Edexcel A Level Physics

Topic Questions

A LevelPhysicsEdexcelTopic Questions12. Gravitational FieldsGravitational Fields

Gravitational Fields

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1a
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Astronauts on the 1971 Apollo 14 mission to the Moon brought back many rock samples. It is now believed that one of these contains a piece of rock that originated on Earth about 4 billion years (4 × 109 years) ago.

The piece of rock is believed to have been launched into space when an asteroid struck the Earth.

a)
The rock sample contains uranium. The radioactive decay of uranium allows it to be used to determine the time since the rock was formed on the Earth.

i)
The uranium isotope straight U presubscript 92 presuperscript 238 becomes the lead isotope Pb presubscript 82 presuperscript 206 through a series of radioactive decays.

Calculate the number of α particles and the number of β particles emitted for one nucleus of straight U presubscript 92 presuperscript 238 to decay to become a nucleus of Pb presubscript 82 presuperscript 206.

(2)



Number of α particles = ............................................
Number of β particles = ............................................

ii)
The half-life of U presubscript 92 presuperscript 238 is 4.47 × 109 years.

The half-lives of the other stages in the decay to Pb presubscript 82 presuperscript 206 are relatively so short that they can be ignored.

There was no lead in the rock when it formed, so all the Pb presubscript 82 presuperscript 206 in the sample is a product of U presubscript 92 presuperscript 238 decay. In the sample, for every 103 uranium nuclei present at the start, 50 are now lead nuclei.

Show that the age of the sample is about 4 × 109 years.

(3)

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1b
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b)
The gravitational potential between the Earth and the Moon due to the combined effect of their gravitational fields increases to a maximum value of −1.28 MJ kg−1 at a point between them.

Calculate the minimum speed at which a rock would have to leave the Earth in order to reach the Moon.

In your calculation, you may assume the rock has zero kinetic energy when it has maximum potential energy.

mass of Earth = 5.97 × 1024 kg
radius of Earth = 6370 km

(4)






Minimum speed = ............................................

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1c
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c)
Four billion years ago, the Moon had a different orbital period, because it was closer to the Earth than it is today.

Calculate the period of the Moon’s orbit four billion years ago, when the radius of its orbit was 1.34 × 108 m.

mass of Earth = 5.97 × 1024 kg

(3)





Period = .........................................

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2a
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Astronomers observing stars at the centre of our galaxy have suggested that many of them are orbiting a supermassive black hole. The mass of this black hole is 9.2 × 1036 kg.

a)
Calculate the orbital period for a star in a circular orbit at a distance of 1.9 × 1014 m from a black hole of this mass.

(3)

Orbital period = ....................................................................

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2b
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b)
The star S0-2 is in a highly elliptical orbit around the position of the black hole.

At its point of closest approach, S0-2 is at a distance of 1.8 × 1013 m from the centre of the black hole.

At the most distant point of its orbit, S0-2 is 2.7 × 1014 m from the black hole.

i)
Show that the change in gravitational potential between the closest and most distant points in this orbit is about 3 × 1013 J kg−1.

(2)

ii)
At its point of closest approach, the star is travelling at a speed of 8.1 × 106 ms−1.

Calculate the speed of S0-2 at the furthest point in its orbit using the change in gravitational potential.

mass of S0-2 = 2.4 × 1031 kg

(3)

Speed = ....................................................................

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2c
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c)
Trigonometric parallax and Hubble’s law are two methods used to determine astronomical distances.

Explain whether either of these methods is suitable to determine the distance to S0-2.



(3)

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1a
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In 2015 the Messenger spacecraft crashed into the surface of the planet Mercury after four years in orbit observing the surface of Mercury.

Messenger’s orbit was highly elliptical, varying between 200 km and 15 000 km above the surface of Mercury. Messenger completed one full orbit every 12 hours.

mass of Messenger spacecraft = 565 kg
mass of planet Mercury = 3.30 × 1023 kg
radius of planet Mercury = 2430 km

It has been suggested that the same orbital period of about 12 hours could have been achieved if Messenger was in a circular orbit 7690 km above the surface of Mercury.

i)
Determine whether this suggestion is correct.

(4)

ii)
The elliptical orbit chosen had advantages over this circular orbit.

Explain one advantage.

(2)

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1b
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Calculate the velocity an object would have as it reached the surface of Mercury if it was released from Messenger’s maximum orbital height.

                         
Assume the object is released from rest and that Mercury has no atmosphere.


Velocity = ...................................

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2a
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In 1990, the Hubble Space Telescope (HST) was launched into a low Earth orbit above the Earth’s atmosphere.

HST orbits the Earth in a circular orbit with a speed of 7.59 km s–1.

mass of Earth = 5.97 × 1024 kg
radius of Earth = 6.37 × 106 m

i)
Show that the height of HST above the surface of the Earth is about 6 × 105 m.

(3)

ii)
Calculate the increase in the gravitational potential energy as HST is raised, from its initial position at the Earth’s surface, to its orbital height.

mass of HST = 11 600 kg

(2)

Increase in gravitational potential energy = .......................................................

iii)
A student suggests that giving HST more energy than that required in (ii) would result in the satellite orbiting at a greater height and with a greater speed.

Assess the validity of the student’s suggestion.

(4)

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2b
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The transmission of electromagnetic radiation through the atmosphere is shown on the graph.

 

q6b-june-2019-9ph0-03-edexcel-as-a-level-phy

State one advantage shown by this graph of positioning a telescope above the atmosphere.

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2c
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High resolution images from HST allow astronomers to make detailed measurements of very distant galaxies.

The graph shows how the recessional velocities of distant galaxies depend on their distance from Earth.

 

q6c-june-2019-9ph0-03-edexcel-as-a-level-phy

Determine an age for the universe.

Age for the universe = .......................................................

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