours of the spacecraft is found using:

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Orbital Mechanics Calculator - CalcTree

This calculator computes the orbital distance of planets from the Sun using Kepler's First Law of Planetary Motion. Kepler's laws are fundamental to the understanding of astronomy and physics, describing the motion of planets around the Sun. The first law, in particular, reveals that the orbits of planets are ellipses, with the Sun at one of the two foci, a significant advancement from the circular orbits proposed in earlier models.

Kepler’s First Law, often termed the Law of Ellipses, asserts that planets orbit the Sun along an elliptical path, with the Sun occupying one of the ellipse's two foci. Unlike a circle, which has a single central point, an ellipse is stretched and contains two focal points. The sum of the distances from the ellipse's edge to these two foci remains constant for any point on the ellipse.

In celestial mechanics, the elliptical orbit has two notable points:

The orbit's shape is characterized by its eccentricity (

), a measure of how much the ellipse deviates from being circular. 

This stretching means that the planet's distance from the Sun varies throughout its orbit.

Different planets have distinct eccentricities, influencing how elliptical their orbits are. See below for the 

 values for all the planets in our solar system.

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This calculator computes the orbital distance of planets from the Sun using Kepler's First Law of Planetary Motion.

This calculator computes the length of the semi-major axis of a planet's orbit around a central star using Kepler's Third Law, which provides a relationship between the orbital period and the semi-major axis. This relationship is fundamental in celestial mechanics, highlighting the harmonious patterns of planetary motion within our Solar System and beyond.

Kepler's Third Law, also known as the Law of Periods, establishes a mathematical relationship between the time it takes for a planet to complete an orbit around the Sun (its orbital period) and the size of its orbit, particularly the length of its semi-major axis. This law says that the square of the orbital period 

 of a planet is directly proportional to the cube of the semi-major axis 

Kepler's Third Law exemplifies the elegance and predictability of the cosmos, providing a mathematical framework that ties together the motion of celestial bodies across the universe. Its universal applicability underscores the fundamental role of gravity in shaping the cosmos, offering insights into the dynamics of solar systems and the intricate dance of stars and planets through space.

This calculator computes the length of the semi-major axis of a planet's orbit around a central star using Kepler's Third Law.

This calculator computes the Y coordinate of a body moving in a Keplerian orbit, using Kepler's equation. Kepler's equation is fundamental in the field of orbital mechanics, relating various geometric properties of orbits. 

Derived by Johannes Kepler in the early 17th century, Kepler's equation enables the calculation of the position of celestial bodies subject to central forces, using the 'eccentric anomaly' E. 

 of a body moving in a Keplerian orbit, is a measure of the body's position along the minor axis of its elliptical path. 

Kepler's approach to celestial mechanics revolutionized our understanding of planetary motion, emphasising the elliptical nature of orbits rather than circular. 

This calculator computes the Y coordinate of a planetary body moving in a Keplerian orbit, using Kepler's equation. 

This page provides insight into determining the gravitational force of an object and provides some functions to help you calculate it!

The gravitational force is the force that pulls two objects towards one another. The attraction between two objects depends on the mass of the objects and the distance between them.

This page provides a calculator for the gravitational force acting on an object.