# Homework Help: Urgent Help Needed

1. Oct 7, 2005

### Tom McCurdy

Urgent Help Needed!!!

Alright I have an odd question
I have this point at
42.29179 degrees N, 83.71636 degrees W

and I have this program that calculates distances of a rocket i'm firing that goes like 50 meters north and 100 meters east and i need to calculate the new GPS coordinates...

How Would i do this.... I need to submit my new coordinates in less than 4 hours!!!!

thx
tom

Last edited: Oct 7, 2005
2. Oct 7, 2005

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3. Oct 7, 2005

### Tom McCurdy

I need a more accurate translation of how many meters are in a second

4. Oct 7, 2005

### Tide

The length of 1 second of arc in longitude depends on the latitude.

5. Oct 7, 2005

### Tom McCurdy

So what would be the new coordinates from

42.29179 degrees N, 83.71636 degrees W

That is 50 Meters North and 100 Meters more east
and how would i do the calculations for that

6. Oct 7, 2005

### Tom McCurdy

To get the coordinates of the system first the simulation was run. The simulation shows most of the coordinates landing about 100 meters East and 50 meters North of the starting position. To calculate the new coordinate from this I researched and found that one second is approximetly equal to 30.9 meters. Then I took 100/30.9=3.236 seconds added East. To get the fractional part that 3.236 seconds add I simply take 3.236/(60*60)=0.000899 degrees. A similar method is employed in finding the added north componet. 50/30.9=1.618 seconds 1.618/(60*60)=0.000449

This gives 42.29179 degrees N + 0.000899 degrees N=42.29269

83.71636 degrees W- 0.000449 E (subtract since its in the east direction) =83.71591

7. Oct 7, 2005

### Tide

You have a little bit of a problem here though, practically speaking, it is unlikely to make much real difference but you are displaying 7 significant digits. The coordinates you end up with will be slightly different depending on whether you go 50 m north then 100 m east or 100 m east then 50 m north!

I'll let you work out the details but suppose the radius of the Earth is R (for simplicity take it to be in meters). Then, in travelling north or south, the change in latitude is

$$\Delta latitude = \frac {distance}{R}$$

In travelling east or west the change in longitude is

$$\Delta longitude = \frac {distance}{R \cos latitude}$$

with signs appropriate to the direction of travel. Notice that the change in longitude depends on the latitude at which you begin your east-west travel.

(Unfortunately TeX isn't working so I'm not sure how those equations look.)

8. Oct 7, 2005