Orbits of Planets & Satellites (AQA A Level Physics)

Explain why it is preferable to have a satellite in a geostationary orbit for TV and telephone signals.

Calculate the radius of a geostationary orbit.

Calculate the increase in potential energy of a satellite of mass 830 kg when it is raised from the Earth’s surface into a geostationary orbit.

Using the centripetal acceleration, calculate the speed of the satellite when it is in a geostationary orbit.

Kepler’s Third Law defines the relationship between the period, T and the radius, r of an orbit as:

             ∝  

Derive the full equation for Kepler’s Third Law. State one assumption made.

The Earth’s orbit is of mean radius 1.50 × 10¹¹ m and the Earth’s year is 365 days long. The mean radius of the orbit of Mars is 2.32 × 10¹¹ m. 

Calculate the length of one Mars year in days.

Jupiter orbits the Sun once every 12 Earth years. 

Calculate the ratio

Jupiter has the shortest day compared to any other planet in our solar system at 10 hours. 

Calculate the angular speed of Jupiter’s rotation.

Determine the equation for the escape velocity, v, of a planet with mass M and radius R.

Calculate the escape velocity of the Moon using the following data: 

   Mass of the Moon = 7.33 × 10²² kg

    Density of the Moon = 3300 kg m^–3

A dwarf planet Q has the same mass as the moon but a radius twice as large. 

Calculate the escape velocity on planet Q.

State two reasons why rockets launched from the Earth’s surface do not need to achieve escape velocity to reach their orbit.

Compare the advantages and disadvantages of polar and a geostationary orbit.

State and explain one possible use for a satellite travelling in a polar orbit.

A satellite travels in a polar orbit at an altitude of 300 km. 

Show that the time period of its orbit is around 90 minutes.

Calculate the speed of the satellite when it travels in a polar orbit at an altitude of 300 km.

The International Space Station (ISS) orbits travels around the Earth once every 93 minutes. 

Calculate the angular speed of the ISS, stating an appropriate unit.

Hence, or otherwise, calculate the distance of the ISS above the Earth’s surface.

The Soyuz is a Russian spacecraft that carries astronauts to and from the international space station (ISS). The ISS has a mass of approximately 4.2 × 10⁵ kg. 

Calculate the change in kinetic energy of a Soyuz travelling from the Earth’s surface to the ISS.

Without performing any further calculations, explain how the change in kinetic energy relates to the change of the potential energy when the Soyuz travels from the Earth’s surface to the ISS. 

The orbits of the Earth and Jupiter are very nearly circular, with radii of 150 × 10⁹ m and 778 × 10⁹ m respectively. It takes Jupiter 11.8 years to complete a full orbit of the Sun.

Show that the values in this question are consistent with Kepler’s third law.

Data from the orbits of different planets around our Sun is plotted in a graph of log (T²) against  log (R³) as shown in Figure 1, where T is the orbital period and R is the radius of the planets orbit.

Figure 1

Calculate the percentage error for the mass of the Sun obtained from the graph in Figure 1.

The Sun is about 8 kpc (kilo-parsecs) from the centre of the Milky Way Galaxy and moves at about 230 km/s.  Calculate the orbital period of the Sun around the centre of the Milky Way Galaxy.

      1 kpc = 3260 light years

Pluto is a dwarf planet with a radius of 1.19 × 10⁶ m.  It orbits the Sun in an orbital radius which is 25.9 times greater than that of Mars.

Calculate how many times Mars will completely orbit the Sun in the time it takes Pluto to complete one full orbit of the Sun.

A small mass is released from rest and takes 5.69 s to fall 10 m onto the surface of Pluto. 

Assuming that there is no atmosphere above the surface of Pluto that could provide any resistance to motion, calculate the mass of Pluto.

   The radius of Pluto is 1.19 × 10⁶ m.  

A meteorite hits Pluto and ejects a lump of ice from the surface that travels vertically at an initial speed of 1600 m s^–1.

Determine whether this lump of ice can escape from Pluto.

A satellite X of mass m is in a concentric circular orbit around a planet of mass M, as shown in Figure 1.The radius of the orbit is 4R, where R is the radius of the planet. 

Figure 1

Show that the kinetic energy of X, can be expressed as:

      KE =

The orbital radius of satellite X is reduced to a distance r from the centre of the planet.

Show that the gravitational potential difference between the surface of the planet and a point on satellite X’s new orbit can be expressed as:

         ∆V = GM

A satellite in the closest orbit to the Earth has a period of 90 minutes.

Calculate the kinetic energy of a 1000 kg satellite in the closest orbit to Earth.

Unused satellites are often referred to as ‘space junk’. 

1000 kg of the explosive TNT yields approximately 4.1 × 10⁹ J. 

Suggest why ‘space junk’ poses a significant problem to future space missions.

A space mission is being planned to launch a spacecraft from Earth to land a robotic probe on a comet which is in deep space where the gravitational field strength is negligible. The total mass of the spacecraft is 3000 kg.

Calculate the change in the gravitational potential energy of the spacecraft to move it from the surface of the Earth to the comet.

The comet has a mass of 1.7 × 10¹³ kg.  It is planned that the robotic probe, of mass 145 kg will separate from the spacecraft and land on the comet at a distance of 1.8 km from the comets centre of mass.  The robotic probe will drill a hole into the surface of the comet to anchor itself. The drill will exert a force of 32 N for 5 s.

Determine whether the drilling process would cause the probe to escape from the surface of the comet.

On another mission a spacecraft of mass 1050 kg is being returned to the Earth from the moon. 

Use the information below to calculate the speed at which the spacecraft must be launched from the surface of the moon if it is to reach the surface of the Earth.

   Mass of the moon,   = 7.35 × 10²² kg

   Radius of the moon,   = 1.74 × 10⁶ m

   Separation distance between Earth and moon,   = 3.85 × 10⁸ m

A satellite of mass 150 kg moves from an orbital radius of 6500 km to an orbital radius of 5 500 km above the surface of the Earth.

Calculate the change of energy of the satellite as it moves between the two orbits and state whether the total amount of energy has increased or decreased as the satellite moves between the orbits.

The escape velocity, , from a  planet of mass M is 0.5 × 10⁴ m s^-1. 

The escape velocity, , from a  planet of mass 4M is 1.5 × 10⁴ m s^-1.

Calculate the ratio of the radii of the planets, .