A weather satellite is boosted to a higher orbit. Earth's pull on it…
You know the gravitational force on a probe weakens as the probe travels away from Earth. By how much? Many people guess that doubling the distance halves the force. The numbers say otherwise.
Here are the numbers for one probe coasting away from a planet.
At its starting distance, the force on the probe from the planet is 36 N. The probe coasts to twice the starting distance. The force is now 9 N: one quarter of 36 N.
At three times the starting distance, the force is 4 N: one ninth of 36 N.
The pattern: the force divides by the square of the distance factor. Double the distance: divide the force by 2² = 4. Triple the distance: divide by 3² = 9.
The rule runs backward too. Halve the distance: divide by (1/2)² = 1/4. Dividing by one quarter multiplies the force by 4.
A probe's distance from a moon triples. The force on it was 27 N. What is the force now?
Write down the rule:
Triple the distance: divide the force by 3² = 9.
Divide:
27 ÷ 9 = 3
The force is now 3 N.
The distance between two probes doubles. The pull between them becomes…
The distance between two moons triples. The pull between them becomes…
The same probe later halves its distance from the moon. The force on it was 3 N. What is the force now?
Write down the rule:
Halve the distance: the force multiplies by 4.
Multiply:
3 × 4 = 12
The force is now 12 N.
The distance between two asteroids halves. The pull between them becomes…
Now the drill picks up speed: one step each time, and the computed force goes in as a number.
Two asteroids pull with 60 N. The distance between centers doubles. Enter the new force in newtons.
Two space stations pull with 45 N. The distance between centers triples. Enter the new force in newtons.
A probe moves to four times its distance from a planet. The pull on it becomes…
Earth pulls a probe with 800 N. The probe coasts to twice its distance from Earth's center. Enter the new force in newtons.
The pull between two moons falls to one ninth of its old value, their masses unchanged. The distance between their centers has…
Gravitational force weakens with the square of the distance between centers. Type the name of this law.