- #1
SHISHKABOB
- 541
- 1
Okay so I just had this problem on my astronomy midterm and I was sort of stumped by it. I hope I can remember all of it.
Basically there are two planets orbiting around what appears to be a blank area of space. From observations we can see that they are not in a binary orbit with each other and that there is an object of large mass in the blank spot that does not emit any light. Its mass is much greater than that of each of the two planets. In this problem, the orbital period of the inner planet is defined as a "new year" or yn and the orbital radius is defined as ro. Md is defined as a unit of mass. The gravitational constant is defined as 4[itex]\pi[/itex]2yn-2r0-3Md-1
so basically I saw that I was supposed to use Kepler's third law here, where P2 = [itex]\frac{4\pi^{2}}{GM}[/itex]a3
The first planet has yn = 1 and ro = 1
The second planet has yn = 1 and ro = 3
in each case I needed to solve for the mass of the "invisible" object and I got 1 Md and 3 Md respectively.
The problem then asks me to reconcile the difference between these two numbers and... this is where I had no idea what to do. It tells me that the observations can be made many times without a large error and that the gravitational potential energy is such that no correction from general relativity needs to be made.
I simply had no idea what to do so I jokingly answered that there was a sphere of dark matter beyond the orbit of the second planet.
There's *obviously* something wrong with this system, right? The mass of the central body should be the same in both cases. But I have no idea where I should have gone from there.
Basically there are two planets orbiting around what appears to be a blank area of space. From observations we can see that they are not in a binary orbit with each other and that there is an object of large mass in the blank spot that does not emit any light. Its mass is much greater than that of each of the two planets. In this problem, the orbital period of the inner planet is defined as a "new year" or yn and the orbital radius is defined as ro. Md is defined as a unit of mass. The gravitational constant is defined as 4[itex]\pi[/itex]2yn-2r0-3Md-1
so basically I saw that I was supposed to use Kepler's third law here, where P2 = [itex]\frac{4\pi^{2}}{GM}[/itex]a3
The first planet has yn = 1 and ro = 1
The second planet has yn = 1 and ro = 3
in each case I needed to solve for the mass of the "invisible" object and I got 1 Md and 3 Md respectively.
The problem then asks me to reconcile the difference between these two numbers and... this is where I had no idea what to do. It tells me that the observations can be made many times without a large error and that the gravitational potential energy is such that no correction from general relativity needs to be made.
I simply had no idea what to do so I jokingly answered that there was a sphere of dark matter beyond the orbit of the second planet.
There's *obviously* something wrong with this system, right? The mass of the central body should be the same in both cases. But I have no idea where I should have gone from there.