How does one calculate his distance to the center?

[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?

 

[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.

 

[moonman239]

Equatorial radius = 6378.137 km
Polar radius = 6356.7523 km

 

[moonman239]

Thanks for the answer.

 

[rdl]

Calculating the distance to the center of the Earth involves understanding the shape and dimensions of the Earth. The Earth is not a perfect sphere, but rather an oblate spheroid, meaning it is slightly flattened at the poles and bulging at the equator. To accurately calculate the distance to the center, one must take into account the Earth's shape and the observer's altitude.

In this scenario, the observer is located at an altitude of 600 miles above mean sea level. To calculate the actual distance from the center, we can use the equation d = r + h, where d is the actual distance from the center, r is the radius of the Earth (6372 kilometers), and h is the observer's altitude (600 miles or 965.606 kilometers).

Plugging in the values, we get d = 6372 + 965.606 = 7337.606 kilometers. Therefore, the observer is actually 7337.606 kilometers from the center of the Earth.

It is important to note that this calculation assumes a perfectly ellipsoidal Earth. In reality, the Earth's shape is constantly changing and fluctuating, making it difficult to determine an exact distance to the center. Additionally, there are other factors that may affect the accuracy of this calculation, such as variations in altitude and the Earth's gravitational pull.