Gravitational fields and orbital motion
Введено| English | Значение |
|---|---|
| gravitational field/ˌɡrævɪˈteɪʃənl fiːld/ | гравитационное поле |
| centripetal force/senˈtrɪpɪtl fɔːs/ | центростремительная сила |
What would explain this observation?
- An orbiting satellite is continuously falling while moving sideways. Being in orbit does not require gravity to vanish.
Build the model
- Gravitational field 引力场 strength is force per unit mass.
- A gravitational force can provide the centripetal force 向心力 for a circular orbit.
- Field and potential describe different quantities.
- gravitational field: A description of gravitational force per unit mass.
- centripetal force: Net force toward the centre of a curved path.
What direction is the net force in uniform circular motion?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Uniform circular motion needs a resultant force toward the centre to keep changing the velocity's direction. Nothing pushes outward; without the inward force the object would carry on in a straight line.
Match each technical term to its precise meaning.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- For a point mass or outside a spherical mass, field strength follows an inverse-square distance dependence.
- Use distance from the centre, not height above the surface alone.
In the lab: State the circular-orbit approximation and ignore atmospheric drag only when justified. Draw the force toward the central body and velocity tangential to the orbit. Do not add an outward force merely because the path is circular.
Which two habits make the investigation or model in this case more defensible?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Stating the conditions and assumptions lets others repeat the work exactly, and recording the supporting evidence lets them check the conclusion. Hiding disagreeing results removes the evidence that could challenge a wrong conclusion, and one measurement can never establish a wider claim.
Work from known quantities
- Known: field strength is 8 units at distance r from a spherical source.
- At 2r, g2/g1=(r/2r)²=1/4. g2=8/4=2 units.
- The gravitational force on a fixed test mass decreases in the same ratio.
Your turn: Field strength is 18 units at r. Find it at 3r for an inverse-square field.
Field strength is 18 units at r. Find it at 3r for an inverse-square field.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
The result is 2 . Known: field 18 units at r; inverse-square field; distance 3r. Use g proportional to 1/r^2. New field = 18/3^2 = 18/9 = 2 units. The force on a fixed mass falls in the same ratio.
Check the conclusion and its limits
- Weightlessness in an orbiting spacecraft means apparent weight is small in free fall, not that there is no gravitational field.
Not true: Gravity is zero everywhere a spacecraft experiences apparent weightlessness. An orbiting spacecraft is in free fall: gravity is nearly as strong there as on the ground and supplies the centripetal force. Crew and craft fall together, so nothing presses them down - that is apparent weightlessness, not zero gravity.
- Gravitational field strength is force per unit mass.
- For a point mass or outside a spherical mass, field strength follows an inverse-square distance dependence.
- Watch for: weightlessness in an orbiting spacecraft means apparent weight is small in free fall, not that there is no gravitational field.
Write from a field strength of 5 units
- Field strength is 45 units at distance r from a spherical source.
- Find it at 3r. Apparent weightlessness in orbit does not mean gravity is zero.
An orbiting spacecraft is in free fall: gravity is nearly as strong there as on the ground and supplies the centripetal force.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
True. An orbiting spacecraft is in free fall: gravity is nearly as strong there as on the ground and supplies the centripetal force. Crew and craft fall together, so nothing presses them down - that is apparent weightlessness, not zero gravity.
A description of gravitational force per unit mass: write the technical term.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
gravitational field means A description of gravitational force per unit mass.
Field strength is 45 units at distance r. What is it at 3r for an inverse-square field, and why is gravity not zero in an orbiting spacecraft?
An inverse-square field falls with the square of the distance. Free fall still has a gravitational force.
What is the field strength at 3r?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
45 divided by 9 is 5 units. Tripling the distance does not divide the field by 3.