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AP Physics C: Mechanics : Understanding Orbits

Study concepts, example questions & explanations for AP Physics C: Mechanics

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All AP Physics C: Mechanics Resources

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Example Questions

Example Question #1 : Understanding Orbits

If $v_{escape}$ 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 .25R , to escape the gravitational pull of this smaller, denser planet?

Possible Answers:

$\frac{1}{4}v_{escape}$

$2v_{escape}$

$4v_{escape}$

Not enough information

$v_{escape}$ (the same velocity for both planets)

Correct answer:

$2v_{escape}$

Explanation:

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:

$\frac{1}{2}mv^{2}=\frac{GMm}{r}$

$mv^{2}=\frac{2GMm}{r}$

$v^{2}=\frac{2GM}{r}$

$v=\sqrt{\frac{2GM}{r}}$

In this case, $v=v_{escape}$ . Substitute.

$v_{escape}=\sqrt{\frac{2GM}{r}}$

Since the radius of the new planet is 0.25 or $\frac{1}{4}$ the radius of the original planet, and they have the same masses, we can equate:

$v^{*}=\sqrt{\frac{2GM}{\frac{R}{4}}}=\sqrt{4}\sqrt{\frac{2GM}{R}}=2\sqrt{\frac{2GM}{R}}=2v_{escape}$

Where $v_{escape}$ is the escape velocity of the larger planet and $v^{*}$ is the escape velocity of the smaller planet.

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Example Question #2 : Understanding Orbits

A comet is in an elliptical orbit about the Sun, as diagrammed below:

Eliptical orbit

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?

Possible Answers:

It cannot be determined from the information given

The torque is the same at points a and b, but it is not zero

The torque is zero at both a and b

The torque is greater at point a

The torque is greater at point b

Correct answer:

The torque is zero at both a and b

Explanation:

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 $\small r\cdot F = Fr\sin \theta$ , the torque is always zero. That is why the comet's angular momentum is conserved in orbit.

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Example Question #111 : Ap Physics C

A satellite of mass is in an elliptical orbit about the Earth. It's velocity at perigee is $\small v_{p}$ and its orbital radius at perigee is $\small r_{p}$ . If the radius at apogee is $\small 2r_{p}$ , what is its velocity at apogee?

Possible Answers:

$\small 4v_p$

$\frac{v_{p}}{4}$

$\small \frac{v_{p}}{2}$

$\small v_{p}$

$\small 2v_p$

Correct answer:

$\small \frac{v_{p}}{2}$

Explanation:

Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:

$\small L_p=L_a$

$\small mv_pr_p=mv_ar_a$

$\small v_pr_p=v_a(2r_p)$

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Example Question #112 : Ap Physics C

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?

Possible Answers:

This maneuver cannot be accomplished

Opposite the direction of travel

Away from Earth

Towards Earth

In the direction of travel

Correct answer:

In the direction of travel

Explanation:

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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All AP Physics C: Mechanics Resources

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AP Physics C: Mechanics : Understanding Orbits

Study concepts, example questions & explanations for AP Physics C: Mechanics

All AP Physics C: Mechanics Resources

Example Questions

Example Question #1 : Understanding Orbits

Example Question #2 : Understanding Orbits

Example Question #111 : Ap Physics C

Example Question #112 : Ap Physics C

All AP Physics C: Mechanics Resources

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