In the following, what are the quantities
which that are conserved?
a) Linear momentum of planet
b) Angular momentum of planet
c) Total energy of planet
d) Potential energy of a planet
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The answer will be (c) The total energy of the planet.
Here's why...
One of Kepler's laws states that the areal velocity of a planet is always constant.
This means that the planet sweeps equal area in equal intervals of time.
Kepler's laws also state that the orbit of a planet is elliptical, and the sun is at one of the ellipse's foci.
These two points lead to this answer.
Now, since the planet is in an elliptical orbit, its linear velocity will obviously not be constant, as its direction will keep changing.
The angular velocity too will not be constant, because a planet slows down when away from the sun. This causes it to cover different lengths of arcs in equal intervals of time as compared to the planet close to the sun. Due to this, the rate of change of angular displacement is variable. However, the area subtended by these arcs at the focus remains equal at all time.
The potential energy too will be variable as the distance of the planet from the sun keeps changing as it orbits the sun. Due to this, its distance from the source of the conservative field's source keeps changing. This causes differences in the potential energy.
If we assume that the there is no other force on the planet, however, it would mean that the only force is the sun's gravity. This means that the total energy of the planet is conserved, as it is in a conservative field and its kinetic and potential energy will always add up to a constant value.
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Here's your answer...
The answer will be (c) The total energy of the planet.
Here's why...
One of Kepler's laws states that the areal velocity of a planet is always constant.
This means that the planet sweeps equal area in equal intervals of time.
Kepler's laws also state that the orbit of a planet is elliptical, and the sun is at one of the ellipse's foci.
These two points lead to this answer.
Now, since the planet is in an elliptical orbit, its linear velocity will obviously not be constant, as its direction will keep changing.
The angular velocity too will not be constant, because a planet slows down when away from the sun. This causes it to cover different lengths of arcs in equal intervals of time as compared to the planet close to the sun. Due to this, the rate of change of angular displacement is variable. However, the area subtended by these arcs at the focus remains equal at all time.
The potential energy too will be variable as the distance of the planet from the sun keeps changing as it orbits the sun. Due to this, its distance from the source of the conservative field's source keeps changing. This causes differences in the potential energy.
If we assume that the there is no other force on the planet, however, it would mean that the only force is the sun's gravity. This means that the total energy of the planet is conserved, as it is in a conservative field and its kinetic and potential energy will always add up to a constant value.
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