I was thinking of the trading of kinetic energy during a gravitational slingshot maneuver and wondered if the kinetic energy lost during that process makes any noticeable impact on the orbit of the planet. Since the planet we are performing this maneuver on loses kinetic energy, it is realistically possible to do enough slingshots that we noticeably change the orbit of the planet? And what would be the consequences of changing the orbit?
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1$\begingroup$ Hi Bradford Le. Welcome to Phys.SE. Did you try to do a back-of-an-envelope estimate of the effect? $\endgroup$– Qmechanic ♦Commented Oct 29, 2023 at 4:38
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2 Answers
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Typically if a satellite of mass $m$ increases its orbital velocity by $x$ meters per second from the slingshot maneuver the planet of mass $M$ will decrease its orbital velocity by $x(\frac{m}{M})$ meters per second in order for angular momenta around the sun to be conserved. Venus has a mass of $4.867\times10^{24}$ kg. If the satellite has a mass of 1000 kg and increases its orbital velocity by 20 000 meters per second from a slingshot maneuver around Venus then Venus will reduce its orbital velocity by $20000\frac{1000}{4.867\times 10^{24}}\approx4.1\times10^{-18}$ meters per second. The orbit of Venus will shift slightly towards the sun.
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$\begingroup$ It might also be worth noting that the fractional change in orbital velocity here is (4.8E-18)/(35,000) = $10^{-22}$ approximately $\endgroup$– RC_23Commented Oct 29, 2023 at 5:41
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$\begingroup$ This answer is actually incomplete as the net result of slowing down a planet is the planet taking a new orbit closer to the Sun with increased orbital velocity. $\endgroup$– AgerhellCommented Oct 29, 2023 at 12:03
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Sometimes seeing educational cartoon diagrams and animations too much can mess up our physical intuition.
Try this: a man-made satellite is about as big as a car. The Earth contains all the cars, machines, skyscrapers, cities, Egyptian pyramids, mountains, glaciers, all the oceans and continents, including all the countries and histories you've ever seen or heard of. Everything just mentioned is on the surface of the Earth's crust – which is under 1% of the mass of the whole planet. And Earth is one of the smaller planets.
This isn't a direct answer, but an invitation to recalibrate your mental model of the Solar System in comparison to everyday things. I think the planetary orbits are safe from our machinations. What is of modest concern however, is biological contamination of ecosystems (either artificial introduction of life to a viable world, or the wiping out of a fragile existing ecosystem by an "invasive" Earth microbe). Space agencies take some pains to prevent this.
