Orbital Speed and Eccentricity Calculator

Orbital speed is the velocity at which an object orbits a celestial body. Eccentricity measures the shape of that orbit. As eccentricity increases, the orbit becomes more elongated, affecting the object’s speed. Highly eccentric orbits have varying speeds along their paths, while low eccentricity results in more stable, nearly circular orbits with relatively constant speeds.

Eccentricity	Orbital Speed	Description
0 (Circular)	Constant	Nearly circular orbit with stable speed.
0 < e < 1	Variable	Elliptical orbit with varying speeds.
1 (Parabolic)	Variable	Parabolic orbit with speed changes along path.
e > 1 (Hyperbolic)	Variable	Hyperbolic orbit with unbound trajectory.

FAQs

What is the formula for eccentricity of an orbital speed?

There is no direct formula for eccentricity of orbital speed because eccentricity and orbital speed are two different parameters in orbital mechanics.

Does eccentricity affect orbital speed?

Yes, eccentricity can affect orbital speed. In elliptical orbits, where eccentricity is greater than 0, the speed of an object will vary at different points along its orbit. At the periapsis (closest point to the central body), the object will have its highest speed, and at the apoapsis (farthest point), it will have its lowest speed.

How do you calculate orbital speed?

Orbital speed (v) can be estimated using the formula:

v ≈ √(G * M / r)

Where:

• G is the gravitational constant (approximately 6.67430 x 10^-11 N·m^2/kg^2).
• M is the mass of the central body (e.g., a planet or star).
• r is the distance from the center of the central body to the object in orbit.

How will increasing eccentricity affect the change in orbital speed?

Increasing eccentricity in an elliptical orbit will lead to larger variations in orbital speed. As eccentricity increases, the difference in speed between periapsis and apoapsis becomes more significant. At higher eccentricities, the speed difference will be more pronounced.

How do I calculate eccentricity?

Eccentricity (e) of an orbit can be calculated using the following formula:

e ≈ (r_a – r_p) / (r_a + r_p)

Where:

• e is the eccentricity.
• r_a is the apoapsis distance (farthest point from the central body).
• r_p is the periapsis distance (closest point to the central body).

What is the formula for eccentricity?

The formula for eccentricity is provided above.

What happens when eccentricity is more than 1?

Eccentricity values greater than 1 represent hyperbolic orbits, indicating that the object is not in a closed, bound orbit. Instead, it follows a hyperbolic trajectory and is not gravitationally bound to the central body. It will approach the central body once and then move away indefinitely.

How does eccentricity affect orbital?

Eccentricity determines the shape of an orbit. It defines how stretched or elongated the orbit is. Lower eccentricities (closer to 0) indicate nearly circular orbits, while higher eccentricities (closer to or greater than 1) indicate more elongated, elliptical or hyperbolic orbits.

What happens if eccentricity increases?

Increasing eccentricity makes an orbit more elongated and elliptical. It also leads to greater variations in speed along the orbit, as mentioned earlier.

What is the law of orbital speed?

The law of orbital speed states that an object in orbit around a central body will travel at varying speeds along its path. The speed is highest at the closest point to the central body (periapsis) and lowest at the farthest point (apoapsis). This variation in speed is due to the conservation of angular momentum.

How do you increase orbital speed?

To increase orbital speed, you need to provide additional energy to the object in orbit. This can be achieved by firing thrusters or engines in the direction of motion (prograde) to boost the object’s velocity. However, increasing orbital speed may also raise the object’s orbit to a higher altitude.

Is orbital speed and orbital velocity the same?

Yes, orbital speed and orbital velocity are often used interchangeably. They both refer to the speed at which an object travels in orbit around a central body.

What does high eccentricity mean?

A high eccentricity means that the orbit is highly elongated or stretched. It deviates significantly from a circular shape. Orbits with high eccentricity are more elongated and have greater variations in speed along the orbital path.

What is the relationship between eccentricity and orbital period?

Eccentricity affects the orbital period. In general, as eccentricity increases, the orbital period also changes. Highly elliptical orbits (high eccentricity) have longer orbital periods than nearly circular orbits (low eccentricity) with the same semi-major axis.

Why is eccentricity important?

Eccentricity is important in orbital mechanics because it describes the shape of an orbit. It affects the object’s speed, energy requirements for orbital changes, and the characteristics of its trajectory.

What is the average eccentricity?

There is no single “average” eccentricity for all objects in space. Eccentricity varies widely depending on the specific orbit of an object. Some objects, like planets, have nearly circular orbits (low eccentricity), while others, like comets, can have highly eccentric orbits.

Why is eccentricity 0 and 1?

Eccentricity values of 0 represent perfectly circular orbits, where the distance between the object and the central body remains constant. Eccentricity values of 1 represent parabolic orbits, which are on the boundary between bound (elliptical) and unbound (hyperbolic) orbits.

Is an eccentricity of 1 a line?

An eccentricity of 1 does not represent a line but a parabolic orbit. In a parabolic orbit, the object follows a trajectory that is neither elliptical nor hyperbolic. It approaches the central body once and then moves away along a path that resembles an open curve.

What is the maximum for eccentricity?

The maximum eccentricity for a bound orbit is 1. An eccentricity greater than 1 signifies a hyperbolic orbit, indicating that the object is not gravitationally bound and will not return to the central body.

What factors affect eccentricity?

Eccentricity is primarily influenced by the initial conditions and gravitational interactions of an object in orbit. Factors such as the object’s initial velocity, distance from the central body, and interactions with other celestial bodies can all affect eccentricity.

What happens when eccentricity is less than 0?

Eccentricity cannot be less than 0; it is a dimensionless number ranging from 0 to 1 for bound orbits and greater than 1 for hyperbolic orbits. Negative values do not have physical significance in the context of eccentricity.

Does eccentricity increase with distance?

Eccentricity is not directly related to distance but is determined by the shape of the orbit. Increasing the distance from the central body can lead to higher eccentricities if the object’s velocity and initial conditions are appropriate for an elliptical orbit.

What if eccentricity is negative?

Eccentricity is not defined as negative. It is a non-negative dimensionless value between 0 and 1 for bound orbits and greater than 1 for hyperbolic orbits. Negative values are not meaningful in the context of eccentricity.

What happens when eccentricity is negative?

As mentioned earlier, eccentricity cannot be negative in the context of orbital mechanics. Negative values are not used to describe orbits.

What determines orbital eccentricity?

Orbital eccentricity is determined by a combination of factors, including the object’s initial velocity, the shape of its trajectory, and the gravitational influence of the central body and other celestial objects.

What is a highly eccentric orbit?

A highly eccentric orbit is one in which the eccentricity value is close to 1. It means the orbit is highly elongated and deviates significantly from a circular shape.

Which object has the most eccentric orbit?

Comets are known for having some of the most eccentric orbits in our solar system. Their eccentricities can be quite high, approaching or even exceeding 1.

Does eccentricity affect precession?

Eccentricity can affect the precession of an orbit, especially in the case of highly eccentric orbits. The precession rate can change due to variations in gravitational forces along the elliptical path.

What changes orbital speed?

Orbital speed can change due to changes in altitude, changes in the gravitational force exerted by the central body, or propulsion maneuvers by the object in orbit.

What is the effect of orbital speed?

Orbital speed determines the object’s ability to remain in orbit. If the orbital speed is too low, the object will fall to the central body; if it’s too high, the object will escape its orbit.

What is the fastest orbital speed?

The fastest orbital speed in our solar system is achieved by objects in low Earth orbit (LEO) at an altitude of about 160-2,000 kilometers. These objects travel at speeds around 7.8 kilometers per second (km/s) or approximately 28,000 kilometers per hour (km/h).

Are lower orbits faster?

Yes, lower orbits are faster. Objects in lower orbits experience stronger gravitational forces, which require them to travel at higher speeds to maintain their orbits.

What happens when orbital speed decreases?

When orbital speed decreases, an object may no longer have sufficient velocity to maintain its current orbit. It can result in a decay of the orbit, causing the object to re-enter the central body’s atmosphere or fall into a lower orbit.

What happens if a satellite orbits too fast?

If a satellite orbits too fast, it may enter a higher orbit or escape the central body’s gravitational influence altogether. This would require additional energy to bring the satellite back to its intended orbit.

Is orbital speed the same as angular speed?

No, orbital speed and angular speed are not the same. Orbital speed is the linear speed at which an object travels in its orbit, while angular speed (angular velocity) refers to the rate at which the object sweeps out angles in its orbit.

How does orbital speed depend on radius?

Orbital speed depends on the radius of the orbit through the inverse square root relationship. As the radius (distance from the central body) increases, orbital speed decreases, and vice versa.

Is orbital speed constant?

Orbital speed is not constant; it varies along the orbital path. It is highest at periapsis and lowest at apoapsis for elliptical orbits. In a circular orbit, the speed remains relatively constant.

Why is low eccentricity better?

Low eccentricity is often preferred for stable, predictable orbits. It results in nearly circular orbits with relatively constant speeds, making it easier to maintain and control spacecraft.

What is 0.1 eccentricity?

An eccentricity of 0.1 indicates a somewhat elongated orbit but is still relatively close to a circular orbit. The orbit has some deviation from perfect circularity, but it is not highly eccentric.

What is the perfect eccentricity?

The concept of a “perfect” eccentricity depends on the specific requirements of a mission or orbit. In some cases, a perfect eccentricity might mean an eccentricity of 0 (a perfectly circular orbit). In other cases, it might refer to an eccentricity that serves a particular scientific or engineering purpose.

Does planetary distance affect eccentricity?

Planetary distance can indirectly affect eccentricity. As an object’s distance from a planet changes, it may enter a different type of orbit, which can have a different eccentricity.

What are the three types of eccentricity?

There are three main types of eccentricity in orbital mechanics:

1. Low eccentricity (close to 0) for nearly circular orbits.
2. Moderate eccentricity for elliptical orbits.
3. High eccentricity (approaching 1) for highly elongated orbits.

What is eccentricity for dummies?

Eccentricity describes how stretched or elongated an orbit is. Low values mean the orbit is nearly circular, while high values indicate a more elongated shape.

Is high eccentricity good?

High eccentricity can be useful for specific mission objectives, such as interplanetary transfers or studying distant celestial bodies. However, for many applications, low eccentricity is preferred for stability and predictability.

What does an eccentricity of 0.9 mean?

An eccentricity of 0.9 indicates a highly elongated orbit. It deviates significantly from circularity, with the closest approach to the central body (periapsis) being much closer than the farthest point (apoapsis).

What is an example of eccentricity?

An example of eccentricity is the orbit of a comet. Comets often have highly eccentric orbits that bring them close to the Sun (periapsis) and then take them far away (apoapsis) before they return.

What is the eccentricity of a satellite?

The eccentricity of a satellite’s orbit depends on its specific mission and intended purpose. Satellites can have a wide range of eccentricities, from nearly circular (low eccentricity) to highly elliptical (high eccentricity) orbits.

Is eccentricity always a number?

Yes, eccentricity is always a dimensionless number between 0 and 1 for bound orbits, or greater than 1 for hyperbolic orbits. It is a numerical value that quantifies the shape of the orbit.

What orbit has an eccentricity of 1?

An orbit with an eccentricity of 1 is on the boundary between bound and unbound orbits. It is called a parabolic orbit. Objects on parabolic orbits approach the central body once and then move away along a path resembling an open curve.

What is the minimum value that an eccentricity can be?

The minimum value for eccentricity is 0, which corresponds to a perfectly circular orbit.

What planet has the least eccentric orbit?

Among the planets in our solar system, Venus has one of the least eccentric orbits. Its eccentricity is close to 0.007, making its orbit nearly circular.

Does eccentricity affect speed?

Yes, eccentricity affects speed in orbit. In elliptical orbits, eccentricity determines the variation in speed along the orbital path, with higher eccentricities leading to more significant speed variations.

What is the error of eccentricity?

The error of eccentricity refers to the difference between the calculated eccentricity of an orbit and its actual eccentricity. It quantifies the accuracy of the eccentricity determination.

What is the force due to eccentricity?

The force due to eccentricity is not a common term in orbital mechanics. Gravitational forces are the primary forces acting on objects in orbit, and eccentricity affects the shape of the orbit rather than being a force itself.

How to calculate eccentricity?

Eccentricity can be calculated using the formula provided earlier in this response: e = (r_a – r_p) / (r_a + r_p), where r_a is the apoapsis distance, and r_p is the periapsis distance.

What does it mean if an object has an eccentricity greater than 1?

If an object has an eccentricity greater than 1, it is on a hyperbolic orbit. This means it is not gravitationally bound to the central body and will not complete a closed orbit. Instead, it follows a trajectory that takes it away from the central body indefinitely.

What is the eccentricity of Earth?

The eccentricity of Earth’s orbit is approximately 0.0167, which means Earth’s orbit is slightly elliptical but very close to being circular.

When eccentricity gets closer to 1?

When eccentricity gets closer to 1, the orbit becomes more elongated and stretched, deviating further from circularity. The difference in distance between periapsis and apoapsis becomes more significant.

What happens when eccentricity increases?

As eccentricity increases, the orbit becomes more elongated, and the object’s speed varies more significantly along its path. The orbit also becomes more eccentric, deviating further from a perfect circle.

Does eccentricity affect orbital period?

Yes, eccentricity affects orbital period. Orbits with higher eccentricities have longer orbital periods than those with lower eccentricities, given the same semi-major axis.

Which object would have an eccentricity closest to 0?

Among the planets in our solar system, Earth has one of the closest eccentricities to 0, making its orbit nearly circular.