Gravitational and electric fields summary GR 10 – 12 IEB
Gravitational Fields
Every particle in the universe attracts every other particle with a force that is directly
proportional to the product of their masses and inversely proportional to the square of
the distance between their centers.
Formulae:
𝐺𝑚1𝑚2
1) F =
𝑟2
Symbol Meaning Unit of measurement
F force N
−11
G Universal gravitational constant 6.67 × 10 N.𝑚2 . 𝑘𝑔−2
m mass kg
r Distance between centers m
𝐺𝑀
2) g =
𝑟2
𝐹
3) g =
𝑚
Symbol Meaning Unit of measurement
g Gravitational acceleration 𝑚. 𝑠 −2
G Universal gravitational constant 6.67 × 10−11 N.𝑚2 . 𝑘𝑔−2
m mass kg
r Radius of object m
• If they give you the diameter of the object, remember to divide it by two to get the
radius of the object.
Example:
1) An object of unknown mass has a gravitational force of 6.7 × 10−10 N on a 2kg mass
which is 800 mm away, what is the mass of the object?
𝐺𝑚1𝑚2
F=
𝑟2
6.7 ×10−10 ×2𝑚 Remember to
6.7 × 10−10 =
(0.8)2 change mm to m.
M=3.21kg
1|P age
, Gravitational and electric fields summary GR 10 – 12 IEB
Example:
a) An unknown planet has a diameter of 2000 m and a mass of 20 000 kg, what is it’s
acceleration due to gravity?
𝐺𝑀
g=
𝑟2
(6.7 ×10−10)(20 000)
g=
(1000)2
g = 1.34 × 10−11 𝑚. 𝑠 −2 towards the earth.
b) What can we observe from this planet by looking at its gravitational acceleration?
The unknown planet’s gravitational acceleration is 1.34 × 10−11 𝑚. 𝑠 −2 , while the
earth’s gravitational acceleration is 9.8 𝑚. 𝑠 −2. The further you go away from the surface
of the earth, the more the gravitational acceleration decreases. This tells us that this
unknown planet is extremely far away from the surface of the earth because its gravity
is significantly smaller than the earth’s.
Let’s prove that gravitational acceleration decreases the further you go from the earth’s
surface:
1) F = mg
𝐹
g=
𝑚
∴g𝛼𝐹
∴ If g increases, F increases.
𝐺𝑚1𝑚2
2) F =
𝑟2
1
F𝛼 (force is inversely proportional to the square of the distances between the
𝑟2
objects centers).
∴ If r increases, F decreases (when the distances between the planet’s centers increase, the
force decreases and therefore their gravitational acceleration).
2|P age
Gravitational Fields
Every particle in the universe attracts every other particle with a force that is directly
proportional to the product of their masses and inversely proportional to the square of
the distance between their centers.
Formulae:
𝐺𝑚1𝑚2
1) F =
𝑟2
Symbol Meaning Unit of measurement
F force N
−11
G Universal gravitational constant 6.67 × 10 N.𝑚2 . 𝑘𝑔−2
m mass kg
r Distance between centers m
𝐺𝑀
2) g =
𝑟2
𝐹
3) g =
𝑚
Symbol Meaning Unit of measurement
g Gravitational acceleration 𝑚. 𝑠 −2
G Universal gravitational constant 6.67 × 10−11 N.𝑚2 . 𝑘𝑔−2
m mass kg
r Radius of object m
• If they give you the diameter of the object, remember to divide it by two to get the
radius of the object.
Example:
1) An object of unknown mass has a gravitational force of 6.7 × 10−10 N on a 2kg mass
which is 800 mm away, what is the mass of the object?
𝐺𝑚1𝑚2
F=
𝑟2
6.7 ×10−10 ×2𝑚 Remember to
6.7 × 10−10 =
(0.8)2 change mm to m.
M=3.21kg
1|P age
, Gravitational and electric fields summary GR 10 – 12 IEB
Example:
a) An unknown planet has a diameter of 2000 m and a mass of 20 000 kg, what is it’s
acceleration due to gravity?
𝐺𝑀
g=
𝑟2
(6.7 ×10−10)(20 000)
g=
(1000)2
g = 1.34 × 10−11 𝑚. 𝑠 −2 towards the earth.
b) What can we observe from this planet by looking at its gravitational acceleration?
The unknown planet’s gravitational acceleration is 1.34 × 10−11 𝑚. 𝑠 −2 , while the
earth’s gravitational acceleration is 9.8 𝑚. 𝑠 −2. The further you go away from the surface
of the earth, the more the gravitational acceleration decreases. This tells us that this
unknown planet is extremely far away from the surface of the earth because its gravity
is significantly smaller than the earth’s.
Let’s prove that gravitational acceleration decreases the further you go from the earth’s
surface:
1) F = mg
𝐹
g=
𝑚
∴g𝛼𝐹
∴ If g increases, F increases.
𝐺𝑚1𝑚2
2) F =
𝑟2
1
F𝛼 (force is inversely proportional to the square of the distances between the
𝑟2
objects centers).
∴ If r increases, F decreases (when the distances between the planet’s centers increase, the
force decreases and therefore their gravitational acceleration).
2|P age
