Theoretical gravity

Key takeaways

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

Reference excerpt

In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of Earth's gravity, on or near its surface, by means of a mathematical model. The most common theoretical model is a rotating Earth ellipsoid of revolution (i.e., a spheroid). Other representations of gravity can be used in the study and analysis of other bodies, such as asteroids. Widely used representations of a gravity field in the context of geodesy include spherical harmonics, mascon models, and polyhedral gravity representations.

Principles

The type of gravity model used for the Earth depends upon the degree of fidelity required for a given problem. For many problems such as aircraft simulation, it may be sufficient to consider gravity to be a constant, defined as:

g = g 45 = {\displaystyle g=g_{45}=} 9.80665 m/s2 (32.1740 ft/s2) based upon data from World Geodetic System 1984 (WGS-84), where g {\displaystyle g} is understood to be pointing 'down' in the local frame of reference. If it is desirable to model an object's weight on Earth as a function of latitude, one could use the following:

g = g 45 − 1 2 ( g p o l e s − g e q u a t o r ) cos ⁡ ( 2 φ ⋅ π 180 ) {\displaystyle g=g_{45}-{\tfrac {1}{2}}(g_{\mathrm {poles} }-g_{\mathrm {equator} })\cos \left(2\,\varphi \cdot {\frac {\pi }{180}}\right)}

where

g p o l e s {\displaystyle g_{\mathrm {poles} }} = 9.832 m/s2 (32.26 ft/s2)

g 45 {\displaystyle g_{45}} = 9.806 m/s2 (32.17 ft/s2)

g e q u a t o r {\displaystyle g_{\mathrm {equator} }} = 9.780 m/s2 (32.09 ft/s2)

φ {\displaystyle \varphi } = latitude, between −90° and +90° Neither of these accounts for changes in gravity with changes in altitude, but the model with the cosine function does take into account the centrifugal relief that is produced by the rotation of the Earth. On the rotating sphere, the sum of the force of the gravitational field and the centrifugal force yields an angular deviation of approximately

sin ⁡ ( 2 φ ) 2 g R Ω 2 {\displaystyle {\frac {\sin(2\varphi )}{2g}}{R\Omega ^{2}}}

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Theoretical gravity

Start with the simplest possible case. Write down what Theoretical gravity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, 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 Theoretical gravity 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 Theoretical gravity 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 Theoretical gravity

In research: Theoretical gravity appears in physics 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 Theoretical gravity 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: Theoretical gravity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Geodesy, Geophysics, Gravimetry, so understanding it makes those chapters shorter.
In everyday life: Look for Theoretical gravity 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.

How to study Theoretical gravity in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Theoretical gravity 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 Theoretical gravity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Theoretical gravity in simple terms?

In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of Earth's gravity, on or near its surface, by means of a mathematical model. The most common theoretical model is a rotating Earth ellipsoid of revolution (i.e., a spheroid).

Why does Theoretical gravity matter?

Because it connects several physics 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 Theoretical gravity?

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 Theoretical gravity.