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If earth has a mass 9 times and radius twice that of the planet mass. calculate the minimum velocity required by the rocket to pull off gravitational force of mass. (take escape velocity on the surface of earth is 11.2kms-¹?
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If earth has a mass 9 times and radius twice that of the planet mass. ...
Understanding Escape Velocity
The escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any additional propulsion. For Earth, this velocity is approximately 11.2 km/s.
Given Conditions
- Mass of the new planet (M) = 9 times the mass of Earth (Me)
- Radius of the new planet (R) = 2 times the radius of Earth (Re)
Escape Velocity Formula
Escape velocity (Ve) can be calculated using the formula:
Ve = sqrt((2 * G * M) / R)
Where:
- G is the gravitational constant
- M is the mass of the planet
- R is the radius of the planet
Calculating New Escape Velocity
1. Substituting the values:
- Mass of the new planet: M = 9 * Me
- Radius of the new planet: R = 2 * Re
2. Plugging into the formula:
Ve = sqrt((2 * G * (9 * Me)) / (2 * Re))
3. Simplifying:
- This simplifies to: Ve = sqrt((9 * G * Me) / Re)
4. Relating to Earth's escape velocity:
- Since Ve(Earth) = sqrt((2 * G * Me) / Re), we can express the new escape velocity in terms of Earth's escape velocity.
5. Final Calculation:
- The new escape velocity becomes: Ve(new planet) = sqrt(9) * Ve(Earth) = 3 * Ve(Earth) = 3 * 11.2 km/s ≈ 33.6 km/s.
Conclusion
Thus, the minimum velocity required by a rocket to escape the gravitational pull of this new planet is approximately 33.6 km/s.
The escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any additional propulsion. For Earth, this velocity is approximately 11.2 km/s.
Given Conditions
- Mass of the new planet (M) = 9 times the mass of Earth (Me)
- Radius of the new planet (R) = 2 times the radius of Earth (Re)
Escape Velocity Formula
Escape velocity (Ve) can be calculated using the formula:
Ve = sqrt((2 * G * M) / R)
Where:
- G is the gravitational constant
- M is the mass of the planet
- R is the radius of the planet
Calculating New Escape Velocity
1. Substituting the values:
- Mass of the new planet: M = 9 * Me
- Radius of the new planet: R = 2 * Re
2. Plugging into the formula:
Ve = sqrt((2 * G * (9 * Me)) / (2 * Re))
3. Simplifying:
- This simplifies to: Ve = sqrt((9 * G * Me) / Re)
4. Relating to Earth's escape velocity:
- Since Ve(Earth) = sqrt((2 * G * Me) / Re), we can express the new escape velocity in terms of Earth's escape velocity.
5. Final Calculation:
- The new escape velocity becomes: Ve(new planet) = sqrt(9) * Ve(Earth) = 3 * Ve(Earth) = 3 * 11.2 km/s ≈ 33.6 km/s.
Conclusion
Thus, the minimum velocity required by a rocket to escape the gravitational pull of this new planet is approximately 33.6 km/s.
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If earth has a mass 9 times and radius twice that of the planet mass. calculate the minimum velocity required by the rocket to pull off gravitational force of mass. (take escape velocity on the surface of earth is 11.2kms-¹?
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If earth has a mass 9 times and radius twice that of the planet mass. calculate the minimum velocity required by the rocket to pull off gravitational force of mass. (take escape velocity on the surface of earth is 11.2kms-¹? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If earth has a mass 9 times and radius twice that of the planet mass. calculate the minimum velocity required by the rocket to pull off gravitational force of mass. (take escape velocity on the surface of earth is 11.2kms-¹? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If earth has a mass 9 times and radius twice that of the planet mass. calculate the minimum velocity required by the rocket to pull off gravitational force of mass. (take escape velocity on the surface of earth is 11.2kms-¹?.
If earth has a mass 9 times and radius twice that of the planet mass. calculate the minimum velocity required by the rocket to pull off gravitational force of mass. (take escape velocity on the surface of earth is 11.2kms-¹? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If earth has a mass 9 times and radius twice that of the planet mass. calculate the minimum velocity required by the rocket to pull off gravitational force of mass. (take escape velocity on the surface of earth is 11.2kms-¹? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If earth has a mass 9 times and radius twice that of the planet mass. calculate the minimum velocity required by the rocket to pull off gravitational force of mass. (take escape velocity on the surface of earth is 11.2kms-¹?.
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