• Support PF! Buy your school textbooks, materials and every day products Here!

Radius of a planet

  • Thread starter johnsholto
  • Start date
  • #1
10
0
A person stands on a cliff overlooking the sea. He is 100m above the sea level and he observes the horizon to be 5mrad below the local horizontal.

How do you calculate the radius from this information without using a calculator? Trigonometry I am guessing, but I need a better hint.
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,848
1,645
Always draw the picture.

Place an origin O and draw a circle radius R about it. That's your planet.

The observer is at point A, a distance R+h from O - draw the line OA.
The point B, on the circle, is where the tangent to the circle also goes through point A.
The angle between BA and the tangent to OA (through A) is ##\alpha##.

In your case, h=100m and ##\alpha##=5mrad.
This will give you two right-angle triangles to work your trig on.
You may be able to make an approximation based on h<<R.
 
  • #3
10
0
I tried it with:

AB^2 + R^2 = (R+100)^2

AB = (R+100)sinA

But i can't solve the equation without the calculator.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
955
Why do you need to solve it without a calculator?
 
  • #5
10
0
Punishment.

Alas, I just remembered small angle approximation.

cosA = 1-(A^2/2)

cosA = R/R+100

R ≈ 8000000

I did not enjoy this problem.
 
  • #6
Simon Bridge
Science Advisor
Homework Helper
17,848
1,645
hehehe well done.
They get easier.

@hallsofivy: I suspect that it's part of the instructions in the homework - however: does not mean that a calculator cannot be used to figure out how to do it without a calculator.
 

Related Threads on Radius of a planet

  • Last Post
Replies
3
Views
22K
Replies
4
Views
7K
Replies
4
Views
11K
  • Last Post
Replies
0
Views
3K
  • Last Post
Replies
1
Views
6K
Replies
1
Views
5K
Replies
1
Views
1K
Replies
0
Views
1K
Replies
3
Views
5K
Replies
13
Views
1K
Top