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# Mechanics Kepler orbits Watch

1. Hello I'm just wondering if anyone could help me with the following question, thanks
2. Hi,
I assume you're ok with part a) since it's just a definition but Kepler's third law is
where k is a constant.
For part b) you need to use this equation to find r for Jupiter- you have it's period, you just need k, which you can find using the data you know about Earth, because Jupiter and Earth orbit the same star.

Once you have period and radius of orbit you can find speed using the circumference of the orbit- the complicated bit here is converting the units- I assume you have the AU conversion on a datasheet.

For a circular orbit
Previous parts have given you all these figures so just plug them in.
See how you get on with those first 4 parts then tell me which of the others you're stuck on.
3. (Original post by sindyscape62)
Hi,
I assume you're ok with part a) since it's just a definition but Kepler's third law is
where k is a constant.
For part b) you need to use this equation to find r for Jupiter- you have it's period, you just need k, which you can find using the data you know about Earth, because Jupiter and Earth orbit the same star.

Once you have period and radius of orbit you can find speed using the circumference of the orbit- the complicated bit here is converting the units- I assume you have the AU conversion on a datasheet.

For a circular orbit
Previous parts have given you all these figures so just plug them in.
See how you get on with those first 4 parts then tell me which of the others you're stuck on.
Hi thanks for this, I've been trying to do this problem for the last few days anyway can you explain what l is in the second equation that you stated, thank you again for the method to do part b and if you could go over the remaining parts
4. (Original post by Scary)
Hi thanks for this, I've been trying to do this problem for the last few days anyway can you explain what l is in the second equation that you stated, thank you again for the method to do part b and if you could go over the remaining parts
Scrap the bit about L I've just realised what it is.
5. For part e) calculate the moment of inertia (I) using the given equation.
angular velocity and
and you have the period, so you can find angular momentum.
For part f) you're looking for Jupiter's acceleration in terms of T and r. Start with and substitute
Use r and T to find acceleration.
For g) use the expression you found and substitute Kepler's third law into it to get an equation for centripetal acceleration only in terms of r and constants. In an orbit the centripetal acceleration is provided by gravity, so gravitational field strength is equal to centripetal acceleration. Because r is to the power of negative 2 gravitational field strength follows the inverse square law.
If you need clarification for any parts let me know
6. (Original post by sindyscape62)
For part e) calculate the moment of inertia (I) using the given equation.
angular velocity and
and you have the period, so you can find angular momentum.
For part f) you're looking for Jupiter's acceleration in terms of T and r. Start with and substitute
Use r and T to find acceleration.
For g) use the expression you found and substitute Kepler's third law into it to get an equation for centripetal acceleration only in terms of r and constants. In an orbit the centripetal acceleration is provided by gravity, so gravitational field strength is equal to centripetal acceleration. Because r is to the power of negative 2 gravitational field strength follows the inverse square law.
If you need clarification for any parts let me know
Hi thanks for your response i've managed all of the parts execpt the last part, i'm not too sure where to substitute keplers law into, if you could show me i would be greatful it's been doing my head in for the past week haha
7. The expression you should have got in part f) is

Kepler's third law states that

T^2 is in both expressions, so by substituting you get

You've got r's on the top and the bottom so it simplifies to

where k is a constant for the solar system. The only part that isn't a constant is
so centripetal acceleration (which is the same as acceleration due to gravity in this context) follow the inverse square law with distance.
8. (Original post by sindyscape62)
The expression you should have got in part f) is

Kepler's third law states that

T^2 is in both expressions, so by substituting you get

You've got r's on the top and the bottom so it simplifies to

where k is a constant for the solar system. The only part that isn't a constant is
so centripetal acceleration (which is the same as acceleration due to gravity in this context) follow the inverse square law with distance.
ahh obviously thank you for clearing this up i didnt expand the expression like you did, thanks for all the help

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