Question
Download Solution PDFA satellite moving in a circular orbit around earth has a total (kinetic + potential) energy Eo. Its potential energy will be ____
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Some definition of energy:
| Terms | Gravitational Potential Energy (U) | The kinetic energy of a satellite (KE) | The total energy of a system (T) |
| Definition |
The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force. |
The kinetic energy of a satellite in a circular orbit is half its gravitational energy and is positive instead of negative. |
The sum of the kinetic and gravitational potential energy of a system is its total energy and this total energy is conserved in orbital motion. |
| Mathematical expression | |||
| Where M = mass of earth, m = mass of the body, r = distance from the earth | Where M = mass of earth, m = mass of the body, r = distance from the earth | Where M = mass of earth, m = mass of the body, r = distance from the earth |
EXPLANATION:
Given - The total energy of a system (T) = Eo
- As we know, Gravitational Potential Energy (U) is
Equation 1 can be written as
⇒ U = 2Eo
- Hence option 1 is the answer.
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