Question

Wavelength and Frequency (a) How long in minutes) does it take light to reach the Earth from the Sun? (Light travels at 3.00x 10 m/s. The distance from the Earth to the Sun is 93.0 million miles.) (b) A signal sent from the Earth would currently take 6.09618 hours to reach the NASA probe New Horizons, which recently passed Kupier Belt Object 2014 MU69 ("'Ultima Thule). What is the distance from Earth to New Horizons in astronomical units, AU, if I AU 1.495978707x10 m? (An Astronomical Unit, is the distance between the Sun and the Earth, and is a common unit of measurement in astronomy.) (10 pts)

im having trouble with part b

Answer 1

a) The time taken for the sunlight to reach earth

Given velocity of light is 3.00 x 10⁸ m/s

The distance from earth to sun is 93 million miles = 93 x 10⁶ miles

We have 1 mile = 1609.344 meters

Then 93 x 10⁶ miles = 93 x 1609.344 x 10⁶ meters = 149.67 x 10⁹ meters

Thus we have the distance and velocity, we need to find out time.

We know that

Velocity = Distance / Time

Then Time = Distance / velocity

Time = 149.67 x 10⁹m / 3.00 x 10⁸ m/s = 498.9 $\approx$ 500 secs = 8.33 minutes

Thus the time required for the sunlight to reach earth is 8.33 minutes.

b) Distance from earth to New Horizons

Given that the time taken for the signal to reach New Horizons is 6.09618 Hrs

In terms of seconds, it is 6.09618 x 60 x 60 secs = 21946.248 sec

The satellite signals are also a part of electromagnetic spectrum and are nearly moves with the velocity of light.

Thus the velocity of signal is 3.00 x 10⁸ m/s

Now, we have velocity and time. We need to find out distance. From the formula,

Velocity = Distance / Time

Distance = Velocity x Time

Therefore Distance = 3.00 x 10⁸ m/s x 21946.248 s = 65.838744 x 10¹¹ m

We should answer the distance in terms of astronomical units

Given 1.495978707 x 10¹¹ m is equal to 1 AU then

65.838744 x 10¹¹ m is

= 65.838744 x 10¹¹ m / 1.495978707 x 10¹¹ = 44.0104820 AU

Thus the required distance between Earth and NASA New Horizons in terms of AU is 44.0104820 AU