Gravitational Field Strength (CIE IGCSE Physics)

• The strength of a gravitational field around a planet depends on 
  • the mass of the planet
  • the distance from the planet

Gravitational field strength and mass

• The relationship between gravitational field strength and mass is:

The greater the mass of a planet, the greater the strength of the gravitational field at its surface

• The value of  (gravitational field strength) varies from planet to planet depending on their mass and radius

Gravitational field strength of bodies in the Solar System

The strength of the gravitational field at the surface of a planet depends on its mass and radius

Gravitational field strength and distance

• The relationship between gravitational field strength and distance is:

As the distance from a planet increases, the strength of the gravitational field decreases

• At the surface of a planet, the value of  (gravitational field strength) is constant, but it decreases with distance from the planet

• Orbital motion is a result of the gravitational force of attraction acting between two bodies
• This gravitational force
  • always acts towards the centre of the larger body
  • causes the orbiting body to move in a circular path

• The Sun contains most of the mass (>99%) of the Solar System
• Therefore, for objects orbiting around the Sun
  • the Sun's gravitational attraction keeps them in orbit
  • the force is directed from the orbiting object to the centre of the Sun

Orbital motion of the Earth around the Sun

The Sun's gravitational force of attraction keeps the Earth in orbit around the Sun

Extended tier only

• As the distance from the Sun increases:
  
  • the Sun's gravitational field strength decreases
  • the orbital speed of a planet decreases

• For an object to maintain a circular orbit, it must have a centripetal force
  • For planets orbiting the Sun, this force is the Sun's gravitational attraction

• Therefore, the centripetal force on a planet depends on
  • the strength of the Sun's gravitational field
  • the distance of the planet from the Sun

• The further away a planet is from the Sun, the weaker the strength of the Sun's gravitational attraction and the weaker the centripetal force

• The centripetal force on a planet is proportional to its orbital speed
• Therefore, the further a planet is from the Sun:
  • the smaller its orbital speed
  • the longer its orbital period

Orbital speed and distance

The closest planets to the Sun have the fastest orbital speeds, and the furthest have the slowest

• This trend in orbital speed and distance can be seen in the data of the planets in the Solar System:

Orbital radius, speed and period data

Planet	Orbital radius (million km)	Orbital speed (km/s)	Orbital period (days or years)
Mercury	57.9	47.9	88 days
Venus	108.2	35.0	225 days
Earth	149.6	29.8	365 days
Mars	227.9	24.1	687 days
Jupiter	778.6	13.1	11.9 years
Saturn	1433.5	9.7	29.5 years
Uranus	2872.5	6.8	75 years
Neptune	4495.1	5.4	165 years