Diameter of the moon = 3480 km
Distance from surface of the earth
= Distance to centre - radius of the earth
= 384400-6400 km
= 378000 km
Since the angle is very small, we can approximate the arc-length by the chord length, equal to the diameter.
Angle subtended
= 3480/378000
= 0.0092 radian
If we had used the chord instead, the difference in angle calculated would have been 0.0000000325 radians more.
i.e.
angle
= 2*sin-1(1740/37800)
= 0.0092 radian
The Moon has a diameter of about 3480 km and an orbital radius of about 384 400 km from the centre of Earth. Suppose that the Moon is directly overhead. What is the measure of the angle subtended by the diameter to the Moon as measured by an astronomer on the surface of Earth? Answer in both radians and degrees.
3 answers
Sorry, I actually have a question. According to the question that was posted. If I were to solve this question, without knowing the radius of the earth before hand. Is there any other solution??
The other answer didn't really help me at all so I hope my explanation works better.
What we're trying to find is the angle subtended from the diameter of the moon right? That's the angle that's right opposite the side-length aka diameter of the moon if you need to rephrase that in your head to make sense.
We'll call that angle ø. Hopefully you already know that how to find angle ø but if you don't —> ø = a/r.
a means arc-length
r means radius
So the question has really just handed us the answer.
The earth is where angle ø is. The orbital radius is just the radius. The diameter of the moon is our arc length. You don't need to know anything about the radius of the earth because it's not given to you, and the question isn't asking for you to find that.
Let's go over it again.
ø = a/r
a (arc length) = diameter = 3480 km
r (radius) = orbital radius = 384400 km
thus ø = 3480/384400 (MAKE SURE YOU PUT IT INTO YOUR CALCULATOR RIGHT THE FIRST TIME. That was what kept me stuck on this lol)
ø = approx. 0.009 radian.
Which in degrees is
0.009 rad x 180/π = 0.5˚ approx.
There you go.
What we're trying to find is the angle subtended from the diameter of the moon right? That's the angle that's right opposite the side-length aka diameter of the moon if you need to rephrase that in your head to make sense.
We'll call that angle ø. Hopefully you already know that how to find angle ø but if you don't —> ø = a/r.
a means arc-length
r means radius
So the question has really just handed us the answer.
The earth is where angle ø is. The orbital radius is just the radius. The diameter of the moon is our arc length. You don't need to know anything about the radius of the earth because it's not given to you, and the question isn't asking for you to find that.
Let's go over it again.
ø = a/r
a (arc length) = diameter = 3480 km
r (radius) = orbital radius = 384400 km
thus ø = 3480/384400 (MAKE SURE YOU PUT IT INTO YOUR CALCULATOR RIGHT THE FIRST TIME. That was what kept me stuck on this lol)
ø = approx. 0.009 radian.
Which in degrees is
0.009 rad x 180/π = 0.5˚ approx.
There you go.
0 answers