Halley's comet moves about the Sun in a highly elliptical orbit. At its closest approach, it is a distance of 8.90 1010 m from the Sun and has a speed of 54 km/s. When it is farthest from the Sun, the two are separated by 5.30 1012 m. Find the comet's speed at that point in its orbit.

Nevermind figured it out, just have to use m1v1=m2v2.

v² =G•M/R²

(v1/v2)²=R2/R1,
v2=v1•sqrt(R1/R2)

To find the comet's speed at its farthest point from the Sun, we can make use of the conservation of angular momentum.

Angular momentum is given by the product of mass, velocity, and the radius:

L = m * v * r

Since the mass of the comet remains constant, we can express the angular momentum at its closest approach as:

L_initial = m * v_initial * r_closest

And at its farthest point as:

L_final = m * v_final * r_farthest

Since angular momentum is conserved, we can equate these two expressions:

L_initial = L_final

m * v_initial * r_closest = m * v_final * r_farthest

We can solve for v_final, the comet's speed at its farthest point from the Sun:

v_final = (v_initial * r_closest) / r_farthest

Let's plug in the given values:

v_initial = 54 km/s = 54,000 m/s
r_closest = 8.90 * 10^10 m
r_farthest = 5.30 * 10^12 m

Calculating:

v_final = (54,000 m/s * 8.90 * 10^10 m) / (5.30 * 10^12 m)
v_final = 91.13 m/s (rounded to two decimal places)

Therefore, the comet's speed at its farthest point from the Sun is approximately 91.13 m/s.

To find the comet's speed when it is farthest from the Sun, we can use the principle of conservation of angular momentum.

The principle of conservation of angular momentum states that the angular momentum of an object remains constant as long as no external torques are acting on it. In the case of an object orbiting around a central body, such as the comet orbiting the Sun, the angular momentum is given by:

Angular Momentum = mass × velocity × radius

At its closest approach, the comet's distance from the Sun is 8.90 × 10^10 m, and its speed is 54 km/s. We can calculate the angular momentum at this point:

Angular Momentum(closeset) = mass × velocity(closeset) × radius(closeset)
= mass × 54 × 10^3 m/s × 8.90 × 10^10 m

Now, when the comet is farthest from the Sun, it is separated by a distance of 5.30 × 10^12 m. We want to find the comet's speed at this point. Since the angular momentum is conserved, we can set the angular momentum at the closest approach equal to the angular momentum when it is farthest from the Sun:

Angular Momentum(closeset) = Angular Momentum(farthest)

mass × 54 × 10^3 m/s × 8.90 × 10^10 m = mass × velocity(farthest) × radius(farthest)

We can rearrange this equation to solve for the velocity(farthest):

velocity(farthest) = (mass × 54 × 10^3 m/s × 8.90 × 10^10 m) / (mass × radius(farthest))

The mass of the comet is the same in both cases, so it cancels out. We are left with:

velocity(farthest) = 54 × 10^3 m/s × 8.90 × 10^10 m / radius(farthest)

Substituting the given value for the radius(farthest):

velocity(farthest) = 54 × 10^3 m/s × 8.90 × 10^10 m / 5.30 × 10^12 m

Calculating this expression gives us the speed of the comet when it is farthest from the Sun.