# Calculate the latitude,longitude 1000 kilometers east from a given location [closed]

I am trying to calculate what would the Google maps latitude and longitude be, for a given location, 1000 east from it. I am not looking for an application which can do, this, but rather a manual way, by using equations.

I found out that there is a way of doing this, if one would know the initial bearing Angle:

``````bearingAngle = 90
d = 1000 kilometers / 6371 kilometers
x = asin( sin lat1 * cos d + cos lat1 * sin d * cos bearingAngle)
y = lon1 + atan2( sin bearingAngle * sin d * cos lat1, cos d - sin lat1 * sin x)
``````

(Equations are taken from: movable-type.co.uk/scripts/latlong.html, section "Destination point given distance and bearing from start point")

However, the upper equations are giving the following result:

As you can see the "x,y" location has a bit lower latitude then starting "lan,lon" (Paris). Basically this is what I am trying to achieve:

The problem is that, to do this, I need to know the initial "bearing angle", which I do not.

How can I solve this problem?

## closed as off-topic by Vince, Brad Nesom, Mapperz♦Oct 19 '15 at 20:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Questions describing a problem that can't be reproduced and seemingly went away on its own (or went away when a typo was fixed) are off-topic as they are unlikely to help future readers." – Vince, Brad Nesom, Mapperz
If this question can be reworded to fit the rules in the help center, please edit the question.

• A thousand kilometers is a long distance to travel using a spherical earth model. The geodetic inverse problem could solve the bearing and distance between two points short of antipodal distance, much as the direct geodetic problem can solve location for strating point, distance, and bearing. – Vince Oct 19 '15 at 18:17
• Thank you for the reply Vince. The "Second (inverse) geodetic problem" you are mentioning requires the second point (its latitude and longitude) to be known. Which is not known in this case. – Bernard Oct 19 '15 at 18:28
• If you don't know the point or the bearing, the problem can't be solved. – Vince Oct 19 '15 at 19:15
• If you use units of radians in computer trig functions, they're more likely to produce correct results. – Vince Oct 19 '15 at 19:39
• All upper variables are in radians (except for the "d" - angular distance). I checked the calculated "x","y" variables on Google maps. And they correspond the upper first photo. I thought this problem could have been solved somehow by replacing "x" to be equal to "lat", and from there (by using a formula for bearingAngle) somehow calculating the "bearingAngle", and after that "y". – Bernard Oct 19 '15 at 20:08
The text passage describes a problem related to calculating the latitude and longitude of a point 1000 kilometers east of a given location using mathematical equations. The author mentions a specific set of equations and discusses the issue of not knowing the initial bearing angle, which is necessary to solve the problem.
single_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Calculate the latitude,longitude 1000 kilometers east from a given location [closed]

I am trying to calculate what would the Google maps latitude and longitude be, for a given location, 1000 east from it. I am not looking for an application which can do, this, but rather a manual way, by using equations.

I found out that there is a way of doing this, if one would know the initial bearing Angle:

``````bearingAngle = 90
d = 1000 kilometers / 6371 kilometers
x = asin( sin lat1 * cos d + cos lat1 * sin d * cos bearingAngle)
y = lon1 + atan2( sin bearingAngle * sin d * cos lat1, cos d - sin lat1 * sin x)
``````

(Equations are taken from: movable-type.co.uk/scripts/latlong.html, section "Destination point given distance and bearing from start point")

However, the upper equations are giving the following result:

As you can see the "x,y" location has a bit lower latitude then starting "lan,lon" (Paris). Basically this is what I am trying to achieve:

The problem is that, to do this, I need to know the initial "bearing angle", which I do not.

How can I solve this problem?

## closed as off-topic by Vince, Brad Nesom, Mapperz♦Oct 19 '15 at 20:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Questions describing a problem that can't be reproduced and seemingly went away on its own (or went away when a typo was fixed) are off-topic as they are unlikely to help future readers." – Vince, Brad Nesom, Mapperz
If this question can be reworded to fit the rules in the help center, please edit the question.

• A thousand kilometers is a long distance to travel using a spherical earth model. The geodetic inverse problem could solve the bearing and distance between two points short of antipodal distance, much as the direct geodetic problem can solve location for strating point, distance, and bearing. – Vince Oct 19 '15 at 18:17
• Thank you for the reply Vince. The "Second (inverse) geodetic problem" you are mentioning requires the second point (its latitude and longitude) to be known. Which is not known in this case. – Bernard Oct 19 '15 at 18:28
• If you don't know the point or the bearing, the problem can't be solved. – Vince Oct 19 '15 at 19:15
• If you use units of radians in computer trig functions, they're more likely to produce correct results. – Vince Oct 19 '15 at 19:39
• All upper variables are in radians (except for the "d" - angular distance). I checked the calculated "x","y" variables on Google maps. And they correspond the upper first photo. I thought this problem could have been solved somehow by replacing "x" to be equal to "lat", and from there (by using a formula for bearingAngle) somehow calculating the "bearingAngle", and after that "y". – Bernard Oct 19 '15 at 20:08
user
The text passage describes a problem related to calculating the latitude and longitude of a point 1000 kilometers east of a given location using mathematical equations. The author mentions a specific set of equations and discusses the issue of not knowing the initial bearing angle, which is necessary to solve the problem.

TYPE: SINGLE_QUESTION