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Gravitational Force worksheet

Grades 11–12 · CCSS HSA.CED.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Mass of object 2
- Object 1: Enter a mass
- Mass of object 1 (m₁): 1,300 kg
- Distance between centers (r): 475,000 km
- Gravitational force (F): 165,000,000,000,000,000,000 N
- Show mass in: Metric tonnes (t)
Find: Mass of object 2
Answer
2.
Problem 2.
- Solve for: Force
- Object 1: Earth (≈ 5.9722 × 10²⁴ kg)
- Object 2: Enter a mass
- Mass of object 2 (m₂): 920 kg
- Distance between centers (r): 425,000 km
- Show force in: Kilonewtons (kN)
Find: Gravitational force
Answer
3.
Problem 3.
- Solve for: Force
- Object 1: Moon (≈ 7.346 × 10²² kg)
- Object 2: Moon (≈ 7.346 × 10²² kg)
- Distance between centers (r): 375,000 km
- Show force in: Pounds-force (lbf)
Find: Gravitational force
Answer
4.
Problem 4.
- Solve for: Distance
- Object 1: Enter a mass
- Mass of object 1 (m₁): 825 kg
- Object 2: Sun (≈ 1.9885 × 10³⁰ kg)
- Gravitational force (F): 190,000,000,000,000,000,000 N
- Show distance in: Meters (m)
Find: Distance between centers
Answer
5.
Problem 5.
- Solve for: Force
- Object 1: Moon (≈ 7.346 × 10²² kg)
- Object 2: Sun (≈ 1.9885 × 10³⁰ kg)
- Distance between centers (r): 475,000 km
- Show force in: Newtons (N)
Find: Gravitational force
Answer
6.
Problem 6.
- Solve for: Distance
- Object 1: Sun (≈ 1.9885 × 10³⁰ kg)
- Object 2: Sun (≈ 1.9885 × 10³⁰ kg)
- Gravitational force (F): 290,000,000,000,000,000,000 N
- Show distance in: Miles (mi)
Find: Distance between centers
Answer
7.
Problem 7.
- Solve for: Force
- Object 1: Sun (≈ 1.9885 × 10³⁰ kg)
- Object 2: Earth (≈ 5.9722 × 10²⁴ kg)
- Distance between centers (r): 480,000 km
- Show force in: Pounds-force (lbf)
Find: Gravitational force
Answer
8.
Problem 8.
- Solve for: Distance
- Object 1: Sun (≈ 1.9885 × 10³⁰ kg)
- Object 2: Enter a mass
- Mass of object 2 (m₂): 725 kg
- Gravitational force (F): 200,000,000,000,000,000,000 N
- Show distance in: Feet (ft)
Find: Distance between centers
Answer
9.
Problem 9.
- Solve for: Force
- Object 1: Sun (≈ 1.9885 × 10³⁰ kg)
- Object 2: Sun (≈ 1.9885 × 10³⁰ kg)
- Distance between centers (r): 360,000 km
- Show force in: Newtons (N)
Find: Gravitational force
Answer
10.
Problem 10.
- Solve for: Force
- Object 1: Moon (≈ 7.346 × 10²² kg)
- Object 2: Moon (≈ 7.346 × 10²² kg)
- Distance between centers (r): 240,000 km
- Show force in: Newtons (N)
Find: Gravitational force
Answer

Answer key: Gravitational Force worksheet

1. Mass of object 2: 4.29e+41 t
1. Change distance to m, the standard unit the formula uses (1 km = 1,000 m)
  $475,000 km \times 1,000$ $= 475,000,000 m$
2. Find the second mass by working Newton's law backward from the known force and distance
  $\frac{1.65e+20 \times {475,000,000}^{2}}{6.6743e-11 \times 1,300}$ $= 4.29064e+44 kg$
3. Change the answer to t, the unit you picked: divide by 1,000
  $\frac{4.29064e+44}{1,000}$ $= 4.29064e+41 t$
2. Gravitational force: 2.03e-3 kN
1. Use the approximate mass of Earth for object 1
  $m₁$ $= 5.9722e+24 kg$
2. Change distance to m, the standard unit the formula uses (1 km = 1,000 m)
  $425,000 km \times 1,000$ $= 425,000,000 m$
3. Multiply G by both masses and divide by the distance squared, because the pull grows with mass and fades with distance
  $\frac{6.6743e-11 \times 5.9722e+24 \times 920}{{425,000,000}^{2}}$ $= 2.030252 N$
4. Change the answer to kN, the unit you picked: divide by 1,000
  $\frac{2.030252}{1,000}$ $= 0.00203 kN$
3. Gravitational force: 5.76e+17 lbf
1. Use the approximate mass of the Moon for object 1
  $m₁$ $= 7.346e+22 kg$
2. Use the approximate mass of the Moon for object 2
  $m₂$ $= 7.346e+22 kg$
3. Change distance to m, the standard unit the formula uses (1 km = 1,000 m)
  $375,000 km \times 1,000$ $= 375,000,000 m$
4. Multiply G by both masses and divide by the distance squared, because the pull grows with mass and fades with distance
  $\frac{6.6743e-11 \times 7.346e+22 \times 7.346e+22}{{375,000,000}^{2}}$ $= 2.561209e+18 N$
5. Change the answer to lbf, the unit you picked: divide by 4.448221615261
  $\frac{2.561209e+18}{4.448221615261}$ $= 5.757827e+17 lbf$
4. Distance between centers: 24.01 m
1. Use the approximate mass of the Sun for object 2
  $m₂$ $= 1.9885e+30 kg$
2. Find the distance by working Newton's law backward from the known force and both masses
  $\sqrt{\frac{6.6743e-11 \times 825 \times 1.9885e+30}{1.9e+20}}$ $= 24.005781 m$
5. Gravitational force: 4.32e+25 N
1. Use the approximate mass of the Moon for object 1
  $m₁$ $= 7.346e+22 kg$
2. Use the approximate mass of the Sun for object 2
  $m₂$ $= 1.9885e+30 kg$
3. Change distance to m, the standard unit the formula uses (1 km = 1,000 m)
  $475,000 km \times 1,000$ $= 475,000,000 m$
4. Multiply G by both masses and divide by the distance squared, because the pull grows with mass and fades with distance
  $\frac{6.6743e-11 \times 7.346e+22 \times 1.9885e+30}{{475,000,000}^{2}}$ $= 4.321107e+25 N$
6. Distance between centers: 592,762,297,969.4 mi
1. Use the approximate mass of the Sun for object 1
  $m₁$ $= 1.9885e+30 kg$
2. Use the approximate mass of the Sun for object 2
  $m₂$ $= 1.9885e+30 kg$
3. Find the distance by working Newton's law backward from the known force and both masses
  $\sqrt{\frac{6.6743e-11 \times 1.9885e+30 \times 1.9885e+30}{2.9e+20}}$ $= 953,958,447,663,263.5 m$
4. Change the answer to mi, the unit you picked: divide by 1,609.344
  $\frac{953,958,447,663,263.5}{1,609.344}$ $= 592,762,297,969.3984 mi$
7. Gravitational force: 7.73e+26 lbf
1. Use the approximate mass of the Sun for object 1
  $m₁$ $= 1.9885e+30 kg$
2. Use the approximate mass of Earth for object 2
  $m₂$ $= 5.9722e+24 kg$
3. Change distance to m, the standard unit the formula uses (1 km = 1,000 m)
  $480,000 km \times 1,000$ $= 480,000,000 m$
4. Multiply G by both masses and divide by the distance squared, because the pull grows with mass and fades with distance
  $\frac{6.6743e-11 \times 1.9885e+30 \times 5.9722e+24}{{480,000,000}^{2}}$ $= 3.440196e+27 N$
5. Change the answer to lbf, the unit you picked: divide by 4.448221615261
  $\frac{3.440196e+27}{4.448221615261}$ $= 7.733868e+26 lbf$
8. Distance between centers: 71.96 ft
1. Use the approximate mass of the Sun for object 1
  $m₁$ $= 1.9885e+30 kg$
2. Find the distance by working Newton's law backward from the known force and both masses
  $\sqrt{\frac{6.6743e-11 \times 1.9885e+30 \times 725}{2e+20}}$ $= 21.934092 m$
3. Change the answer to ft, the unit you picked: divide by 0.3048
  $\frac{21.934092}{0.3048}$ $= 71.962245 ft$
9. Gravitational force: 2.04e+33 N
1. Use the approximate mass of the Sun for object 1
  $m₁$ $= 1.9885e+30 kg$
2. Use the approximate mass of the Sun for object 2
  $m₂$ $= 1.9885e+30 kg$
3. Change distance to m, the standard unit the formula uses (1 km = 1,000 m)
  $360,000 km \times 1,000$ $= 360,000,000 m$
4. Multiply G by both masses and divide by the distance squared, because the pull grows with mass and fades with distance
  $\frac{6.6743e-11 \times 1.9885e+30 \times 1.9885e+30}{{360,000,000}^{2}}$ $= 2.036348e+33 N$
10. Gravitational force: 6.25e+18 N
1. Use the approximate mass of the Moon for object 1
  $m₁$ $= 7.346e+22 kg$
2. Use the approximate mass of the Moon for object 2
  $m₂$ $= 7.346e+22 kg$
3. Change distance to m, the standard unit the formula uses (1 km = 1,000 m)
  $240,000 km \times 1,000$ $= 240,000,000 m$
4. Multiply G by both masses and divide by the distance squared, because the pull grows with mass and fades with distance
  $\frac{6.6743e-11 \times 7.346e+22 \times 7.346e+22}{{240,000,000}^{2}}$ $= 6.252952e+18 N$