Understanding Orbits - AP Physics C: Electricity and Magnetism
Card 1 of 44
If 
is the escape velocity from the surface of a planet of mass 
and radius 
. What is the velocity necessary for an object launched from the surface of a planet of the same mass, but with a radius that is 
, to escape the gravitational pull of this smaller, denser planet?
If
Tap to reveal answer
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case, 
. Substitute.
Since the radius of the new planet is 
or 
the radius of the original planet, and they have the same masses, we can equate:
Where 
is the escape velocity of the larger planet and 
is the escape velocity of the smaller planet.
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case,
Since the radius of the new planet is
Where
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A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
Tap to reveal answer
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is 
, the torque is always zero. That is why the comet's angular momentum is conserved in orbit.
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is
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A satellite of mass 
is in an elliptical orbit about the Earth. It's velocity at perigee is 
and its orbital radius at perigee is 
. If the radius at apogee is 
, what is its velocity at apogee?
A satellite of mass
Tap to reveal answer
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
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A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
Tap to reveal answer
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
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If is the escape velocity from the surface of a planet of mass and radius . What is the velocity necessary for an object launched from the surface of a planet of the same mass, but with a radius that is , to escape the gravitational pull of this smaller, denser planet?
If
Tap to reveal answer
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case, . Substitute.
Since the radius of the new planet is or the radius of the original planet, and they have the same masses, we can equate:
Where is the escape velocity of the larger planet and is the escape velocity of the smaller planet.
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case,
Since the radius of the new planet is
Where
← Didn't Know|Knew It →
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
Tap to reveal answer
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is , the torque is always zero. That is why the comet's angular momentum is conserved in orbit.
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is
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A satellite of mass is in an elliptical orbit about the Earth. It's velocity at perigee is and its orbital radius at perigee is . If the radius at apogee is , what is its velocity at apogee?
A satellite of mass
Tap to reveal answer
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
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A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
Tap to reveal answer
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
← Didn't Know|Knew It →
If is the escape velocity from the surface of a planet of mass and radius . What is the velocity necessary for an object launched from the surface of a planet of the same mass, but with a radius that is , to escape the gravitational pull of this smaller, denser planet?
If
Tap to reveal answer
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case, . Substitute.
Since the radius of the new planet is or the radius of the original planet, and they have the same masses, we can equate:
Where is the escape velocity of the larger planet and is the escape velocity of the smaller planet.
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case,
Since the radius of the new planet is
Where
← Didn't Know|Knew It →
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
Tap to reveal answer
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is , the torque is always zero. That is why the comet's angular momentum is conserved in orbit.
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is
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A satellite of mass is in an elliptical orbit about the Earth. It's velocity at perigee is and its orbital radius at perigee is . If the radius at apogee is , what is its velocity at apogee?
A satellite of mass
Tap to reveal answer
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
← Didn't Know|Knew It →
A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
Tap to reveal answer
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
← Didn't Know|Knew It →
If is the escape velocity from the surface of a planet of mass and radius . What is the velocity necessary for an object launched from the surface of a planet of the same mass, but with a radius that is , to escape the gravitational pull of this smaller, denser planet?
If
Tap to reveal answer
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case, . Substitute.
Since the radius of the new planet is or the radius of the original planet, and they have the same masses, we can equate:
Where is the escape velocity of the larger planet and is the escape velocity of the smaller planet.
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case,
Since the radius of the new planet is
Where
← Didn't Know|Knew It →
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
Tap to reveal answer
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is , the torque is always zero. That is why the comet's angular momentum is conserved in orbit.
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is
← Didn't Know|Knew It →
A satellite of mass is in an elliptical orbit about the Earth. It's velocity at perigee is and its orbital radius at perigee is . If the radius at apogee is , what is its velocity at apogee?
A satellite of mass
Tap to reveal answer
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
← Didn't Know|Knew It →
A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
Tap to reveal answer
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
← Didn't Know|Knew It →
If is the escape velocity from the surface of a planet of mass and radius . What is the velocity necessary for an object launched from the surface of a planet of the same mass, but with a radius that is , to escape the gravitational pull of this smaller, denser planet?
If
Tap to reveal answer
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case, . Substitute.
Since the radius of the new planet is or the radius of the original planet, and they have the same masses, we can equate:
Where is the escape velocity of the larger planet and is the escape velocity of the smaller planet.
Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:
In this case,
Since the radius of the new planet is
Where
← Didn't Know|Knew It →
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
A comet is in an elliptical orbit about the Sun, as diagrammed below:
The mass of the comet is very small compared to the mass of the Sun.
In the diagram above, how does the net torque on the comet due to the Sun's gravitational force compare at the two marked points?
Tap to reveal answer
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is , the torque is always zero. That is why the comet's angular momentum is conserved in orbit.
Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is
← Didn't Know|Knew It →
A satellite of mass is in an elliptical orbit about the Earth. It's velocity at perigee is and its orbital radius at perigee is . If the radius at apogee is , what is its velocity at apogee?
A satellite of mass
Tap to reveal answer
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:
← Didn't Know|Knew It →
A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
A satellite is in an elliptical orbit about the Earth. If the satellite needs to enter a circular orbit at the apogee of the ellipse, in what direction will it need to accelerate?
Tap to reveal answer
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.
← Didn't Know|Knew It →