I recently studied that Voyager 1 has traveled a distance of 125.01 AU as of August 3rd, 2013. I wonder, how would it be able to communicate with the Earth? How much time does it take for the signal from ground station to reach Voyager 1?
The radio communication system of Voyager 1 was designed to be used up to and beyond the limits of the Solar System during the extremely long flight of this space probe. The communication system includes a 3.7 meter diameter parabolic dish high-gain antenna to send and receive radio waves via the three Deep Space Network stations on the Earth. These modulated waves are placed in the S-band (about 13 cm in wavelength) and X-band (about 3.6 cm in wavelength) which provided a bit rate as high as 115.2 kilobits per second when Voyager 1 was at the distance of Jupiter from the Earth, and many fewer kilobits per second at larger distances.
The Voyager 1 communication is received on Earth by the Deep Space Network (DSN):
NASA's Deep Space Network (DSN) has been in partnership with Voyager 1 and Voyager 2 since 1977, providing daily communications support to the two very distant spacecraft. The excellent partnership continues as the Voyager twin spacecraft explore the regions of our universe near the area where the solar wind meets the interstellar winds – areas never before explored by human-made objects.
Because of the enormous distances and the resultant weak signals from the spacecraft, the large antennas and the very sensitive receivers of the DSN are required to provide the necessary communications capabilities. The DSN is the world's largest and most sensitive spacecraft communications network. It consists of three deep space communications complexes located approximately 120 degrees of longitude apart around the world: at Goldstone, California; near Madrid, Spain; and near Canberra, Australia. This placement permits continuous communication with a spacecraft.
Source: JPL Voyager - Deep Space Network
Radio communications travel at the speed of light, or
299,792,458 m / s. And one Astronomical Unit (AU) is
149,597,871 km. The quoted
125.01 AU is Voyager 1's distance it travelled as it navigated through our Solar system, and not the distance from the Earth on that date, so we'll first have to find an accurate distance from the Earth, and do our calculations on the time it takes for its signals to reach the Earth after we find that information.
JPL has a convenient web page with exact current Voyager's distance from the Earth. It also provides the calculation for how long it takes the light from the Sun to reach it, but that's not exactly what we need (we want the time to reach the Earth with the speed of light). We could make a shortcut in our calculations, since the Sun is on average
1 AU away from the Earth, but that would result in some margin of error due to the Earth not necessarily along the direct path between Voyager 1 and the Sun (it could be closer, or farther, depending on the time of the year and the Earth's position in the orbit around the Sun).
So let's do our own calculations; Currently, Voyager 1 is
124.56269764 AU, or
18,634,314,372.96 km away from the Earth. Entering these numbers and the speed of light in our calculator (distance divided by speed of light, after we do unit conversion from kilometers to meters), we get the
62157.382 seconds or 17 hours, 15 minutes, 57 seconds and 382 milliseconds, and increasing every day.