physics

Lense–Thirring precession

Lense–Thirring precession is a physics 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 Lense–Thirring precession rather than just read about it. In short: In general relativity, Lense–Thirring precession or the Lense–Thirring effect (Austrian German: [ˈlɛnsɛ ˈtɪrɪŋ]; named after Josef Lense and Hans Thirring) is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth. It is a gravitomagnetic frame-dragging effect.

Key takeaways

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

Reference excerpt

In general relativity, Lense–Thirring precession or the Lense–Thirring effect (Austrian German: [ˈlɛnsɛ ˈtɪrɪŋ]; named after Josef Lense and Hans Thirring) is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth. It is a gravitomagnetic frame-dragging effect. It is a prediction of general relativity consisting of secular precessions of the longitude of the ascending node and the argument of pericenter of a test particle freely orbiting a central spinning mass endowed with angular momentum S {\displaystyle S} . The difference between de Sitter precession and the Lense–Thirring effect is that the de Sitter effect is due simply to the presence of a central mass, whereas the Lense–Thirring effect is due to the rotation of the central mass. The total precession is calculated by combining the de Sitter precession with the Lense–Thirring precession. According to a 2007 historical analysis by Herbert Pfister, the effect should be renamed the Einstein–Thirring–Lense effect.

Lense–Thirring metric The gravitational field of a spinning spherical body of constant density was studied by Lense and Thirring in 1918, in the weak-field approximation. They obtained the metric

d s 2 = ( 1 − 2 G M r c 2 ) c 2 d t 2 − ( 1 + 2 G M r c 2 ) d σ 2 + 4 G ϵ i j k S k x i c 3 r 3 c d t d x j , {\displaystyle \mathrm {d} s^{2}=\left(1-{\frac {2GM}{rc^{2}}}\right)c^{2}\,\mathrm {d} t^{2}-\left(1+{\frac {2GM}{rc^{2}}}\right)\,\mathrm {d} \sigma ^{2}+4G\epsilon _{ijk}S^{k}{\frac {x^{i}}{c^{3}r^{3}}}c\,\mathrm {d} t\,\mathrm {d} x^{j},}

where the symbols represent:

d s 2 {\displaystyle \mathrm {d} s^{2}} the metric,

d σ 2 = d x 2 + d y 2 + d z 2 = d r 2 + r 2 d θ 2 + r 2 sin 2 ⁡ θ d φ 2 {\displaystyle \mathrm {d} \sigma ^{2}=\mathrm {d} x^{2}+\mathrm {d} y^{2}+\mathrm {d} z^{2}=\mathrm {d} r^{2}+r^{2}\mathrm {d} \theta ^{2}+r^{2}\sin ^{2}\theta \,\mathrm {d} \varphi ^{2}} the flat-space line element in three dimensions,

r = x 2 + y 2 + z 2 {\textstyle r={\sqrt {x^{2}+y^{2}+z^{2}}}} the "radial" position of the observer,

c {\displaystyle c} the speed of light,

G {\displaystyle G} the gravitational constant,

ϵ i j k {\displaystyle \epsilon _{ijk}} the completely antisymmetric Levi-Civita symbol,

M = ∫ T 00 d 3 x {\textstyle M=\int T^{00}\,\mathrm {d} ^{3}x} the mass of the rotating body,

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Lense–Thirring precession

Start with the simplest possible case. Write down what Lense–Thirring precession 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 Lense–Thirring precession 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 Lense–Thirring precession 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 Lense–Thirring precession

In research: Lense–Thirring precession 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 Lense–Thirring precession 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: Lense–Thirring precession is common in secondary-school and first-year university syllabi. It links to neighbouring topics General relativity, Precession, so understanding it makes those chapters shorter.
In everyday life: Look for Lense–Thirring precession 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Lense–Thirring precession” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Lense–Thirring precession in 20 minutes

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

Frequently asked questions

What is Lense–Thirring precession in simple terms?

Why does Lense–Thirring precession 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 Lense–Thirring precession?

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 Lense–Thirring precession.