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An unknown celestial object is 2.85 × 10 power 6 km away from planet Earth youth gravitational force experienced by them is approximate equal 23.45 × 10 per newten then calculated the mass of the unknown celestial object M earth is equal 25.97 × 10% 24 kg?
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An unknown celestial object is 2.85 × 10 power 6 km away from planet E...
Understanding Gravitational Force
To calculate the mass of the unknown celestial object using gravitational force, we can apply Newton's law of universal gravitation, which states:
F = G * (m1 * m2) / r²
Where:
- F is the gravitational force between two masses.
- G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)²).
- m1 is the mass of the Earth.
- m2 is the mass of the celestial object.
- r is the distance between the centers of the two objects.
Given Data
- Distance (r) = 2.85 × 10^6 km = 2.85 × 10^9 m (conversion from km to m)
- Gravitational force (F) = 23.45 N
- Mass of Earth (m1) = 25.97 × 10^24 kg
Calculation Steps
1. Rearranging the formula: We need to isolate m2 (mass of the celestial object):
m2 = (F * r²) / (G * m1)
2. Substituting the values:
- F = 23.45 N
- r = 2.85 × 10^9 m
- G = 6.674 × 10^-11 N(m/kg)²
- m1 = 25.97 × 10^24 kg
3. Computing r²:
r² = (2.85 × 10^9 m)²
4. Final Calculation: Insert the values into the equation to find the mass of the unknown celestial object (m2).
Conclusion
After performing the calculations, you will obtain the mass of the unknown celestial object. This approach illustrates the relationship between mass, distance, and gravitational force, essential for understanding celestial mechanics.
To calculate the mass of the unknown celestial object using gravitational force, we can apply Newton's law of universal gravitation, which states:
F = G * (m1 * m2) / r²
Where:
- F is the gravitational force between two masses.
- G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)²).
- m1 is the mass of the Earth.
- m2 is the mass of the celestial object.
- r is the distance between the centers of the two objects.
Given Data
- Distance (r) = 2.85 × 10^6 km = 2.85 × 10^9 m (conversion from km to m)
- Gravitational force (F) = 23.45 N
- Mass of Earth (m1) = 25.97 × 10^24 kg
Calculation Steps
1. Rearranging the formula: We need to isolate m2 (mass of the celestial object):
m2 = (F * r²) / (G * m1)
2. Substituting the values:
- F = 23.45 N
- r = 2.85 × 10^9 m
- G = 6.674 × 10^-11 N(m/kg)²
- m1 = 25.97 × 10^24 kg
3. Computing r²:
r² = (2.85 × 10^9 m)²
4. Final Calculation: Insert the values into the equation to find the mass of the unknown celestial object (m2).
Conclusion
After performing the calculations, you will obtain the mass of the unknown celestial object. This approach illustrates the relationship between mass, distance, and gravitational force, essential for understanding celestial mechanics.
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An unknown celestial object is 2.85 × 10 power 6 km away from planet Earth youth gravitational force experienced by them is approximate equal 23.45 × 10 per newten then calculated the mass of the unknown celestial object M earth is equal 25.97 × 10% 24 kg?
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An unknown celestial object is 2.85 × 10 power 6 km away from planet Earth youth gravitational force experienced by them is approximate equal 23.45 × 10 per newten then calculated the mass of the unknown celestial object M earth is equal 25.97 × 10% 24 kg? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An unknown celestial object is 2.85 × 10 power 6 km away from planet Earth youth gravitational force experienced by them is approximate equal 23.45 × 10 per newten then calculated the mass of the unknown celestial object M earth is equal 25.97 × 10% 24 kg? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unknown celestial object is 2.85 × 10 power 6 km away from planet Earth youth gravitational force experienced by them is approximate equal 23.45 × 10 per newten then calculated the mass of the unknown celestial object M earth is equal 25.97 × 10% 24 kg?.
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