A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.70 × 104 m/s, and the radius of the orbit is 5.80 × 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.50 × 106 m. What is the orbital speed of the second satellite?

My physics optional extra work: This would be helpful so I can compare the solutions here as I do the work by myself.

Well, well, well, looks like we have some space travelers here! Let's calculate the orbital speed of that second satellite, shall we?

To do this, we can use the principle of conservation of angular momentum. According to this principle, the product of an object's moment of inertia and its angular velocity is constant as long as no external torques are acting on it. In simpler terms, it means that as long as the radius of the orbit changes, the orbital speed will also change to keep that product constant.

In the case of the first satellite, we have a speed of 1.70 × 10^4 m/s and a radius of 5.80 × 10^6 m. We can calculate the angular momentum (L1) of the first satellite using the formula L = mvr, where "m" is the mass of the satellite, "v" is the speed, and "r" is the radius.

Now, let's move on to the second satellite, with a radius of 8.50 × 10^6 m. The angular momentum (L2) of the second satellite will be the same as the first one. We can use the same formula to find the orbital speed (v2) of the second satellite, but this time we have the radius (r2), and we need to solve for "v2."

So, we have L1 = L2, which means m1v1r1 = m2v2r2. As we can see, the mass of the satellites cancels out, leaving us with v1r1 = v2r2.

Now, we just need to plug in the values: (1.70 × 10^4 m/s)(5.80 × 10^6 m) = v2(8.50 × 10^6 m). Solving for v2, we get:

v2 = (1.70 × 10^4 m/s)(5.80 × 10^6 m) / (8.50 × 10^6 m)

And voila! You should be able to calculate the orbital speed of that second satellite. Just be careful not to get stuck in space traffic! Safe travels!

To find the orbital speed of the second satellite, you can use the concept of conservation of angular momentum.

The formula for angular momentum is given by:

L = mvr

Where L is the angular momentum of the satellite, m is the mass of the satellite, v is the orbital speed of the satellite, and r is the radius of the orbit.

Since both satellites are in circular orbits around the same planet, we can assume that their masses are the same. Therefore, we can set up the equation:

mv₁r₁ = mv₂r₂

Where v₁ and v₂ are the orbital speeds of the first and second satellites, and r₁ and r₂ are the radii of their respective orbits.

We know the orbital speed of the first satellite (v₁ = 1.70 × 10⁴ m/s) and the radius of its orbit (r₁ = 5.80 × 10⁶ m). We want to find the orbital speed of the second satellite (v₂) and we are given the radius of its orbit (r₂ = 8.50 × 10⁶ m).

Rearranging the equation, we can solve for v₂:

v₂ = (v₁r₁) / r₂

Substituting the given values, we get:

v₂ = (1.70 × 10⁴ m/s * 5.80 × 10⁶ m) / (8.50 × 10⁶ m)

Calculating this expression will give you the orbital speed of the second satellite.