Science Podcasts

Question of the Week episode

Sun, 16th Oct 2016

How much younger would you be after 50 years on Jupiter?

Jupiter's Great Red Spot (c) NASA/Jet Propulsion Lab

Could a jaunt to Jupiter be the physics-version of anti-wrinkle cream? This week, Kerstin Göpfrich convinced physicist Dr Stuart Higgins to go on a mission to answer Troy's question...

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I assume you will be on the same day on the planet... That means you will only spend part of 'Jupiter's day'. eric.emmanuel, Sat, 29th Oct 2016

A couple of points I'd like to add to this thread.

The comparison between clock on Earth and clock on Jupiter so far is a bit incomplete as it only takes into account the difference in the respective Planet's gravitational fields.  In other words, if all else is equal a clock on Jupiter would run some 20 nanoseconds slower per sec than the clock on Earth.  However, all other things are not equal.  Jupiter orbits further from the Sun than the Earth does.  This means that not only is the Earth deeper in the Sun's gravitational field, it has a greater orbital speed.  These two factor both add up to cause a clock sharing an orbit with the Earth around the Sun to run slower than one sharing Jupiter's orbit.

When you factor this in, it turns out that the clock on Jupiter runs only ~7 nanoseconds per sec slower than the Earth clock when you do a clock to clock comparison.

We do this same combination of gravitational time dilation and time dilation due to speed when dealing with satellites orbiting the Earth and comparing their clock rates to ones on the surface of the Earth.  For lower satellites, the speed factor dominates and the satellite clocks run slow, for higher satellites, the position in the field dominates and the clocks run fast. The dividing line is at an altitude which is equal to half the radius of the Earth.
GPS satellites orbit below this altitude, so they run slower than a clock on the surface.

One last point, Someone mentioned that clocks at high altitude run fast because they are in a weaker gravity field. This, I fear, is misleading as people can take this to mean that it is the local strength of gravity that is the factor that determines gravitational time dilation. This is not the case, It is the difference in gravitational potential.

To illustrate the difference, let's use two different planets to compare clocks, Earth and Uranus.  We will use the " all other things being equal" approach and compare clocks just due to the the planets' gravitational fields.
Doing this, we find that that a clock, according to Gravitational time dilation, will run slower on Uranus than it does on the Earth, However, if we compare surface gravity of the two clocks, Earth's surface gravity is the greater of the two.  A clock on the surface of the Earth will feel a greater gravitational force, but the clock on Uranus will run slower by virtue of being in a deeper gravity well. Janus, Sun, 30th Oct 2016

What interesting points. I'd not thought about the relative speeds of the two orbiting bodies. Thank you. chris, Mon, 31st Oct 2016

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