What is the effect of increasing the mass of a satellite on its orbital radius if the orbital speed is to remain constant?
Practice Questions
1 question
Q1
What is the effect of increasing the mass of a satellite on its orbital radius if the orbital speed is to remain constant?
The orbital radius must increase
The orbital radius must decrease
The orbital radius remains the same
It has no effect on the orbital radius
If the orbital speed is to remain constant, increasing the mass of the satellite requires an increase in the orbital radius due to the balance of gravitational and centripetal forces.
Questions & Step-by-step Solutions
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Q
Q: What is the effect of increasing the mass of a satellite on its orbital radius if the orbital speed is to remain constant?
Solution: If the orbital speed is to remain constant, increasing the mass of the satellite requires an increase in the orbital radius due to the balance of gravitational and centripetal forces.
Steps: 7
Step 1: Understand that a satellite orbits a planet due to the balance between gravitational force and centripetal force.
Step 2: Recognize that gravitational force depends on the mass of the satellite and the mass of the planet, as well as the distance between them.
Step 3: Know that centripetal force is related to the speed of the satellite and its distance from the planet.
Step 4: If we want to keep the orbital speed constant while increasing the mass of the satellite, we need to adjust the distance (orbital radius).
Step 5: Increasing the mass of the satellite means that the gravitational force acting on it increases.
Step 6: To maintain the same orbital speed, the satellite must move further away from the planet, which means increasing the orbital radius.
Step 7: Therefore, if the mass of the satellite increases, the orbital radius must also increase to keep the speed constant.
