calculating orbital speed of planet, given distance and time

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a) The average distance of Saturn from the sun is 1.43 times ten to the 9 km and its period of revolution is 29.5 years. Calculate the length of Saturn's oribt and its average speed in km per hour...correct to nearest km per hour. Remember speed is distance divided by time.

My question is in calculating the circumference of the orbit as 2*pi*r. Is the radius equal to the radius of the sun plus 1.43 times ten to the 9 km?

The same sort of question I have for the this question...

b) The moon is an Earth satellite and has an average distance of 390000 kilometres from the Earth. It orbital period is 28 days. Calculate its average orbital speed in kilometres per second, correct to 1 decimal place.

Your help is appreciated...
 
americo74 said:
Is the radius equal to the radius of the sun plus 1.43 times ten to the 9 km?
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Technically, yes, but what is the radius of the sun? If they didn't give you this information, then you're probably not expected to use it.

Plus, since that value must necessarily be much, much smaller than the given distance (which is obviously a rounded value), they probably figure that there's no point in bothering with it. You could add the value in, but then you'd effectively subtract it right back out when you rounded to two decimal places.

The Earth and Moon, however, are much closer than are the sun and Saturn, so you might be expected to include the Earth's radius (and the moon's? treating the two bodies as point-masses?) for part (b).

That's my guess, anyway; I could be wrong....

Eliz.
 
Orbital radius is defined as the distance from center of mass to center of mass.

You do not need to take the radius of either celestial body into account.
 
Re: calculating orbital speed of planet, given distance and

a) The average distance of Saturn from the sun is 1.43 times ten to the 9 km and its period of revolution is 29.5 years. Calculate the length of Saturn's oribt and its average speed in km per hour...correct to nearest km per hour. Remember speed is distance divided by time.

My question is in calculationg the circumference of the orbit as 2*pi*r. Is the radius equal to the radius of the sun plus 1.43 times ten to the 9 km?

The same sort of question I have for the this question...

b) The moon is an Earth satellite and has an average distance of 390000 kilometres from the Earth. It orbital period is 28 days. Calculate its average orbital speed in kilometres per second, correct to 1 decimal place.

Your help is appreciated
Click to expand...
Distances of planets from the sun are usually measured to the center of the sun. Therefore, the circumfers of the orbit would be C = 2Pi(1.43x10^9) km.

The average orbital speed derives from V = 2Pi(1.43x10^9)/[29.5(365.25)24] km/hr = 34,745 km/hr = 9.65 km/sec. = 34,740 km/hr.

The mean orbital speed can also be derived from V = sqrt(µ/r) where V = the speed, µ = the sun's gravitational constant = 1.3273x10^20 m^3/sec^2, and r = the orbital radius = 1.43x10^9 km. = 1430x10^9m
V = sqrt[(1.3272x10^20)/(1.43x10^12)] = 9634m/sec = 9.63 km/sec.

The length of the Moon's orbit is given by C = 2Pi(390,000)= 2,450,442 km.

Therefore, its mean orbital speed is V = 2,450,442/28(24) = 3646 km/hr = 1.013 km/sec.

Using the earth's gravitational constant of 3.986x10^14,

V = sqrt[3.986x10^14/390,000,000] = 1011 m/s = 1.011 km.sec.
 
Many thanks for your explanation

and the answers... I will double check them.
 
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