# Horizon distance and observers altitude problem

1. Jun 30, 2011

### trina1990

Here's a problem from an astronomy book
"the top of the mountain 1000 m in height can just be visible seen from a ship approaching the land where the mountain is situated. . If the observer's eye is 30 m above sea level. Then how far the ship is from the mountain? "

The main problem is i don't know to measure the horizon distance from a mountain top when the observer itself has some altitude. . Plz suggest me what correction should i need here in the formula of horizon distance "root over 2RH " to determine this distance?

2. Jun 30, 2011

### BobG

You essentially have two mountaintops - one 1000 meters high and one 30 meters high.

Find the distance to the horizon for each and add them together.

Since your elevation is 30 m high, your elevation + the Earth's radius forms a hypotenuse of a second triangle, etc. Both you and the mountain top lie on the local horizon, allowing you to just barely see the mountaintop "over" the Earth's curvature that lies between you.

I don't know what the letters in your formula stand for, since I don't know what book you have, but it's probably a shortcut for getting the approximate distance and the same principle almost certainly applies.

3. Jul 1, 2011

### trina1990

Yes, i tried with this. . Thanks a lot for helping

4. Jul 3, 2011

### Redbelly98

Staff Emeritus
Can you show your calculation? Maybe there's just a arithmetic error somewhere, but we can't help with what went wrong unless we see the details of what you did.