levo

Orbits and the Wider Universe

The centre of mass of a two-body system

  • 3 things to know
  • A2 Unit 4 Section A

Overview

Recall questions on The centre of mass of a two-body system.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

Give the condition that fixes the position of the centre of mass of a two-body system

Key term

Where does the centre of mass lie if one body is far more massive than the other?

Key term

Why must the two bodies always be on opposite sides of the centre of mass?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is the centre of mass of a two-body system?

    Model answer

    It is the point about which both bodies orbit, lying on the line joining them at the position where their moments about it balance.

  2. 2

    Give the condition that fixes the position of the centre of mass.

    Model answer

    M₁r₁ = M₂r₂, where r₁ and r₂ are the distances of the two bodies from the centre of mass.

  3. 3

    How does the position of the centre of mass depend on the two masses?

    Model answer

    It lies nearer the more massive body, and the two distances are in the inverse ratio of the masses.

  4. 4

    Where does the centre of mass lie if one body is far more massive than the other?

    Model answer

    Very close to the centre of the massive body, and it may lie inside it altogether.

  5. 5

    Two bodies of 3.0 × 10³⁰ kg and 1.0 × 10³⁰ kg are 6.0 × 10¹¹ m apart. Find the distance of the heavier from the centre of mass.

    Model answer

    The distances are in the inverse ratio 1 to 3, so the heavier body lies one quarter of the separation away, which is 1.5 × 10¹¹ m.

  6. 6

    Check that position using the moment condition.

    Model answer

    3.0 × 10³⁰ × 1.5 × 10¹¹ = 4.5 × 10⁴¹ and 1.0 × 10³⁰ × 4.5 × 10¹¹ = 4.5 × 10⁴¹, which are equal.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Basic Physics
Kinematics
Dynamics
Energy Concepts

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

R is the .
radiusdiametercircumference

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AF is force.
BB is magnetic flux density.
CI is current.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

A baryon means a particle built from three quarks.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Orbits and the Wider Universe, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.