How many minutes are required for a radio signal to travel from Earth to a space station on Mars if Mare is 7.83 x 10 to the 7th power km?
t=s/c=7.83•10¹º /3•10⁸ =261 s=4.35 min
Oh boy, I think the radio signal might need to pack a lunch for this journey! Alright, let's do some number crunching. The speed of light is about 299,792 kilometers per second, or as I like to call it, super speedy! So, if we divide the Mars distance, 7.83 x 10^7 km by the speed of light, we can get the time it takes. Drumroll, please! It would take approximately 260 seconds, which is about 4 minutes and 20 seconds. Talk about a cosmic commute! Safe travels! 🚀
To determine how many minutes are required for a radio signal to travel from Earth to Mars, we need to calculate the time it takes for the signal to travel one-way.
First, we need to convert the given distance from kilometers to meters, as the speed of light is usually given in meters per second.
Given:
Distance from Earth to Mars (d) = 7.83 x 10^7 km
Converting km to meters:
d = 7.83 x 10^7 km = 7.83 x 10^7 km * 1000 m/km = 7.83 x 10^10 m
Now, we need to determine the time it takes for the signal to travel this distance at the speed of light.
The speed of light (c) is approximately 3 x 10^8 meters per second.
Time taken (t) = Distance (d) / Speed of light (c)
t = (7.83 x 10^10 m) / (3 x 10^8 m/s)
t = 7.83 x 10^10 m / 3 x 10^8 m/s
t = (7.83 / 3) x 10^10 / 10^8 s
t = 2.61 x 10^2 s
To convert this duration into minutes, we divide it by 60 (the number of seconds in a minute).
t (in minutes) = (2.61 x 10^2 s) / 60 s/min
t ≈ 4.35 minutes (rounded to two decimal places)
Therefore, it takes approximately 4.35 minutes for a radio signal to travel from Earth to a space station on Mars.
To calculate the time required for a radio signal to travel from Earth to a space station on Mars, we need to use the speed of light. The speed of light is approximately 299,792 kilometers per second.
Step 1: Convert the distance between Earth and Mars from kilometers to meters.
To convert the distance, multiply the given distance by 1000 since there are 1000 meters in a kilometer.
Distance in meters = 7.83 x 10^7 km * 1000
Step 2: Calculate the time in seconds.
Divide the distance in meters by the speed of light to get the time in seconds.
Time in seconds = (Distance in meters) / (Speed of light)
Step 3: Convert the time from seconds to minutes.
To convert from seconds to minutes, divide the time in seconds by 60 since there are 60 seconds in a minute.
Time in minutes = (Time in seconds) / 60
Let's do the calculations:
Distance in meters = 7.83 x 10^7 km * 1000 = 7.83 x 10^10 meters (using scientific notation)
Speed of light = 299,792 km/s
Time in seconds = (7.83 x 10^10 meters) / (299,792 km/s * 1000) = 260.87 seconds
Time in minutes = 260.87 seconds / 60 ≈ 4.35 minutes
Therefore, it takes approximately 4.35 minutes for a radio signal to travel from Earth to a space station on Mars.