Mean Motion to Semi-Major Axis Calculator

The relationship between Mean Motion (n) and Semi-Major Axis (a) for objects in orbit is governed by Kepler’s third law. It can be expressed as n = (2π) / T, where T is the orbital period. The specific value of ‘a’ depends on the gravitational parameter of the central body and is found using more precise equations.

Here’s a table that shows the relationship between Mean Motion (n) and Semi-Major Axis (a) for objects in orbit:

Mean Motion (n)	Semi-Major Axis (a)
1 revolution/day	~42,164 kilometers (geostationary orbit)
2 revolutions/day	~21,082 kilometers
3 revolutions/day	~14,688 kilometers (Molniya orbit)
4 revolutions/day	~10,541 kilometers
5 revolutions/day	~8,433 kilometers
6 revolutions/day	~7,027 kilometers
7 revolutions/day	~6,020 kilometers
8 revolutions/day	~5,270 kilometers
9 revolutions/day	~4,691 kilometers
10 revolutions/day	~4,236 kilometers

Note: The values in this table are approximate and are based on the simplified formula for mean motion: n = (2π) / T, where T is the orbital period in seconds. The relationship between mean motion and semi-major axis depends on the specific gravitational parameter of the central body (e.g., Earth) and is more accurately calculated using Kepler’s laws and the gravitational constant.

FAQs

1. How do I calculate semi-major axis? The semi-major axis (a) of an elliptical orbit can be calculated using the following formula: a ≈ (Perihelion + Aphelion) / 2 where Perihelion is the closest distance to the focus (e.g., the Sun) and Aphelion is the farthest distance.
2. What is the mean motion semi-major axis? The mean motion semi-major axis is not a standard term in orbital mechanics. It’s possible you may be referring to the mean motion, which is related to the time it takes for an object to complete one orbit around a central body.
3. How do you convert orbital period to semi-major axis? You can use Kepler’s third law to estimate the semi-major axis from the orbital period: a ≈ (T^2 * G * M)^(1/3) where T is the orbital period, G is the gravitational constant, and M is the mass of the central body.
4. What is the semi-major axis in KSP? In the game Kerbal Space Program (KSP), the semi-major axis represents the average distance from a celestial body (e.g., a planet) to its satellite (e.g., a spacecraft or moon).
5. Is the semi-major axis A or B? The semi-major axis is typically denoted by ‘a,’ while the semi-minor axis is denoted by ‘b’ in the context of an ellipse.
6. How do you solve for a semi-minor axis? The semi-minor axis (b) of an ellipse can be calculated using the formula: b ≈ a * √(1 – e^2) where ‘a’ is the semi-major axis, and ‘e’ is the eccentricity of the ellipse.
7. Is the semi-major axis half of the major axis? No, the semi-major axis (a) is not half of the major axis. It is equal to the average of the major axis and minor axis.
8. Where is the semi-minor axis? The semi-minor axis (b) of an ellipse is the shorter radius, perpendicular to the semi-major axis. It lies along the minor axis of the ellipse.
9. What is the length of the semi-major axis of the orbit? The length of the semi-major axis depends on the specific orbit and central body. It represents the average distance from the object in orbit to the central body.
10. How do you calculate the semi-major axis of a binary star system? To calculate the semi-major axis of a binary star system, you need observations of the stars’ orbits, including their period and eccentricity. You can then use Kepler’s laws and relevant equations to determine the semi-major axis.
11. What is the semi-major axis of an orbit quizlet? The semi-major axis of an orbit, in the context of a quizlet or educational resource, would typically refer to the average distance from the center of the orbit to the orbiting object.
12. Is the semi-major axis constant? The semi-major axis of an orbit is not necessarily constant. It can change over time due to gravitational interactions with other celestial bodies, but for simple two-body systems, it remains constant.
13. Is semi-major axis the same as apogee? No, the semi-major axis is not the same as apogee. The semi-major axis is the average distance in an elliptical orbit, while apogee is the point farthest from the central body in an orbit.
14. What is the difference between semi-major and minor axis? The semi-major axis (a) is the longer half of an ellipse, while the semi-minor axis (b) is the shorter half, perpendicular to the semi-major axis.
15. Can semi-major axis be negative? In the context of orbital mechanics, the semi-major axis is typically not negative. It represents a positive distance.
16. What is semi-major axis and Eccentricity? The semi-major axis (a) is a measure of the average distance of an object in an elliptical orbit from the central body, while eccentricity (e) quantifies how much the orbit deviates from a perfect circle, with values between 0 (circular) and 1 (highly elliptical).
17. What is the semi-major axis of a sphere? A sphere does not have a semi-major axis. The concept of semi-major axis applies to elliptical orbits, not spherical objects.
18. What is the semi-minor axis in astronomy? In astronomy, the semi-minor axis (b) refers to the shorter radius of an ellipse, often used to describe the shape of planetary orbits.
19. How do you determine major and minor axis? The major axis is the longer axis of an ellipse and is determined by measuring the longest distance across the ellipse. The minor axis is the shorter axis, perpendicular to the major axis.
20. How do you find the semi-major axis given perihelion and aphelion? You can find the semi-major axis (a) using the formula mentioned in question 1, where a = (Perihelion + Aphelion) / 2.
21. Is semi-major axis the distance from the sun? The semi-major axis is not the distance from the Sun but represents the average distance of an object in orbit from the Sun in the context of solar system objects.
22. Does semi-major axis include Earth radius? When calculating the semi-major axis of Earth’s orbit around the Sun, it does not include Earth’s radius. It is the average distance from the center of the Earth to the center of the Sun.
23. What is the symbol for the semi-major axis? The symbol for the semi-major axis is ‘a.’
24. Is the semi-major axis the mean distance? Yes, the semi-major axis is often referred to as the mean distance because it represents the average distance of an object in an elliptical orbit from the central body.
25. What is the ratio of semi-major and semi-minor axis called? The ratio of the semi-major axis (a) to the semi-minor axis (b) is called the aspect ratio.
26. What is the formula for the minor axis of the ellipse? The length of the minor axis (b) of an ellipse is typically calculated as b = a * √(1 – e^2), where ‘a’ is the semi-major axis and ‘e’ is the eccentricity.
27. How long is the minor axis? The length of the minor axis (b) of an ellipse depends on the specific ellipse and its size. It is always shorter than or equal to the length of the major axis.
28. Is the semi-major axis the aphelion? No, the semi-major axis is not the aphelion. The aphelion is the point in an orbit that is farthest from the central body, whereas the semi-major axis is the average distance of the orbit.
29. What is the semi-major axis of an elliptical planetary orbit equal to quizlet? In the context of a quizlet or educational resource, the semi-major axis of an elliptical planetary orbit would be defined as the average distance from the planet to its central body (e.g., the Sun).
30. What is the semi-major axis of 76 years? The value of the semi-major axis for a specific orbit depends on the celestial body and its period. A semi-major axis of 76 years would correspond to the average distance for an object with that orbital period.
31. What is the formula for orbital motion? The formula for orbital motion depends on the context and specific variables involved. In general, Kepler’s laws of planetary motion and Newton’s laws of gravitation are used to describe orbital motion.
32. Is time period proportional to semi-major axis? Yes, according to Kepler’s third law, the square of the orbital period (T) is proportional to the cube of the semi-major axis (a): T^2 ∝ a^3.
33. What has the largest semi-major axis? The object with the largest semi-major axis in our solar system is typically a distant comet or a Kuiper Belt object, as they can have extremely elongated orbits.
34. What is the relationship between semi-major axis, semi-minor axis, and Eccentricity? The semi-major axis (a), semi-minor axis (b), and eccentricity (e) are related in an elliptical orbit. The semi-major axis is the average distance, the semi-minor axis is related to the shape, and the eccentricity quantifies how elliptical the orbit is.
35. What is the relationship between the semi-major axis, semi-minor axis, and the distance of the focus from the center of the ellipse? The semi-major axis (a), semi-minor axis (b), and the distance from the center of the ellipse to one of its foci are related by the equation: c = √(a^2 – b^2), where ‘c’ is the distance to the focus.
36. Is the minor axis horizontal or vertical? The orientation of the minor axis in an ellipse depends on how the ellipse is positioned. It can be either horizontal or vertical relative to the major axis.
37. Is semi-major axis the same as altitude? No, semi-major axis is not the same as altitude. Semi-major axis refers to the average distance in an elliptical orbit, while altitude typically refers to the height above a reference point, such as the Earth’s surface.
38. What is the mean motion of the ISS? The mean motion of the International Space Station (ISS) is approximately 15.5 orbits per day, which corresponds to an orbital period of about 90 minutes.
39. What does eccentricity of 0.5 mean? An eccentricity (e) of 0.5 in an elliptical orbit indicates a moderately elliptical shape, with the distance between the foci being equal to half of the length of the major axis.
40. What is the formula for the major axis? The length of the major axis (2a) of an ellipse is simply twice the value of the semi-major axis: 2a.
41. What is the equation for a semi-ellipse? The equation for a semi-ellipse is x^2 / a^2 + y^2 / b^2 = 1, where ‘a’ is the semi-major axis and ‘b’ is the semi-minor axis.
42. What is major and minor axis length? The major axis is the longer of the two axes of an ellipse, while the minor axis is the shorter one. Their lengths are 2a and 2b, respectively, where ‘a’ is the semi-major axis and ‘b’ is the semi-minor axis.
43. What planet has the smallest semi-major axis? The planet Mercury has the smallest semi-major axis of all the planets in our solar system, as it orbits closest to the Sun.
44. How long does it take to complete one orbit around the sun, and the semi-major axis of 3 Juno’s orbit is 2.67 AU? To find the orbital period (T) of 3 Juno with a semi-major axis (a) of 2.67 AU, you can use Kepler’s third law: T^2 ∝ a^3. Solving for T: T^2 = (2.67 AU)^3 T ≈ 4.09 years (rounded estimate).
45. How do you find the semi-major axis with orbital velocity? To find the semi-major axis (a) using orbital velocity (v) and the gravitational constant (G), you can use the formula: a = (G * M) / (4π^2 * v^2), where ‘M’ is the mass of the central body.
46. What does the semi-major axis tell you about an orbit? The semi-major axis provides information about the size and shape of an orbit. It represents the average distance from the central body and helps characterize the scale of the orbit.
47. Is the semi-major axis half of the major axis? No, the semi-major axis is not half of the major axis. It is equal to half of the sum of the major and minor axes.
48. How is semi-major axis calculated? The semi-major axis is often calculated as the average of the perihelion and aphelion distances for an object in an elliptical orbit.
49. How do you find the semi-major axis distance? The semi-major axis distance can be found using the formula mentioned in question 1, where a = (Perihelion + Aphelion) / 2.
50. What is the formula for the semi-major axis using the period? You can find the semi-major axis (a) using the formula: a ≈ (T^2 * G * M)^(1/3), where ‘T’ is the orbital period, ‘G’ is the gravitational constant, and ‘M’ is the mass of the central body.
51. What is the meaning of semi-major axis of Earth? The semi-major axis of Earth’s orbit around the Sun represents the average distance from the center of the Earth to the center of the Sun. It is approximately 1 astronomical unit (AU).
52. Is the semi-major axis constant? The semi-major axis of an orbit is not necessarily constant. It can change over time due to gravitational interactions with other celestial bodies, but for simple two-body systems, it remains constant.
53. Is the semi-major axis A or B? The semi-major axis is typically denoted by ‘a,’ while the semi-minor axis is denoted by ‘b’ in the context of an ellipse.
54. What is the difference between semi-minor and semi-major axis? The semi-major axis (a) is the longer half of an ellipse, while the semi-minor axis (b) is the shorter half, perpendicular to the semi-major axis.
55. What is the semi-major minor axis of an ellipse? The terms “semi-major” and “semi-minor” refer to the two main axes of an ellipse. The semi-major axis (a) is the longer one, and the semi-minor axis (b) is the shorter one.
56. What is the length of the semi-minor axis of an ellipse? The length of the semi-minor axis (b) of an ellipse depends on the specific ellipse and its size but is always shorter than or equal to the length of the major axis.
57. What is the ratio of the major to the minor axis of an ellipse? The ratio of the major axis (2a) to the minor axis (2b) of an ellipse is commonly referred to as the aspect ratio and is equal to ‘a/b.’
58. Is the minor axis half of the major axis? No, the minor axis is not half of the major axis. The minor axis is shorter than the major axis, and their lengths are related by the aspect ratio ‘a/b.’
59. How do you find the major and minor radius of an ellipse? The major radius is half of the major axis (a), and the minor radius is half of the minor axis (b) of the ellipse.