# How does one calculate his distance to the center?

1. Jun 5, 2010

### moonman239

Let's assume that an observer on a perfectly ellipsoidal Earth determines that his distance to the center of Earth is 6372 kilometers, not counting his altitude. If his altitude is 600 miles above mean sea level, then approximately how far is he in actuality from the center?

2. Jun 7, 2010

### Rasalhague

Hi Moonman 239, give my regards to the other 238! (Or however many there are; I guess more might have joined since you.)

As no values for the semimajor and semiminor axes are given in your question, I'll take the first and simplest kind of mean radius (mean sea level) estimate by the IUGG, International Union of Geodesy and Geophysics, from here ( http://en.wikipedia.org/wiki/Earth_radius#Mean_radii ), namely 6 371 km. I reckon your observer would be 6 371 km + (6 372 - 6 371) km + 966 km = 6 372 km + 966 km = 7 338 km from the centre. That is, the observer's radial distance not including their altitude, plus the difference between their radial distance and the mean, plus their altitude above the mean. Or, more simply, the observer's altitude above the mean plus the mean. Does that sound reasonable? If it doesn't make sense, try drawing a picture. Don't trust me though, I might have made a mistake, or misunderstood the question.

3. Jun 8, 2010