How does one calculate the distance (or length) on the ground

In summary, calculating the distance on the ground suspended by one minute of arc or one second of arc at a particular point on the Earth's surface requires taking into account the Earth's shape, known as the geoid. While the distance equivalent to one degree of arc in latitude is constant, the distance equivalent to one degree of arc in longitude varies due to the Earth's non-spherical shape. To accurately calculate distance on the ground in terms of both latitude and longitude, one must use geodetic latitude instead of the angle between the equatorial plane and the point. The Earth's radius, which varies depending on latitude, must also be considered when making these calculations.
  • #1
Pollock
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How does one calculate the distance (or length) on the ground suspended by one minute of arc (or one second of arc) at a particular point on the Earth's surface,given its latitude/longitude in degrees/ minutes /seconds ?.Where would one get the Earth radius of sufficient accuracy as a function of latitude ?.

Pollock
 
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  • #2


For a simple answer you can assume the Earth is a sphere then the length of an arc segment is failry simple to work out.

More complete answer require more terms to account for the Earth's shape (geoid) see http://en.wikipedia.org/wiki/Latitude
 
  • #3


The distance on the ground equivalent to one degree of arc will be the same at any latitude (assuming the Earth as a perfect sphere).But this will not be so for the distance equivalent to a degree of longitude as circles of constant latitude get smaller towards the poles.How does one take account of this to calculate distance on the ground in terms of both latitude and longitude anywhereon the Earth's surface
 
  • #4


Pollock said:
The distance on the ground equivalent to one degree of arc will be the same at any latitude (assuming the Earth as a perfect sphere).But this will not be so for the distance equivalent to a degree of longitude as circles of constant latitude get smaller towards the poles.How does one take account of this to calculate distance on the ground in terms of both latitude and longitude anywhereon the Earth's surface
The arc length of one degree change in latitude is very, very close to constant everywhere on the non-spherical surface of the Earth. The reason why is that latitude of a point on the surface is not the angle subtended between the Earth's equatorial plane and the line connecting the center of the Earth and the point in question. The latitude of a point is instead the angle subtended between the Earth's equatorial plane and the line defined by the normal to an idealization of the Earth's non-spherical surface. This angle is more precisely called the geodetic latitude of the point. The word "latitude" without a qualifier means geodetic latitude.
 

1. How is distance on the ground measured?

Distance on the ground is typically measured using a unit of length, such as meters or feet. This can be done by physically measuring the distance using a measuring tool, or by using mathematical calculations based on known distances.

2. What is the formula for calculating distance on the ground?

The formula for calculating distance on the ground is: distance = speed x time. This formula applies when the object is moving at a constant speed.

3. How does one calculate distance on the ground using a map?

To calculate distance on the ground using a map, you will need to use a map scale. The scale will show the ratio of a distance on the map to the actual distance on the ground. You can then measure the distance on the map and use the scale to determine the actual distance on the ground.

4. What factors can affect the accuracy of distance calculations on the ground?

The accuracy of distance calculations on the ground can be affected by several factors, including the precision of the measuring tool, the terrain and obstacles present, and any errors in the input data or calculations.

5. How do scientists use distance calculations on the ground in their research?

Scientists use distance calculations on the ground in a variety of ways, such as measuring the distance between two points to determine the speed or velocity of an object, or using distance measurements to create maps or models of a specific area. Distance calculations are also important in fields such as geology, ecology, and astronomy.

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