How did Dyce, Pettingill and Shapiro do it?

Throughout the years astronomers assumed that Mercury is in synchronous rotation with its period of revolution, i.e. it takes just as long to rotate once on its axis as it takes to revolve around the Sun, 87,97 days. The reason they adduced for this, is that Mercury is very close to the Sun and the Sun's enormous gravity would lock Mercury's rotation in the same way as the Moon's rotation is locked with its period of revolution around the Earth, so that Mercury will always keep the same face towards the Sun, as the Moon does towards the Earth. No clear markings could be discerned on Mercury's surface with the best telescopes.

In an article in the Astronomical Journal, Vol 72 (1967) page 351, R B Dyce, G H Pettingill and I I Shapiro describe how they investigated Mercury's period of rotation in 1965 by using the World's largest radio telescope at Arecibo on Puerto Rico (300 metres wide). They transmitted very short pulses of radar waves of 1 to 5 ten-thousandths of a second at a frequency of 430 megahertz (4,3 x 10⁸ hertz ) to Mercury. They argued that the radar waves reflected from points near to Mercury's nearest point O on Mercury's equator, would have a shorter distance to travel from the Earth and back again, than that covered by radar waves to and from points A and B near Mercury's rim and far from the sub-vertical point O. The extra distance travelled by waves to and from A and B would be 2d. (to and fro). If the spin of the planet is direct, (anti-clockwise), point B will be approaching and point A will be receding. This means that the frequency of waves reflected from B ( = f ) will be increased by a small amount delta f to and the frequency of the radar waves reflected from A will be decreased by delta f, so that the frequency will be . These differences of frequency could be very easily and accurately measured by the radio telescope.

The lapse of time between reception of the waves from O and from A and B was 210 micro-seconds

Looking down on Mercury from above its North Pole

The distance travelled by the radar waves in this time was 2d (there and back). The radar waves travel at the speed of light and cover this distance in ½ ? t x c and this worked out to 0,0315 x 10⁶ metres. Having found this value of d they could find the value of x in the diagram, namely Mercury's radius R - d. They could then, by using Pythagoras' theorem calculate the value of y. y came to 6,3892 x 10 metres. (Mercury's radius is 2,42 x 10 metres).

They were then able to calculate the speed of rotation of the planet at point B. At B this speed of rotation is represented by V (in the diagram) and V has a component V_o along the line of sight from Earth.

The two triangles in the diagram are similar so that sides opposite equal angles are proportional,  i.e .

To find the value of V_o they made use of the Doppler effect for the small change in frequency At. This change in frequency was read from the graph of signal strength of the received waves against the frequency. This change in frequency was revealed as a broadening of the spectral lines (P to Q) because of the spin of the planet. The range from -1,52 to +1,28 is 2,8, giving an average of 1,4. NOW, ? f, THE CHANGE IN FREQUENCY IS HALF OF THIS, NAMELY 0,7. According to this, V_o worked out to 0,488 m. s^-1.

Now they were able to calculate the value of V, the planet's rate of spin. It worked out at 3,03 m. s^-1.

The circumference of Mercury is 2pR = 2(3,14159) times 2,42 x 10⁶ and this comes to 1,52 x 10⁷ metres. To go once around the planet B takes 1,52 x 10⁷ divided by 3,03 = 0,5017 x 10⁷ secs. There are 86400 seconds in 1 day of 24 hours, namely 8,64 x 10⁴ secs.

Therefore Mercury rotates once in 0,5017 x 10⁷ ÷ 8,64 x 10⁴ = 58,07 days.

MERCURY ROTATES ONCE EVERY 58,07 DAYS'

This remarkable achievement by Dyce, Pettingill and Shapiro was the first indication that Mercury is not locked in synchronous rotation, but that it has a period of rotation which is actually in resonance with the period of revolution around the Sun.

or 3 : 2.

What did the Mariner-10 space probe find in 1974 when it three times passed close to Mercury?. By applying the Doppler effect it found that Mercury rotates ONCE EVERY 58,64 days!, giving a resonance

of or exactly 3 : 2.

Jan Eben van Zyl