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A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100m. The orbital angular momentum of the body is 100kg * m ^ 2 * s ^ - 1 The time period of motion of the body is hours.?
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A body of mass 1 kg is moving under a central force in an elliptic orb...
Elliptic Orbit and Orbital Angular Momentum
An elliptic orbit is a type of orbit in which a celestial body moves around another celestial body in an elliptical path. The semi-major axis represents the longest distance between the two bodies, while the semi-minor axis represents the shortest distance.
Givens:
- Mass of the body (m) = 1 kg
- Semi-major axis (a) = 1000 m
- Semi-minor axis (b) = 100 m
- Orbital angular momentum (L) = 100 kg * m^2 * s^-1
Calculating Eccentricity:
The eccentricity (e) of an elliptical orbit can be calculated using the formula:
e = sqrt(1 - (b^2/a^2))
Given b = 100 m and a = 1000 m, we can calculate the eccentricity:
e = sqrt(1 - (100^2/1000^2))
= sqrt(1 - 0.01)
= sqrt(0.99)
≈ 0.995
Calculating Angular Momentum:
The orbital angular momentum (L) of a body moving under a central force can be calculated using the formula:
L = m * sqrt(G * M * a * (1 - e^2))
Where:
- G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the central body (assumed to be much larger than the orbiting body)
Given L = 100 kg * m^2 * s^-1 and e ≈ 0.995, we can rearrange the formula to solve for M:
M = (L^2) / (m^2 * G * a * (1 - e^2))
Substituting the given values:
M = (100^2) / (1^2 * 6.67430 × 10^-11 * 1000 * (1 - 0.995^2))
Calculating Time Period:
The time period (T) of an elliptical orbit can be calculated using Kepler's third law:
T = 2π * sqrt((a^3) / (G * M))
Substituting the calculated value of M and the given values of a and G:
T = 2π * sqrt((1000^3) / (6.67430 × 10^-11 * M))
Finally, we can calculate the time period in hours by dividing the result by 3600 (since there are 3600 seconds in an hour).
An elliptic orbit is a type of orbit in which a celestial body moves around another celestial body in an elliptical path. The semi-major axis represents the longest distance between the two bodies, while the semi-minor axis represents the shortest distance.
Givens:
- Mass of the body (m) = 1 kg
- Semi-major axis (a) = 1000 m
- Semi-minor axis (b) = 100 m
- Orbital angular momentum (L) = 100 kg * m^2 * s^-1
Calculating Eccentricity:
The eccentricity (e) of an elliptical orbit can be calculated using the formula:
e = sqrt(1 - (b^2/a^2))
Given b = 100 m and a = 1000 m, we can calculate the eccentricity:
e = sqrt(1 - (100^2/1000^2))
= sqrt(1 - 0.01)
= sqrt(0.99)
≈ 0.995
Calculating Angular Momentum:
The orbital angular momentum (L) of a body moving under a central force can be calculated using the formula:
L = m * sqrt(G * M * a * (1 - e^2))
Where:
- G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the central body (assumed to be much larger than the orbiting body)
Given L = 100 kg * m^2 * s^-1 and e ≈ 0.995, we can rearrange the formula to solve for M:
M = (L^2) / (m^2 * G * a * (1 - e^2))
Substituting the given values:
M = (100^2) / (1^2 * 6.67430 × 10^-11 * 1000 * (1 - 0.995^2))
Calculating Time Period:
The time period (T) of an elliptical orbit can be calculated using Kepler's third law:
T = 2π * sqrt((a^3) / (G * M))
Substituting the calculated value of M and the given values of a and G:
T = 2π * sqrt((1000^3) / (6.67430 × 10^-11 * M))
Finally, we can calculate the time period in hours by dividing the result by 3600 (since there are 3600 seconds in an hour).
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A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100m. The orbital angular momentum of the body is 100kg * m ^ 2 * s ^ - 1 The time period of motion of the body is hours.?
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A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100m. The orbital angular momentum of the body is 100kg * m ^ 2 * s ^ - 1 The time period of motion of the body is hours.? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100m. The orbital angular momentum of the body is 100kg * m ^ 2 * s ^ - 1 The time period of motion of the body is hours.? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100m. The orbital angular momentum of the body is 100kg * m ^ 2 * s ^ - 1 The time period of motion of the body is hours.?.
A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100m. The orbital angular momentum of the body is 100kg * m ^ 2 * s ^ - 1 The time period of motion of the body is hours.? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100m. The orbital angular momentum of the body is 100kg * m ^ 2 * s ^ - 1 The time period of motion of the body is hours.? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 1 kg is moving under a central force in an elliptic orbit with semi major axis 1000 m and semi minor axis 100m. The orbital angular momentum of the body is 100kg * m ^ 2 * s ^ - 1 The time period of motion of the body is hours.?.
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