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Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor?
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Two planets A and B move around the Sun in elliptic orbits with time p...
Introduction:
In this problem, we are given two planets A and B moving around the Sun in elliptic orbits. We are also given the eccentricity of the orbit of planet B and its distance of closest approach to the Sun. We need to find the maximum possible distance between the planets.
Understanding the problem:
To solve this problem, we need to understand the concept of eccentricity in an ellipse and how it relates to the distance of closest approach and maximum possible distance between the planets.
Eccentricity of an ellipse:
The eccentricity of an ellipse is a measure of how elongated the ellipse is. It is denoted by the symbol ε and is defined as the ratio of the distance between the foci of the ellipse to the length of the major axis. Mathematically, it can be expressed as:
ε = (r_max - r_min) / (r_max + r_min)
Deriving the maximum possible distance:
To find the maximum possible distance between the planets, we need to consider the distances of closest approach for both planets A and B.
Distance of closest approach for planet B:
The distance of closest approach for planet B is given as R.
Distance of closest approach for planet A:
To find the distance of closest approach for planet A, we need to use the relationship between eccentricity and the distances of closest approach.
From the definition of eccentricity, we have:
ε = (r_max - r_min) / (r_max + r_min)
Since the distance of closest approach is the minimum distance from the center of the ellipse to the foci, we can express it as:
r_min = a - c
Where a is the semi-major axis of the ellipse and c is the distance between the center of the ellipse and one of the foci.
Since the distance of closest approach for planet A is not given, we can express it as:
r_min_A = a_A - c_A
Maximum possible distance between the planets:
The maximum possible distance between the planets can be expressed as the sum of the distances of closest approach for both planets.
Max distance = r_min_A + R
Conclusion:
In this problem, we found the maximum possible distance between two planets moving in elliptic orbits around the Sun, given the eccentricity of one of the orbits and the distance of closest approach for planet B. We used the relationship between eccentricity and the distances of closest approach to derive the maximum possible distance.
In this problem, we are given two planets A and B moving around the Sun in elliptic orbits. We are also given the eccentricity of the orbit of planet B and its distance of closest approach to the Sun. We need to find the maximum possible distance between the planets.
Understanding the problem:
To solve this problem, we need to understand the concept of eccentricity in an ellipse and how it relates to the distance of closest approach and maximum possible distance between the planets.
Eccentricity of an ellipse:
The eccentricity of an ellipse is a measure of how elongated the ellipse is. It is denoted by the symbol ε and is defined as the ratio of the distance between the foci of the ellipse to the length of the major axis. Mathematically, it can be expressed as:
ε = (r_max - r_min) / (r_max + r_min)
Deriving the maximum possible distance:
To find the maximum possible distance between the planets, we need to consider the distances of closest approach for both planets A and B.
Distance of closest approach for planet B:
The distance of closest approach for planet B is given as R.
Distance of closest approach for planet A:
To find the distance of closest approach for planet A, we need to use the relationship between eccentricity and the distances of closest approach.
From the definition of eccentricity, we have:
ε = (r_max - r_min) / (r_max + r_min)
Since the distance of closest approach is the minimum distance from the center of the ellipse to the foci, we can express it as:
r_min = a - c
Where a is the semi-major axis of the ellipse and c is the distance between the center of the ellipse and one of the foci.
Since the distance of closest approach for planet A is not given, we can express it as:
r_min_A = a_A - c_A
Maximum possible distance between the planets:
The maximum possible distance between the planets can be expressed as the sum of the distances of closest approach for both planets.
Max distance = r_min_A + R
Conclusion:
In this problem, we found the maximum possible distance between two planets moving in elliptic orbits around the Sun, given the eccentricity of one of the orbits and the distance of closest approach for planet B. We used the relationship between eccentricity and the distances of closest approach to derive the maximum possible distance.
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Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor?
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Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor?.
Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor?.
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Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor?, a detailed solution for Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor? has been provided alongside types of Two planets A and B move around the Sun in elliptic orbits with time periods T_{A} and T_{B} respectively. If the eccentricity of the orbit of B is and its distance of closest approach to the Sun is R, then the maximum possible distance between the planets is [Eccentricity of an ellipse: epsilon= r max -r min r max r min rfloor? theory, EduRev gives you an
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