Astronomical distances

X and Y are identical stars. When viewed from Earth the intensity of star X is four times the intensity of star Y.

Which of the following explanations is possible?

A student carried out an experiment with a light dependent resistor (LDR). He connected the LDR in series with an ammeter and a power supply, as shown in the circuit diagram.

The student placed the LDR a known distance from a desk lamp, as shown.

The student noted the reading on the ammeter as he brought the LDR closer to the lamp.

The student planned to vary the intensity of light incident upon the LDR by adjusting the distance x between the LDR and the lamp.

He thought that the intensity of light on the LDR would increase uniformly if he decreased x by equal intervals. He therefore planned to take ammeter readings as he decreased x from 20.0 cm to 10.0 cm in equal intervals.

Criticise the student’s plan for data collection.

Explain one precaution that the student should take to ensure that results are accurate.

Explain why the ammeter reading increased as the LDR was brought closer to the lamp. Your answer should include reference to the charge carriers in the LDR.

Two stars, P and Q, are observed from Earth. The intensity of radiation from P is less than that from Q. The parallax angle for P is greater than that for Q.

Which row of the table is correct?

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 10³⁶kg.

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

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 10¹³m from the centre of the black hole.

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

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

At its point of closest approach, the star is travelling at a speed of 8.1 10⁶m s⁻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 10³¹kg

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.

There are several different methods that can be used to determine the distance from our solar system to astronomical objects. These include the measurement of red shift, trigonometrical parallax and the use of standard candles.

Which row of the table shows a suitable method for each of the objects named?

There are several different methods that can be used to determine the distance from our solar system to astronomical objects. These include the measurement of red shift, trigonometrical parallax and the use of standard candles.

Which row of the table shows a suitable method for each of the objects named?

Solar panels consisting of combinations of photovoltaic cells use energy in the radiation received from the Sun to generate electricity.

An advertisement for solar panels claims that the intensity of radiation from the Sun incident at the top of the Earth’s atmosphere is more than 2 kW m⁻².

Assess the validity of this claim.

radius of Sun = 6.96 × 10⁸m

surface temperature of Sun = 5790 K

distance from Sun to Earth = 1.50 × 10¹¹m

The average intensity of radiation from the Sun incident at the Earth’s surface over a 24-hour period has been determined to be 164 W m⁻².

The average intensity of radiation from the Sun at the Earth’s surface is much less than the intensity incident at the top of the Earth’s atmosphere.

Explain why.

It is claimed that the area of solar panels needed to generate 100 GW of power is about 0.5% of the surface area of the Earth.

Assess the validity of this claim.

radius of Earth = 6.4 × 10⁶m

typical efficiency of solar panels = 25%

Scientists are developing a space station equipped with large solar panels. The space station would be located in a geostationary orbit. The space station would transfer energy to Earth as microwaves.

A space station in a geostationary orbit is above the equator and has a period of 24 hours.

Explain one advantage of locating the space station in a geostationary orbit.

Calculate the height h of the space station above the equator when it is in a geostationary orbit.

mass of Earth = 6.00 × 10²⁴kg

24 hours = 8.64 10⁴s

Solar panels consisting of combinations of photovoltaic cells use energy in the radiation received from the Sun to generate electricity.

An advertisement for solar panels claims that the intensity of radiation from the Sun incident at the top of the Earth’s atmosphere is more than 2 kW m⁻².

Assess the validity of this claim.

radius of Sun = 6.96 × 10⁸m

surface temperature of Sun = 5790 K

distance from Sun to Earth = 1.50 × 10¹¹m

The average intensity of radiation from the Sun incident at the Earth’s surface over a 24-hour period has been determined to be 164 W m⁻².

The average intensity of radiation from the Sun at the Earth’s surface is much less than the intensity incident at the top of the Earth’s atmosphere.

Explain why.

It is claimed that the area of solar panels needed to generate 100 GW of power is about 0.5% of the surface area of the Earth.

Assess the validity of this claim.

radius of Earth = 6.4 × 10⁶m

typical efficiency of solar panels = 25%

Scientists are developing a space station equipped with large solar panels. The space station would be located in a geostationary orbit. The space station would transfer energy to Earth as microwaves.

A space station in a geostationary orbit is above the equator and has a period of 24 hours.

Explain one advantage of locating the space station in a geostationary orbit.

Calculate the height h of the space station above the equator when it is in a geostationary orbit.

mass of Earth = 6.00 × 10²⁴kg

24 hours = 8.64 10⁴s

The distance to astronomical objects relatively close to the Sun is determined using trigonometric parallax. For objects beyond a certain distance standard candles are used.

State what is meant by a standard candle.

Explain why trigonometric parallax is not used beyond a certain distance.

Describe how distances too large for the use of standard candles can be determined.