Energy needed to reach planets orbit and leave to leave it.

In summary: I believe OP uses decimal commas. 1,756 kg :smile:1.756 kg indeed it is. My mistake, but how do i find the 1.756 kg?
  • #1
Jacobsen
3
0
How many TJ of energy is necessary to get a 300 ton spacecraft from the surface of Venus to 1) orbit at 60520km and 2) to leave the planets gravitational field?

12104km Venus diameter
6052 is Venus radius therefore.

4,9 * 10ˇ24 kg Venus mass

60520km orbit radius

T-1,9 Earth days

spaceship 300 000kg

Given answers: 14,99 TJ; 15,78 TJ

The Attempt at a Solution


1)energy at orbit -1/2Gmm/R -1/2 *(6,67*10ˇ-11)*(4,9 * 10ˇ24)*300000/60520000 (dist to orbit)= -0,81TJ
and then to get the work required i divide -0,81 TJ-(-16,2 TJ) = 15,39 TJ (the other one comes from below)
2) since binding energy=gravity ´-Gmm/R = -(6,67*10ˇ-11)*(4,9 * 10ˇ24)*300000/6052000(Venus radius) =-16,2TJ
So what exactly am calculating here? No match with given answers?
 
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  • #2
Jacobsen said:
How many TJ of energy is necessary to get a 300 ton spacecraft from the surface of Venus to 1) orbit at 60520km and 2) to leave the planets gravitational field?

12104km Venus diameter
6052 is Venus radius therefore.

4,9 * 10ˇ24 kg Venus mass

60520km orbit radius

T-1,9 Earth days

spaceship 300 000kg

Given answers: 14,99 TJ; 15,78 TJ

The Attempt at a Solution


1)energy at orbit -1/2Gmm/R -1/2 *(6,67*10ˇ-11)*(4,9 * 10ˇ24)*300000/60520000 (dist to orbit)= -0,81TJ
and then to get the work required i divide -0,81 TJ-(-16,2 TJ) = 15,39 TJ (the other one comes from below)
2) since binding energy=gravity ´-Gmm/R = -(6,67*10ˇ-11)*(4,9 * 10ˇ24)*300000/6052000(Venus radius) =-16,2TJ
So what exactly am calculating here? No match with given answers?
Hello Jacobsen. Welcome to PF !

What does " T-1,9 Earth days " mean ?

What is the spacecraft 's potential energy when on the surface of Venus?

What is the spacecraft 's potential energy when on the surface of Venus?

What speed does it need to orbit with a radius of 60520 km ? What kinetic energy does this correspond to?

What is the spacecraft 's potential energy when it's in this orbit?
 
  • #3
Jacobsen, it appears to me that your answers look good and that the given answers are not correct. Is there some other information that is not included in the problem description?
 
  • #4
T - 1,9 (164160 sec) Earth days means orbiting period on the orbit. Not not necessary here.
There is also a 3)part - Let's assume that the starting device turns nuclear energy into mechanical at the rate of 1/10000 of fuel mass is into useful work. How much nuclear energy we need? A: 1756 kg - but i should get a different answer with my numbers right?
 
  • #5
Jacobsen said:
There is also a 3)part - Let's assume that the starting device turns nuclear energy into mechanical at the rate of 1/10000 of fuel mass is into useful work. How much nuclear energy we need? A: 1756 kg - but i should get a different answer with my numbers right?

Right. And I think you'll find that there should be a decimal place in that number: 1.756 kg.
 
  • #6
gneill said:
Right. And I think you'll find that there should be a decimal place in that number: 1.756 kg.
I believe OP uses decimal commas. 1,756 kg :smile:
 
  • #7
1.756 kg indeed it is. My mistake, but how do i find the 1.756 kg?
It looks like i need to use the already known amount of work energy of 16,2 TJ and find a the amount of fuel per 1 J? How do i get that?
 
Last edited:

Related to Energy needed to reach planets orbit and leave to leave it.

What is the energy needed to reach a planet's orbit?

The energy needed to reach a planet's orbit depends on multiple factors, such as the distance of the planet from the sun, the mass of the planet, and the spacecraft's velocity. It also varies depending on the desired orbit and the method of travel.

How is the energy needed to reach a planet's orbit calculated?

The energy needed to reach a planet's orbit is calculated using the rocket equation, which takes into account the mass of the spacecraft, the velocity required to reach the orbit, and the specific impulse of the propulsion system. It is a complex calculation that requires precise measurements and calculations.

How much energy is needed to leave a planet's orbit?

The energy needed to leave a planet's orbit, also known as the escape velocity, is determined by the mass and radius of the planet. The larger and more massive the planet, the greater the escape velocity required. For Earth, the escape velocity is about 11.2 kilometers per second.

Can a spacecraft use the planet's gravity to conserve energy?

Yes, a spacecraft can use a planet's gravity to conserve energy and "slingshot" around it to gain speed and change direction. This technique, known as a gravity assist, is commonly used in space missions to save fuel and increase speed.

How much energy is needed to leave our solar system?

The energy needed to leave our solar system is significantly greater than that needed to leave a planet's orbit. It would require a spacecraft to reach the escape velocity of our galaxy, which is approximately 550 kilometers per second. This would require a tremendous amount of energy and is currently beyond our current technology capabilities.

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