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Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?
- a)Larger by a factor of 1.11
- b)Smaller by a factor of 0.63
- c)Smaller by a factor of 0.5
- d)Larger by a factor of 1.23
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Suppose there existed a planet that went around the sun twice as fast ...
Explanation:
Time period of revolution of earth around sun Te= 1 Year
Time period of revolution of planet around sun,Tp=0.5 Year
Orbital size of earth, re= 1 A.U
Orbital size of the planet,rp=?
Applying Kepler's third law we get:
Most Upvoted Answer
Suppose there existed a planet that went around the sun twice as fast ...
To determine the orbital size of the planet that goes around the sun twice as fast as Earth, we can use Kepler's third law of planetary motion. This law states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun.
Let's assume that the orbital size of Earth is represented by r_e, and its orbital period is represented by T_e. The orbital size of the planet in question will be represented by r_p, and its orbital period will be represented by T_p.
According to the question, the planet goes around the sun twice as fast as Earth. This means that its orbital period, T_p, is half of Earth's orbital period, T_e.
Using Kepler's third law, we can write the following equation:
(T_p)^2 / (T_e)^2 = (r_p)^3 / (r_e)^3
Substituting T_p = 0.5T_e and rearranging the equation, we get:
(0.5T_e)^2 / (T_e)^2 = (r_p)^3 / (r_e)^3
0.25 = (r_p)^3 / (r_e)^3
Taking the cube root of both sides of the equation, we get:
0.63 = r_p / r_e
This implies that the ratio of the orbital size of the planet (r_p) to that of Earth (r_e) is 0.63. Therefore, the orbital size of the planet is smaller by a factor of 0.63 compared to Earth.
Hence, the correct answer is option B - Smaller by a factor of 0.63.
Let's assume that the orbital size of Earth is represented by r_e, and its orbital period is represented by T_e. The orbital size of the planet in question will be represented by r_p, and its orbital period will be represented by T_p.
According to the question, the planet goes around the sun twice as fast as Earth. This means that its orbital period, T_p, is half of Earth's orbital period, T_e.
Using Kepler's third law, we can write the following equation:
(T_p)^2 / (T_e)^2 = (r_p)^3 / (r_e)^3
Substituting T_p = 0.5T_e and rearranging the equation, we get:
(0.5T_e)^2 / (T_e)^2 = (r_p)^3 / (r_e)^3
0.25 = (r_p)^3 / (r_e)^3
Taking the cube root of both sides of the equation, we get:
0.63 = r_p / r_e
This implies that the ratio of the orbital size of the planet (r_p) to that of Earth (r_e) is 0.63. Therefore, the orbital size of the planet is smaller by a factor of 0.63 compared to Earth.
Hence, the correct answer is option B - Smaller by a factor of 0.63.
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Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?a)Larger by a factor of 1.11b)Smaller by a factor of 0.63c)Smaller by a factor of 0.5d)Larger by a factor of 1.23Correct answer is option 'B'. Can you explain this answer?
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Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?a)Larger by a factor of 1.11b)Smaller by a factor of 0.63c)Smaller by a factor of 0.5d)Larger by a factor of 1.23Correct answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?a)Larger by a factor of 1.11b)Smaller by a factor of 0.63c)Smaller by a factor of 0.5d)Larger by a factor of 1.23Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?a)Larger by a factor of 1.11b)Smaller by a factor of 0.63c)Smaller by a factor of 0.5d)Larger by a factor of 1.23Correct answer is option 'B'. Can you explain this answer?.
Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?a)Larger by a factor of 1.11b)Smaller by a factor of 0.63c)Smaller by a factor of 0.5d)Larger by a factor of 1.23Correct answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?a)Larger by a factor of 1.11b)Smaller by a factor of 0.63c)Smaller by a factor of 0.5d)Larger by a factor of 1.23Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?a)Larger by a factor of 1.11b)Smaller by a factor of 0.63c)Smaller by a factor of 0.5d)Larger by a factor of 1.23Correct answer is option 'B'. Can you explain this answer?.
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