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Escape Velocity worksheet

Grades 11–12

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

1.
Problem 1.
- Planet, moon or star: Jupiter
- Starting height above the surface (h): 0 km
- Show speed in: Kilometers per second (km/s)
Find: Escape velocity
Answer
2.
Problem 2.
- Planet, moon or star: Jupiter
- Starting height above the surface (h): 0 km
- Show speed in: Miles per hour (mph)
Find: Escape velocity
Answer
3.
Problem 3.
- Planet, moon or star: Custom mass and radius
- Mass of the body (M): 6,500,000,000,000,000,000,000,000 kg
- Radius of the body (R): 5,500 km
- Starting height above the surface (h): 0 km
- Show speed in: Meters per second (m/s)
Find: Escape velocity
Answer
4.
Problem 4.
- Planet, moon or star: Moon
- Starting height above the surface (h): 0 km
- Show speed in: Kilometers per second (km/s)
Find: Escape velocity
Answer
5.
Problem 5.
- Planet, moon or star: Mars
- Starting height above the surface (h): 0 km
- Show speed in: Kilometers per second (km/s)
Find: Escape velocity
Answer
6.
Problem 6.
- Planet, moon or star: Mars
- Starting height above the surface (h): 0 km
- Show speed in: Miles per hour (mph)
Find: Escape velocity
Answer
7.
Problem 7.
- Planet, moon or star: Earth
- Starting height above the surface (h): 0 km
- Show speed in: Meters per second (m/s)
Find: Escape velocity
Answer
8.
Problem 8.
- Planet, moon or star: Jupiter
- Starting height above the surface (h): 0 km
- Show speed in: Kilometers per hour (km/h)
Find: Escape velocity
Answer
9.
Problem 9.
- Planet, moon or star: Sun
- Starting height above the surface (h): 0 km
- Show speed in: Kilometers per second (km/s)
Find: Escape velocity
Answer
10.
Problem 10.
- Planet, moon or star: Sun
- Starting height above the surface (h): 0 km
- Show speed in: Meters per second (m/s)
Find: Escape velocity
Answer

Answer key: Escape Velocity worksheet

1. Escape velocity: 60.2 km/s
1. Use the mass of Jupiter
  $M$ $= 1.89813e+27 kg$
2. Use the mean radius of Jupiter (69,911 km)
  $R$ $= 69,911,000 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 1.89813e+27$ $= 1.266869e+17 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 1.266869e+17}{69,911,000}}$ $= 60,201.606285 m/s$
5. Change the answer to km/s, the unit you picked: divide by 1,000
  $\frac{60,201.606285}{1,000}$ $= 60.201606 km/s$
6. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{1.266869e+17}{{69,911,000}^{2}}$ $= 25.920337 m/s²$
2. Escape velocity: 134,667.16 mph
1. Use the mass of Jupiter
  $M$ $= 1.89813e+27 kg$
2. Use the mean radius of Jupiter (69,911 km)
  $R$ $= 69,911,000 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 1.89813e+27$ $= 1.266869e+17 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 1.266869e+17}{69,911,000}}$ $= 60,201.606285 m/s$
5. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{60,201.606285}{0.44704}$ $= 134,667.157939 mph$
6. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{1.266869e+17}{{69,911,000}^{2}}$ $= 25.920337 m/s²$
3. Escape velocity: 12,560.1 m/s
1. Change the radius to m, the standard unit the formula uses (1 km = 1,000 m)
  $5,500 km \times 1,000$ $= 5,500,000 m$
2. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 6.5e+24$ $= 433,829,499,999,999.94 m³/s²$
3. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 433,829,499,999,999.94}{5,500,000}}$ $= 12,560.102779 m/s$
4. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{433,829,499,999,999.94}{{5,500,000}^{2}}$ $= 14.341471 m/s²$
4. Escape velocity: 2.38 km/s
1. Use the mass of the Moon
  $M$ $= 7.346e+22 kg$
2. Use the mean radius of the Moon (1,737.4 km)
  $R$ $= 1,737,400 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 7.346e+22$ $= 4,902,940,780,000 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 4,902,940,780,000}{1,737,400}}$ $= 2,375.709931 m/s$
5. Change the answer to km/s, the unit you picked: divide by 1,000
  $\frac{2,375.709931}{1,000}$ $= 2.37571 km/s$
6. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{4,902,940,780,000}{{1,737,400}^{2}}$ $= 1.624265 m/s²$
5. Escape velocity: 5.03 km/s
1. Use the mass of Mars
  $M$ $= 6.4171e+23 kg$
2. Use the mean radius of Mars (3,389.5 km)
  $R$ $= 3,389,500 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 6.4171e+23$ $= 42,829,650,530,000 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 42,829,650,530,000}{3,389,500}}$ $= 5,027.122221 m/s$
5. Change the answer to km/s, the unit you picked: divide by 1,000
  $\frac{5,027.122221}{1,000}$ $= 5.027122 km/s$
6. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{42,829,650,530,000}{{3,389,500}^{2}}$ $= 3.727977 m/s²$
6. Escape velocity: 11,245.35 mph
1. Use the mass of Mars
  $M$ $= 6.4171e+23 kg$
2. Use the mean radius of Mars (3,389.5 km)
  $R$ $= 3,389,500 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 6.4171e+23$ $= 42,829,650,530,000 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 42,829,650,530,000}{3,389,500}}$ $= 5,027.122221 m/s$
5. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{5,027.122221}{0.44704}$ $= 11,245.352142 mph$
6. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{42,829,650,530,000}{{3,389,500}^{2}}$ $= 3.727977 m/s²$
7. Escape velocity: 11,186.17 m/s
1. Use the mass of Earth
  $M$ $= 5.9722e+24 kg$
2. Use the mean radius of Earth (6,371 km)
  $R$ $= 6,371,000 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 5.9722e+24$ $= 398,602,544,600,000 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 398,602,544,600,000}{6,371,000}}$ $= 11,186.165197 m/s$
5. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{398,602,544,600,000}{{6,371,000}^{2}}$ $= 9.820302 m/s²$
8. Escape velocity: 216,725.78 km/h
1. Use the mass of Jupiter
  $M$ $= 1.89813e+27 kg$
2. Use the mean radius of Jupiter (69,911 km)
  $R$ $= 69,911,000 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 1.89813e+27$ $= 1.266869e+17 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 1.266869e+17}{69,911,000}}$ $= 60,201.606285 m/s$
5. Change the answer to km/h, the unit you picked: divide by 0.277777777778
  $\frac{60,201.606285}{0.277777777778}$ $= 216,725.782627 km/h$
6. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{1.266869e+17}{{69,911,000}^{2}}$ $= 25.920337 m/s²$
9. Escape velocity: 617.69 km/s
1. Use the mass of the Sun
  $M$ $= 1.9885e+30 kg$
2. Use the mean radius of the Sun (695,700 km)
  $R$ $= 695,700,000 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 1.9885e+30$ $= 1.327185e+20 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 1.327185e+20}{695,700,000}}$ $= 617,688.698888 m/s$
5. Change the answer to km/s, the unit you picked: divide by 1,000
  $\frac{617,688.698888}{1,000}$ $= 617.688699 km/s$
6. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{1.327185e+20}{{695,700,000}^{2}}$ $= 274.21254 m/s²$
10. Escape velocity: 617,688.7 m/s
1. Use the mass of the Sun
  $M$ $= 1.9885e+30 kg$
2. Use the mean radius of the Sun (695,700 km)
  $R$ $= 695,700,000 m$
3. Multiply the mass by the gravitational constant G = 6.6743 × 10⁻¹¹ m³/(kg·s²), the fixed number that sets gravity's strength
  $6.6743e-11 \times 1.9885e+30$ $= 1.327185e+20 m³/s²$
4. Find the escape speed: double that, divide by your distance from the center, then take the square root
  $\sqrt{\frac{2 \times 1.327185e+20}{695,700,000}}$ $= 617,688.698888 m/s$
5. Find the pull of gravity at that distance: divide G × M by the distance squared
  $\frac{1.327185e+20}{{695,700,000}^{2}}$ $= 274.21254 m/s²$