• Pixel-art sticker of Swingby, personifying Gravity Assist, with the caption “Borrow Speed From A Planet.”

IndexRelativity & CosmosSticker

Swingby

Gravity Assist Physics

\[v_{\text{out}} \leq v_{\text{in}} + 2U\]
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Meet Swingby, a space probe who steals speed from a giant planet without fuel. Relative to the planet his speed is unchanged, but the planet's motion around the Sun can add up to twice its speed, about 26 km/s at Jupiter in principle. Voyager hopped planets this way. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Swingby, a space probe who steals a little speed from a giant planet without using fuel.

Seen from the planet, a probe that swings past leaves with the same speed it arrived with, only in a new direction. But the planet is moving around the Sun. Seen from the Sun, the probe can pick up some of the planet's speed.

In the best case, flying head-on into a planet moving at U, the probe gains up to 2U. Jupiter orbits at about 13 km/s, so in principle a probe could gain up to about 26 km/s. Real flybys gain less, because the path bends by less than 180°.

The planet slows down by an amount far too tiny to measure, because it is vastly heavier than the probe.

In 1977 the two Voyager probes used a rare line-up of the outer planets to hop from one to the next, and they are now travelling between the stars.

Equations

\[v_{\text{out}} \leq v_{\text{in}} + 2U\]
Symbols
SymbolMeaningUnit
\(v_{\text{out}}\) speed after the flyby relative to the Sun \(\mathrm{m/s}\)
\(v_{\text{in}}\) speed before the flyby relative to the Sun \(\mathrm{m/s}\)
\(U\) orbital speed of the planet \(\mathrm{m/s}\)