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Fynjy0 [20]
3 years ago
11

The Trojan asteroids are found:_________ a) orbiting around the Kuiper Belt body Hector. b) beyond Neptune, with orbits similar

to Pluto's. c) sixty degrees ahead or behind Jupiter, sharing its orbit about the Sun. d) with the others, between Mars and Jupiter; their red color gives them their name.
Physics
2 answers:
xenn [34]3 years ago
5 0

Answer:

The correct option is;

c) sixty degrees ahead or behind Jupiter, sharing its orbit about the Sun.

Explanation:

The Trojan asteroids are the Jupiter trojans consists of asteroid that are on the same orbit as Jupiter while moving around the Sun. The Trojans can be located at the points Lagrange points L4 and L5, which are 60° ahead and 60°  behind Jupiter's orbit respectively.

The first Trojan asteroid to be detected was 588 Achilles by Max Wolf in 1906. At at October, the total number of the identified Trojan asteroid was  7,040.

Katarina [22]3 years ago
4 0

Answer:

c) sixty degrees ahead or behind Jupiter, sharing its orbit about the Sun.

Explanation:

Trojan Asteroids are one type of co-orbital object. It is a small body that shares the orbit of a larger one, they remain in a stable orbit at approximately 60° ahead or behind the main body near one of its lagrangian points L4 and L5, they can share the orbits of planets or of large moons. Due to the perturbations by other planets, their distributions are elongated along the orbit, there are currently over 4,800 known trojan asteroids associated with Jupiter.

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A charge is divided q1 and (q-q1)what will be the ratio of q/q1 so that force between the two parts placed at a given distance i
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Answer:

q / q_{1} = 2, assuming that q_{1} and (q - q_{1}) are point charges.

Explanation:

Let k denote the coulomb constant. Let r denote the distance between the two point charges. In this question, neither k and r depend on the value of q_{1}.

By Coulomb's Law, the magnitude of electrostatic force between q_{1} and (q - q_{1}) would be:

\begin{aligned}F &= \frac{k\, q_{1}\, (q - q_{1})}{r^{2}} \\ &= \frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\end{aligned}.

Find the first and second derivative of F with respect to q_{1}. (Note that 0 < q_{1} < q.)

First derivative:

\begin{aligned}\frac{d}{d q_{1}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\right] \\ &= \frac{k}{r^{2}}\, \left[\frac{d}{d q_{1}} [q\, q_{1}] - \frac{d}{d q_{1}}[{q_{1}}^{2}]\right]\\ &= \frac{k}{r^{2}}\, (q - 2\, q_{1})\end{aligned}.

Second derivative:

\begin{aligned}\frac{d^{2}}{{d q_{1}}^{2}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q - 2\, q_{1})\right] \\ &= \frac{(-2)\, k}{r^{2}}\end{aligned}.

The value of the coulomb constant k is greater than 0. Thus, the value of the second derivative of F with respect to q_{1} would be negative for all real r. F\! would be convex over all q_{1}.

By the convexity of \! F with respect to \! q_{1} \!, there would be a unique q_{1} that globally maximizes F. The first derivative of F\! with respect to q_{1}\! should be 0 for that particular \! q_{1}. In other words:

\displaystyle \frac{k}{r^{2}}\, (q - 2\, q_{1}) = 0<em>.</em>

2\, q_{1} = q.

q_{1} = q / 2.

In other words, the force between the two point charges would be maximized when the charge is evenly split:

\begin{aligned} \frac{q}{q_{1}} &= \frac{q}{q / 2} = 2\end{aligned}.

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