I need little help in this question

[Soulax]

Homework Statement

here is the question: "on a certain night an observer on the Earth determines that the angle between the direction to Mars and the direction to the sun is 50 degrees.
on that night assuming circular orbits determine the distance to Mars from Earth using the knows radii of the orbits of both planets."

now my teacher said the Re(radius of earth) is 1.5X10^11m Rm(radius of mars) is 2.3X10^11 and he also gave the distance from Earth to the sun which is 150X10^6Km

Homework Equations

Im almost sure you ull need to use the Law of cosines

The Attempt at a Solution

 

[mplayer]

First, notice that the distance from the Earth to the sun is the same as the radius of its orbit around the sun, so don't let that confuse you. Its just given in different units.

I would suggest drawing out a simple diagram on paper - a top down view of the solar system focusing on the Sun and the orbits of Earth and Mars. Using the two given values for the radii of orbits and the angle between the direction of Mars and direction of the Sun, you should be able to construct a triangle with two sides of known length, and a known value for one of the interior angles. You should be able to find the distance between Earth and Mars (the unknown side of the triangle) using this information. Hope that helps.

 

[Soulax]

so basically what you are saying is that he gave me the radius of the orbit which means he simply gave me two distances? I still don't get it can you please explain more about the radius principle like the RE which is 1.5X10^11 simply means the distance betwwen what and what? thank you...

 

[mplayer]

Re=(1.5x10^11 m): radius of Earth's orbit about the Sun. It is the distance between the Earth and the Sun.

Rm=(2.3x10^11 m): radius of Mars' orbit about the Sun. It is the distance between Mars and the Sun.

Re<Rm: Earth is the third planet from the Sun, while Mars is the fourth. If the angle between the direction of Mars and the Sun (viewing from Earth) were 0 degrees (instead of 50 degrees, like in your problem), Earth and Mars would be lined up perfectly and the distance between them would equal Rm - Re. In this problem, though, that is not the case. Mars and Earth are 'out of line' because the orbital velocities of Earth and Mars are different, relative to the Sun. Make sure to draw a diagram of the setup, it will become much clearer.

 

[Soulax]

Mp thank you very much! I understand now I just thought like RE = thr distance from the center of Earth until the edge of it... :)