Astronomy Question help Please?

Question

5) A planet has an angular size of 20 degrees. If the planet moves twice the distance away, its angular size will be

a) 5 degrees
b) 10 degrees
c) 20 degrees
d) 40 degrees
e) can not determine from information given

Answer 1

It would have to be HUGE.

First off, the choiceof the word size is poor, but not critical and the correct answer is b.

Now, just to compare, guess what angular measurement the full moon has?


1/2 a degree, so for a planet to have a measurement of 20 degrees it would have to be huge and close. . .

Answer 2

Consider (better...draw) a right triangle, with side 'a' (the planet in the sky), 'b' (the unknown distance to the planet), and 'c', the hypoteneuse. The angle subtended by a is A and is 20 degrees. The tangent of 20 degrees is a/b (length of the side opposite of the known angle divided by the length of the side adjacent to the unknown angle). Now, tables show that the tangent of 20 degrees is .36397. If the unknown distance is doubled, and the planet stays the same actual size, then the height 'a' stays the same, 'b' doubles, and the tangent to the new angle is a/2b, or .181985. The angle whose tangent is .181985 is just less than 10 degrees 19 minutes of arc. So, the angular size of the planet at the greater distance is just a bit more than half what it was at the closer distance.

By the way, the sky subends 180 degrees of arc, not 45 as suggested by one answerer...remember, the stars move 15 degrees per hour, and a half day is 12 hours...12 X 15 (at the celestial equator) is 180 degrees.

Answer 3

Ramshi has it right. When the planet moves to twice the distance, its angular size (angular diameter) shrinks to half of what it was.

You can check it out with a simple experiment. You'll need a regular sized piece of paper and a pencil, pen, or sharpie, a large ball (a soccer ball or something about the same size), a medium-sized or large room, and optionally, a ruler.

1) Put the ball in one corner of the room.
2) Stand in the middle of the room, and hold the paper up at arms length so it lines up with the ball.
3) Make a mark on the paper that matches where you see the bottom of the ball.
4) Keeping the bottom of the ball and your mark lined up, make a second mark on the paper that matches where you see the top of the ball.
5) Stand in the far (diagonal) corner of the room from the ball.
6) Line up the bottom mark with the bottom of the ball
7) Keeping the bottom of the ball and your first mark lined up, make a mark on the paper that matches where you now see the top of the ball.
8) The last mark you made should be halfway between the the first two, showing that the ball's angular size (angular diameter) is half as big when you are looking at it from the far corner of the room as it was when you were looking at it from the center of the room.
9) Optional. Use your ruler to measure the distances between the marks and compare them.

This all works when the angular size isn't too big. But for things that appear smaller than a sheet of paper held at arm's length it's pretty close.

Answer 4

Regardless of whether these numbers make sense, our 3-dimensional space is very close to being flat or Euclidian, so apparent size with vary inversely with the square of the distance. Therefore the planet will appear to subtend an angle of only 5 degrees at twice the distance (20/2^2).

(Later) I was wrong. The question was about angles, not sizes. The angle at twice the distance is half the size, not a quarter. However, the area covered at twice the distance is 1/4, because areas are proportional to squares: 10^2 / 20^2 = 100 / 400.

Answer 5

Agreed your question is a bit awkward, but easily understood. The answerer who stated that "there is no such thing as angular size" needs to head back for some basic reading in astronomy, and needs to stop jumping in with answers about subjects he knows nothing about--as all too many people do on Y!A.

All that said, the rule you are fishing for is that the angular width of a sky object goes as the square of the reciprocal of its distance away. So the answer is that if the planet moved to twice the distance away, it would appear 4.4721 degrees across.

Also, it is true that a 20 degree wide object is not likely. The whole visible sky is only about 45 degrees across. So a 20 degree wide object is the Goodyear Blimp about 15 feet above your head. You owe them rent.

Answer 6

Sir:

A planet with the angular size of 20 degrees is so cotton picking big we would be sucked right into it and never survive. On a given night, the angular size of the visible sky is only something like 45 degrees.

So, I choose answer "e" based upon what I think is unreasonable basic starting information.

Answer 7

I believe that angular size is relative to the distance of the object from the measurment source. Therefore unless you know the original distance to the source you cannot determine the new angular size with movement. I would choose E.

Answer 8

The answer is "e".
An "angular size" does not exist. Does not make geometric sense.
You may say "angular speed" or momentum, or the angle of its axis referred to the ecliptic.

Unless by "angular size" they mean the visual angle from the center of the orbit of the two lines tangents to the planet, but then 20° is enormous. Not even Jupiter measures that and not even Mercury although it is very close to the Sun.
Now, if angular size is the apparent angle of a planet as it is seen through a telescope, it may well be correct. In such case the right answer could be 10.
Sorry, I am not an Astronomer.

Answer 9

b. 10 degrees