SME
Grade 8 Science · Earth & Space Science
Gravity and orbits in the solar system
Use this for “How does the sun’s pull change if a planet is twice as far away, or has twice the mass?”
Diagram
The sun’s pull bends the planet’s path into an orbit.
F = m ÷ d² = 1 ÷ 1² = 1
This is an example. Type your own values to start a new problem.
F
=
m (Earth mass)
÷
(
d (AU)
)
2
Formulas
F
=
m
÷
d
2
(pull
of
the
sun,
in
Earth’s
pull
=
mass
÷
distance
from
the
sun²)
1
=
1
÷
1
2
Assumptions
•
Gravity pulls every mass toward every other mass. The sun’s pull keeps the planets on their orbits; without it each would fly off in a straight line.
•
The pull grows with the planet’s mass and falls with the square of its distance.
•
Pull is counted in Earth’s pull (1), mass in Earth masses, distance in AU: Earth’s distance from the sun, 150 million km.
•
The same law holds the moon round Earth and the stars in a galaxy. Drag the planet in or out.
Step-by-step
WE KNOW
d = 1 AU (distance from the sun), m = 1 Earth mass (mass)
FIND
pull of the sun, in Earth’s pull (F)
Step 1 · Find pull of the sun, in Earth’s pull (F)
Use F = m ÷ d² (pull of the sun, in Earth’s pull = mass ÷ distance from the sun²)
Square the distance, then divide the mass by it: twice as far, a quarter of the pull.
F
=
1
1
2
F
=
1
1
F
=
1
Check
Put the numbers back in. Both sides should match.
1
=
1
÷
1
2
✓
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