Gravitation & Orbital Motion Calculators
Understand gravitational interactions, energy, and orbital behavior.
Gravitational Force Calculator
Calculate the gravitational force between two objects based on their masses and the distance between them.
Newton’s Law of Universal Gravitation
Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Where:
– F is the gravitational force between the objects (N)
– G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
– m₁ is the mass of the first object (kg)
– m₂ is the mass of the second object (kg)
– r is the distance between the centers of the masses (m)
Result
—
Equation:
Where G = 6.674 × 10⁻¹¹ N·m²/kg²
Interesting Fact
The gravitational force is extremely weak compared to other fundamental forces. For example, the electromagnetic force between two protons is about 10³⁶ times stronger than their gravitational attraction!
Gravitational Potential Energy Calculator
Calculate the gravitational potential energy between two objects based on their masses and the distance between them.
Gravitational Potential Energy
Gravitational potential energy is the energy stored in a system of massive objects that interact with each other gravitationally. It is negative because it is defined relative to the zero point at infinite separation.
Where:
– U is the gravitational potential energy (J)
– G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
– m₁ is the mass of the first object (kg)
– m₂ is the mass of the second object (kg)
– r is the distance between the centers of the masses (m)
The negative sign indicates that work must be done against the gravitational force to separate two objects from a finite distance to infinite distance.
Result
—
Equation:
Where G = 6.674 × 10⁻¹¹ N·m²/kg²
What Does This Mean?
The negative value indicates that the objects are bound by gravity. To separate them completely (to infinity), you would need to add energy equal to the absolute value of this potential energy.
Escape Velocity Calculator
Calculate the minimum speed needed for an object to escape the gravitational influence of a celestial body.
Select a celestial body
Escape Velocity
Escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body, without further propulsion. At this speed, an object will continue moving away from the body, eventually reaching an infinite distance from it.
Where:
– ve is the escape velocity (m/s)
– G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
– M is the mass of the celestial body (kg)
– r is the distance from the center of the body (m)
Earth’s escape velocity from its surface is approximately 11.2 km/s (40,270 km/h or 25,020 mph).
Result
—
Equation:
Where G = 6.674 × 10⁻¹¹ N·m²/kg²
Did you know?
This calculation assumes there is no atmospheric drag. In reality, a rocket leaving Earth needs additional speed to overcome air resistance. Black holes have such strong gravity that their escape velocity exceeds the speed of light!
Orbital Velocity & Period Calculator
Calculate the velocity and period for circular orbits around a celestial body.
Select a central body
Orbital Motion Calculations
For an object to maintain a stable circular orbit, the centripetal force must equal the gravitational force. From this balance, we can derive the orbital velocity and period.
Where:
– v is the orbital velocity (m/s)
– T is the orbital period (s)
– G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
– M is the mass of the central body (kg)
– r is the orbit radius (m)
These calculations assume a perfect circular orbit and that the orbiting body’s mass is negligible compared to the central body.
Results
Orbital Velocity:
—
Orbital Period:
—
Equations:
Where G = 6.674 × 10⁻¹¹ N·m²/kg²