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A geostationary satellite orbits the earth at a height of nearly 36000km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite?
Most Upvoted Answer
A geostationary satellite orbits the earth at a height of nearly 36000...
Mass of the Earth, M = 6.0 × 1024 kg
Radius of the Earth, R = 6400 km = 6.4 × 106 m
Height of a geostationary satellite from the surface of the Earth,
h = 36000 km = 3.6 × 107 m
Gravitational potential energy due to Earth’s gravity at height h,
= -GM / (R + h)
= – 6.67 × 10-11 × 6 × 1024 / (3.6 × 107 + 0.64 × 107)
= -9.4 × 106 J/kg.
Found help full follow me!
Radius of the Earth, R = 6400 km = 6.4 × 106 m
Height of a geostationary satellite from the surface of the Earth,
h = 36000 km = 3.6 × 107 m
Gravitational potential energy due to Earth’s gravity at height h,
= -GM / (R + h)
= – 6.67 × 10-11 × 6 × 1024 / (3.6 × 107 + 0.64 × 107)
= -9.4 × 106 J/kg.
Found help full follow me!
Community Answer
A geostationary satellite orbits the earth at a height of nearly 36000...
Potential Due to Earth's Gravity at Geostationary Satellite Orbit
At a height of nearly 36000km from the surface of the earth, a geostationary satellite orbits the earth. Let's find out the potential due to earth's gravity at the site of this satellite.
Formula for Potential Due to Earth's Gravity
The formula to calculate the potential due to earth's gravity is:
V(r) = - G M / r
Where:
- V(r) is the potential at a distance r from the center of the earth
- G is the universal gravitational constant
- M is the mass of the earth
- r is the distance from the center of the earth
Calculation
Using the above formula, we can calculate the potential at a height of 36000km from the surface of the earth as follows:
V(r) = - G M / r
V(r) = - (6.67 × 10^-11 N m^2/kg^2) × (5.97 × 10^24 kg) / (6.378 × 10^6 m + 3.6 × 10^7 m)
V(r) = - 2.66 × 10^7 J/kg
Explanation
The potential due to earth's gravity at the site of a geostationary satellite orbit is negative because it is a measure of the work that needs to be done to bring a unit mass from infinity to that point against the force of gravity. At this height, the gravitational force is balanced with the centrifugal force due to the satellite's orbital velocity, which keeps the satellite in a fixed position relative to the earth's surface. This height is known as the geostationary orbit, and satellites placed in this orbit are used for communication, weather monitoring, and other applications.
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A geostationary satellite orbits the earth at a height of nearly 36000km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite?
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A geostationary satellite orbits the earth at a height of nearly 36000km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite? 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 A geostationary satellite orbits the earth at a height of nearly 36000km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A geostationary satellite orbits the earth at a height of nearly 36000km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite?.
A geostationary satellite orbits the earth at a height of nearly 36000km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite? 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 A geostationary satellite orbits the earth at a height of nearly 36000km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A geostationary satellite orbits the earth at a height of nearly 36000km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite?.
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