This problem can be solved using the law of conservation of angular momentum, which states that the angular momentum of a body remains constant if no external torque acts on it.

In the case of the asteroid, the force of gravity acts as a central force, providing no torque. Therefore, the asteroid's angular momentum when it is at its closest approach to the sun is the same as when it is at its greatest distance.

Angular momentum (L) can be calculated using the formula L = mvr, where m is the mass of the asteroid, v is its linear speed, and r is its distance from the sun.

At closest approach (d), L1 = m * 4 km/s * d.
At greatest distance (4d), L2 = m * v2 * 4d.

Since L1 = L2 (due to the conservation of angular momentum), we can set the two equations equal to each other and solve for v2:

m * 4 km/s * d = m * v2 * 4d
4 km/s = v2 * 4
v2 = 1 km/s

So, the asteroid's linear speed at its greatest distance from the sun is 1 km/s. Therefore, the correct answer is d. 1 km/s.

Question

This problem can be solved using the law of conservation of angular momentum, which states that the angular momentum of a body remains constant if no external torque acts on it.

In the case of the asteroid, the force of gravity acts as a central force, providing no torque. Therefore, the asteroid's angular momentum when it is at its closest approach to the sun is the same as when it is at its greatest distance.

Angular momentum (L) can be calculated using the formula L = mvr, where m is the mass of the asteroid, v is its linear speed, and r is its distance from the sun.

At closest approach (d), L1 = m * 4 km/s * d.
At greatest distance (4d), L2 = m * v2 * 4d.

Since L1 = L2 (due to the conservation of angular momentum), we can set the two equations equal to each other and solve for v2:

m * 4 km/s * d = m * v2 * 4d
4 km/s = v2 * 4
v2 = 1 km/s

So, the asteroid's linear speed at its greatest distance from the sun is 1 km/s. Therefore, the correct answer is d. 1 km/s.

Knowee AI · Accepted Answer

This problem can be solved using the law of conservation of angular momentum, which states that the angular momentum of a body remains constant if no external torque acts on it.

In the case of the asteroid, the force of gravity acts as a central force, providing no torque. Therefore, the asteroid's angular momentum when it is at its closest approach to the sun is the same as when it is at its greatest distance.

Angular momentum (L) can be calculated using the formula L = mvr, where m is the mass of the asteroid, v is its linear speed, and r is its distance from the sun.

At closest approach (d), L1 = m * 4 km/s * d.
At greatest distance (4d), L2 = m * v2 * 4d.

Since L1 = L2 (due to the conservation of angular momentum), we can set the two equations equal to each other and solve for v2:

m * 4 km/s * d = m * v2 * 4d
4 km/s = v2 * 4
v2 = 1 km/s

So, the asteroid's linear speed at its greatest distance from the sun is 1 km/s. Therefore, the correct answer is d. 1 km/s.

An asteroid in orbit about the Sun has a linear speed of 4 km/s when at a distance of closest approach d from the sun. What is its linear speed when it is at its greatest distance from the sun, a distance 4d?Select one:a.16 km/sb.2 km/sc.8 km/sd.1 km/s

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