The moon has a period of 27.3 days and a mean distance of 3.90 x 10^5 km from the center of Earth.
a) Use Kepler's laws to find the period of a satellite in orbit 6.70 x 10^3 km from the center of Earth
--- I was able to do this and the answer i got was: 88.6 mins, but was stuck on the 2nd part of this question, which is below:
b)How far above Earth's surface is this satellite?
You have the mean distance from the center of Earth. Normally, one might subtract the thickness of the Earth from the center to get the distance from the Surface .
you have to subtract the radius of earth from the total radius
so:
6.7x10^3-6.38x10^3
=0.4 km
or
=400 m
To determine how far above Earth's surface the satellite is, we need to subtract the radius of the Earth from the distance of the satellite from the center of the Earth.
Given:
Distance of the satellite from the center of the Earth = 6.70 x 10^3 km
Radius of the Earth = 3.90 x 10^5 km
To find the distance above Earth's surface:
1. Subtract the radius of the Earth from the distance of the satellite from the center of the Earth:
Distance above Earth's surface = Distance of the satellite from the center of the Earth - Radius of the Earth
Distance above Earth's surface = (6.70 x 10^3 km) - (3.90 x 10^5 km)
2. Calculate the result:
Distance above Earth's surface = -3.83 x 10^5 km
Therefore, the satellite is approximately 3.83 x 10^5 km above Earth's surface.
To find the distance above Earth's surface of a satellite, you need to subtract the radius of the Earth from the satellite's distance from the center of Earth.
Let's break it down step by step:
1. Convert the distance of the satellite from the center of Earth to meters.
Given: Distance from center of Earth = 6.70 x 10^3 km
Conversion: 1 km = 1000 m
Calculation: Distance from center of Earth = 6.70 x 10^3 km * 1000 m/km = 6.70 x 10^6 m
2. Convert the mean distance of the moon from the center of Earth to meters.
Given: Mean distance of the moon from the center of Earth = 3.90 x 10^5 km
Calculation: Mean distance of the moon from the center of Earth = 3.90 x 10^5 km * 1000 m/km = 3.90 x 10^8 m
3. Calculate the distance above Earth's surface.
Calculation: Distance above Earth's surface = Distance from center of Earth - Radius of Earth
The radius of Earth is approximately 6.37 x 10^6 m.
Calculation: Distance above Earth's surface = (6.70 x 10^6 m) - (6.37 x 10^6 m)
Finally, calculate the distance above Earth's surface in scientific notation or decimal form.
If you have the result in scientific notation, you can rewrite it as a decimal by multiplying by 10 raised to the appropriate power. If you have the result in decimal form, you can write it in scientific notation by moving the decimal point and adjusting the exponent.
Please note that the value of Earth's radius used in this explanation is an approximation and can vary slightly depending on the reference used.