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An example of an elastic collision is The gravitational slingshot effect . A spacefship of mass 650 kg is moving at 9.5 km/s in the +x direction.  It approaches the planet Saturn, mass 5.68 x10 26kg , which is moving in the –x- direction as shown in the figure.  The gravitational attraction of Saturn accelerates the spaceship as it approaches and causes to swing around the planet and heads off in the same direction as Saturn.  Several probes such as Voyager have used this to save on “gas”.    Estimate the final speed of the spacecraft after it is far enough to be considered free of Saturn’s gravitational pull.  Assume that the speed of Saturn is not affect due to its large mass.  Express your answer in km/s.  HINT:  perfectly ELASTIC COLLISION.

An example of an elastic collision is The gravitational slingshot effect . A spacefship of mass 650 kg is moving at 9.5 km/s in the +x direction.  It approaches the planet Saturn, mass 5.68 x10 26kg , which is moving in the –x- direction as shown in the figure.  The gravitational attraction of Saturn accelerates the spaceship as it approaches and causes to swing around the planet and heads off in the same direction as Saturn.  Several probes such as Voyager have used this to save on “gas”.    Estimate the final speed of the spacecraft after it is far enough to be considered free of Saturn’s gravitational pull.  Assume that the speed of Saturn is not affect due to its large mass.  Express your answer in km/s.  HINT:  perfectly ELASTIC COLLISION.

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An example of an elastic collision is The gravitational slingshot effect . A spacefship of mass 650 kg is moving at 9.5 km/s in the +x direction.  It approaches the planet Saturn, mass 5.68 x10 26kg , which is moving in the –x- direction as shown in the figure.  The gravitational attraction of Saturn accelerates the spaceship as it approaches and causes to swing around the planet and heads off in the same direction as Saturn.  Several probes such as Voyager have used this to save on “gas”.    Estimate the final speed of the spacecraft after it is far enough to be considered free of Saturn’s gravitational pull.  Assume that the speed of Saturn is not affect due to its large mass.  Express your answer in km/s.  HINT:  perfectly ELASTIC COLLISION.

The image depicts a spacecraft performing a gravity assist maneuver around a planet with rings, which can be identified as Saturn. The trajectory is shown as a dashed line, indicating the path of the spacecraft. Key Elements: 1. **Spacecraft Approach Speed (\( v_{Sp} \)):** - The spacecraft is shown approaching Saturn from the left with an initial speed represented by \( v_{Sp} \). The specific numerical value for the approach speed is not provided in this instance. 2. **Planet's Speed (\( v_{S} \)):** - The speed of Saturn is given as \( v_{S} = -9.6 \, \text{km/s} \). The negative sign indicates the direction of Saturn’s movement is opposite to the reference direction (indicated by an arrow labeled \( x \)). 3. **Spacecraft Departure Speed (\( v'_{Sp} \)):** - As the spacecraft exits the gravitational influence of Saturn, the diagram queries the new speed (\( v'_{Sp} \)) after the gravity assist. This speed would typically increase compared to the approach speed if the maneuver is successful. 4. **Direction Arrows:** - Green arrows illustrate the direction of velocities for both the spacecraft and Saturn. These arrows guide the viewer’s understanding of the motion dynamics within the maneuver. This diagram visually explains the concept of a gravity assist, where a spacecraft uses a planet's gravitational field to alter its path and speed, conserving fuel and increasing velocity relative to its trajectory before the maneuver.
Transcribed Image Text:The image depicts a spacecraft performing a gravity assist maneuver around a planet with rings, which can be identified as Saturn. The trajectory is shown as a dashed line, indicating the path of the spacecraft. Key Elements: 1. **Spacecraft Approach Speed (\( v_{Sp} \)):** - The spacecraft is shown approaching Saturn from the left with an initial speed represented by \( v_{Sp} \). The specific numerical value for the approach speed is not provided in this instance. 2. **Planet's Speed (\( v_{S} \)):** - The speed of Saturn is given as \( v_{S} = -9.6 \, \text{km/s} \). The negative sign indicates the direction of Saturn’s movement is opposite to the reference direction (indicated by an arrow labeled \( x \)). 3. **Spacecraft Departure Speed (\( v'_{Sp} \)):** - As the spacecraft exits the gravitational influence of Saturn, the diagram queries the new speed (\( v'_{Sp} \)) after the gravity assist. This speed would typically increase compared to the approach speed if the maneuver is successful. 4. **Direction Arrows:** - Green arrows illustrate the direction of velocities for both the spacecraft and Saturn. These arrows guide the viewer’s understanding of the motion dynamics within the maneuver. This diagram visually explains the concept of a gravity assist, where a spacecraft uses a planet's gravitational field to alter its path and speed, conserving fuel and increasing velocity relative to its trajectory before the maneuver.
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