science

Space-oblique Mercator projection

Space-oblique Mercator projection is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Space-oblique Mercator projection rather than just read about it. In short: Space-oblique Mercator projection is a map projection devised in the 1970s for preparing maps from Earth-survey satellite data. It is a generalization of the oblique Mercator projection that incorporates the time evolution of a given satellite ground track to optimize its representation on the map.

Key takeaways

Space-oblique Mercator projection belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Space-oblique Mercator projection to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Space-oblique Mercator projection from memory before moving on to harder problems.

Reference excerpt

Space-oblique Mercator projection is a map projection devised in the 1970s for preparing maps from Earth-survey satellite data. It is a generalization of the oblique Mercator projection that incorporates the time evolution of a given satellite ground track to optimize its representation on the map. The oblique Mercator projection, on the other hand, optimizes for a given geodesic.

History The space-oblique Mercator projection (SOM) was developed by John P. Snyder, Alden Partridge Colvocoresses and John L. Junkins in 1976. Snyder had an interest in maps dating back to his childhood; he regularly attended cartography conferences whilst on vacation. In 1972, the United States Geological Survey (USGS) needed to develop a system for reducing the amount of distortion caused when satellite pictures of the ellipsoidal Earth were printed on a flat page. Colvocoresses, the head of the USGS's national mapping program, asked attendees of a geodetic sciences conferences for help solving the projection problem in 1976. Snyder work on the problem with his newly purchased pocket calculator and devised the mathematical formulas needed to solve the problem. After submitting his calculations to Waldo Tobler for review, Snyder submitted these to the USGS at no charge. Impressed with his work, USGS officials offered Snyder a job, and he promptly accepted. His formulas were then used to produce maps from Landsat 4, which launched in the summer of 1978 .

Projection description The space-oblique Mercator projection provides continual, nearly conformal mapping of the swath sensed by a satellite. Scale is true along the ground track, varying 0.01 percent within the normal sensing range of the satellite. Conformality is correct within a few parts per million for the sensing range. Distortion is essentially constant along lines of constant distance parallel to the ground track. The space-oblique Mercator is the only projection which takes the rotation of Earth into account.

Equations The forward equations for the Space-oblique Mercator projection for the sphere are as follows:

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Space-oblique Mercator projection

Start with the simplest possible case. Write down what Space-oblique Mercator projection claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Space-oblique Mercator projection before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Space-oblique Mercator projection ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Space-oblique Mercator projection

In research: Space-oblique Mercator projection appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Space-oblique Mercator projection in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Space-oblique Mercator projection is common in secondary-school and first-year university syllabi. It links to neighbouring topics Map projections, so understanding it makes those chapters shorter.
In everyday life: Look for Space-oblique Mercator projection outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Space-oblique Mercator projection in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Space-oblique Mercator projection means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Space-oblique Mercator projection out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Space-oblique Mercator projection in simple terms?

Why does Space-oblique Mercator projection matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Space-oblique Mercator projection?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Space-oblique Mercator projection.