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Orbital Speed Formula - Definition , Solved Examples 

Orbital speed formula is used to calculate the velocity required for an object to stay in a stable orbit around another celestial body, orbital speed formula is used to stay in a stable orbit around another celestial body, such as a planet, moon, or star.
authorImageMurtaza Mushtaq25 Oct, 2023
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Orbital Speed Formula

Definition Of Orbital Speed Formula

Orbital Speed Formula: Orbital speed, in simple terms, is the velocity at which an object needs to travel to stay in a stable orbit around another celestial body. It is a delicate balance between the gravitational force pulling the object towards the central body and its tangential velocity. Units Orbital speed can be expressed in various units, but the most common ones are meters per second (m/s) and kilometers per hour (km/h).

Orbital Speed Formula

Orbital Speed Formula: The orbital speed formula is used to calculate the velocity required for an object to stay in a stable orbit around another celestial body, such as a planet, moon, or star. The formula is as follows: V = √(GM/R) Here's what each component of the formula represents:
  1. V (Orbital Speed): This is the velocity, or speed, at which the object must travel to maintain a stable orbit. It's usually measured in units like meters per second (m/s) or kilometers per hour (km/h), depending on the context.
  2. G (Universal Gravitational Constant): This is a fundamental physical constant that signifies the strength of the gravitational force between two objects. The value of G is constant and is used in various gravitational calculations.
  3. M (Mass of the Central Body): This refers to the mass of the celestial body around which the object is orbiting. For Earth, the mass of M is approximately 5.972 × 10^24 kilograms. For other celestial bodies, you would use their respective mass values.
  4. R (Distance from the Center of the Central Body): R represents the distance between the center of the central body and the orbiting object. It is crucial in determining the orbital speed.

Solved Questions Of Orbital Speed Formula

  1. Calculate the orbital speed of a satellite orbiting Earth at an altitude of 300 kilometers.
- Mass of Earth (M) ≈ 5.972 × 10^24 kg - Radius of Earth (R) ≈ 6,371,000 m + 300,000 m (300 km in meters) - Using the formula V = sqrt(GM / R), calculate the orbital speed. V = sqrt((6.674 × 10^-11 m^3/kg/s^2) * (5.972 × 10^24 kg) / (6,371,000 m + 300,000 m)) V ≈ 7,671.45 m/s
  1. What is the orbital speed of the International Space Station (ISS) orbiting at an altitude of approximately 420 kilometers?
- Use the same formula as in question 1. V = sqrt((6.674 × 10^-11 m^3/kg/s^2) * (5.972 × 10^24 kg) / (6,371,000 m + 420,000 m)) V ≈ 7,667.82 m/s
  1. If we increase the altitude of a satellite in orbit, will its orbital speed increase or decrease? Explain.
- When you increase the altitude, the orbital speed will decrease. This is because the distance from the central body (Earth) increases, and to maintain a stable orbit, the object needs a lower velocity.
  1. Calculate the orbital speed required for a satellite to orbit Mars (mass of Mars ≈ 6.417 × 10^23 kg) at an altitude of 400 kilometers above its surface.
- Use the same formula but with the mass and radius of Mars. V = sqrt((6.674 × 10^-11 m^3/kg/s^2) * (6.417 × 10^23 kg) / (3,371,000 m + 400,000 m)) V ≈ 3,377.93 m/s
  1. What happens to the orbital speed if the mass of the central body (e.g., Earth) increases while keeping the altitude constant?
- If the mass of the central body increases while keeping the altitude constant, the orbital speed will also increase. This is because the gravitational force is directly proportional to the mass of the central body, so a higher mass requires a higher velocity to maintain the orbit.
  1. Find the orbital speed of a hypothetical moon with a mass of 1.2 × 10^22 kg orbiting a gas giant planet with a mass of 1.9 × 10^27 kg at a distance of 1.5 million kilometers.
- Use the same formula with the respective masses and distance. V = sqrt((6.674 × 10^-11 m^3/kg/s^2) * (1.9 × 10^27 kg) / (1.5 × 10^9 m)) V ≈ 28,640.68 m/s
  1. Why is it more fuel-efficient for spacecraft to perform a gravitational slingshot maneuver using a planet's gravity to increase their speed instead of using their engines?
- Gravitational slingshot uses the planet's orbital speed to boost the spacecraft's velocity, conserving fuel. This maneuver takes advantage of the planet's motion, allowing the spacecraft to gain kinetic energy without expending its own fuel.
  1. How does the orbital speed of a geostationary satellite (orbiting at an altitude of approximately 36,000 kilometers) compare to that of a satellite in low Earth orbit?
- The orbital speed of a geostationary satellite is much lower than that of a satellite in low Earth orbit. A geostationary satellite orbits at the same rate as the Earth's rotation, approximately 3.07 kilometers per second (km/s), while a satellite in low Earth orbit typically travels at speeds ranging from 7 to 8 km/s.
  1. Explain the concept of escape velocity and its relationship to orbital speed.
- Escape velocity is the minimum velocity an object must reach to break free from a celestial body's gravitational influence and move into space. It is related to orbital speed in that escape velocity is higher than orbital speed. To escape Earth's gravity, an object must achieve an escape velocity of about 11.2 km/s, whereas orbital speed is much lower, as we've seen in previous calculations.
  1. Can a satellite remain in orbit indefinitely, or does it require periodic adjustments to its speed? Explain.
- A satellite cannot remain in orbit indefinitely without periodic adjustments. Over time, it will experience drag from the Earth's atmosphere, which slows it down. Without adjustments to its speed, the satellite will eventually re-enter the Earth's atmosphere and burn up. Therefore, satellites in low Earth orbit require occasional boosts to maintain their orbital speeds and altitudes.

Orbital Speed Formula FAQs

What is orbital speed, and why is it important?

Orbital speed is the velocity required for an object to stay in a stable orbit around another celestial body. It's important because it enables satellites and space objects to remain in space without falling back to Earth.

How is orbital speed calculated?

Orbital speed is calculated using the formula: V = sqrt(GM / R), where G is the universal gravitational constant, M is the mass of the central body, and R is the distance from the center of the central body to the orbiting object.

Does increasing the altitude of a satellite increase its orbital speed?

No, increasing the altitude of a satellite decreases its orbital speed. A higher altitude means a greater distance from the central body, which requires a lower orbital speed to maintain a stable orbit.

How does the mass of the central body affect orbital speed?

The mass of the central body directly affects orbital speed. A higher mass central body requires a higher orbital speed for an object to remain in orbit around it.
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