Lesson test: The moon test

1.[3p]
Substituting Kepler's third law into the expression for circular acceleration gives what?

An acceleration towards the sun falling off as the inverse square of the distance

Correct

An acceleration independent of distance

The answer is: An acceleration towards the sun falling off as the inverse square of the distance

An acceleration proportional to the distance

The answer is: An acceleration towards the sun falling off as the inverse square of the distance

An acceleration falling off as the inverse cube of the distance

The answer is: An acceleration towards the sun falling off as the inverse square of the distance

2.[3p]
Suppose observation had given the period squared as proportional to the distance squared. The acceleration would then fall off as the inverse of the distance raised to what power?

CorrectNot quite: 1

3.[3p]
The moon is 3.844e8 m away with a sidereal period of 2.3606e6 seconds. What is its centripetal acceleration, in units of 1e-3 metres per second squared?

CorrectNot quite: 2.72

4.[3p]
The moon is 60.3 earth radii away. What does an inverse square law anchored at g = 9.81 predict for its acceleration, in units of 1e-3 metres per second squared?

CorrectNot quite: 2.70

5.[3p]
Why is the shell theorem needed before the moon test means anything?

Without it there is no defensible value for the distance between an apple and the whole body of the earth

Correct

Without it Kepler's third law cannot be stated

The answer is: Without it there is no defensible value for the distance between an apple and the whole body of the earth

Without it the moon's distance cannot be measured

The answer is: Without it there is no defensible value for the distance between an apple and the whole body of the earth

Without it the earth's rotation would spoil the value of g

The answer is: Without it there is no defensible value for the distance between an apple and the whole body of the earth

6.[2p]
The shell theorem holds for any law of attraction, not just the inverse square.

True

The answer is: False

False

Correct

7.[3p]
Predicting the moon's period from g and the two distances gives 27.47 days against an observed 27.32. What accounts for most of the difference?

The earth and moon both circle their common centre of mass, so the moon's own mass enters the relation

Correct

The measured value of g is wrong by half a per cent

The answer is: The earth and moon both circle their common centre of mass, so the moon's own mass enters the relation

The moon's orbit is an ellipse rather than a circle

The answer is: The earth and moon both circle their common centre of mass, so the moon's own mass enters the relation

The moon's distance was measured in the wrong units

The answer is: The earth and moon both circle their common centre of mass, so the moon's own mass enters the relation

8.[3p]
What does the moon test establish on its own?

Select all that apply

That one attraction towards the earth, falling as the inverse square, fits both a stone and the moon

Correct

That the old division between celestial and terrestrial physics is untenable

Correct

That every body in the universe attracts every other

The answer is: That one attraction towards the earth, falling as the inverse square, fits both a stone and the moon, That the old division between celestial and terrestrial physics is untenable

That the moon pulls back on the earth

The answer is: That one attraction towards the earth, falling as the inverse square, fits both a stone and the moon, That the old division between celestial and terrestrial physics is untenable

9.[3p]
Where did the inverse square exponent actually come from?

It was read off Kepler's third law, which came from Tycho's measurements

Correct

It was deduced from the definition of matter

The answer is: It was read off Kepler's third law, which came from Tycho's measurements

It was the only exponent for which the mathematics could be done

The answer is: It was read off Kepler's third law, which came from Tycho's measurements

Newton chose it because it made the moon test succeed

The answer is: It was read off Kepler's third law, which came from Tycho's measurements

1.[3p] Substituting Kepler's third law into the expression for circular acceleration gives what?

2.[3p] Suppose observation had given the period squared as proportional to the distance squared. The acceleration would then fall off as the inverse of the distance raised to what power?

3.[3p] The moon is 3.844e8 m away with a sidereal period of 2.3606e6 seconds. What is its centripetal acceleration, in units of 1e-3 metres per second squared?

4.[3p] The moon is 60.3 earth radii away. What does an inverse square law anchored at g = 9.81 predict for its acceleration, in units of 1e-3 metres per second squared?

5.[3p] Why is the shell theorem needed before the moon test means anything?

6.[2p] The shell theorem holds for any law of attraction, not just the inverse square.

7.[3p] Predicting the moon's period from g and the two distances gives 27.47 days against an observed 27.32. What accounts for most of the difference?

8.[3p] What does the moon test establish on its own?

9.[3p] Where did the inverse square exponent actually come from?

1.[3p]
Substituting Kepler's third law into the expression for circular acceleration gives what?

2.[3p]
Suppose observation had given the period squared as proportional to the distance squared. The acceleration would then fall off as the inverse of the distance raised to what power?

3.[3p]
The moon is 3.844e8 m away with a sidereal period of 2.3606e6 seconds. What is its centripetal acceleration, in units of 1e-3 metres per second squared?

4.[3p]
The moon is 60.3 earth radii away. What does an inverse square law anchored at g = 9.81 predict for its acceleration, in units of 1e-3 metres per second squared?

5.[3p]
Why is the shell theorem needed before the moon test means anything?

6.[2p]
The shell theorem holds for any law of attraction, not just the inverse square.

7.[3p]
Predicting the moon's period from g and the two distances gives 27.47 days against an observed 27.32. What accounts for most of the difference?

8.[3p]
What does the moon test establish on its own?

9.[3p]
Where did the inverse square exponent actually come from?