How much more would you weigh on Jupiter than Earth? Show your work.

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UpStudy AI · Accepted Answer

To determine how much more you would weigh on Jupiter compared to Earth, we'll use the concept of **gravitational force**, which is commonly referred to as weight. Weight depends on both your mass and the gravitational acceleration of the planet you're on.

### **Formula for Weight**

The weight $$ W $$ of an object is calculated using the formula:

$$
W = m \times g
$$

Where:
- $$ W $$ is the weight,
- $$ m $$ is the mass of the object (your mass),
- $$ g $$ is the gravitational acceleration at the planet's surface.

### **Gravitational Acceleration Values**

- **Earth**: The standard gravitational acceleration ($$ g_{\text{Earth}} $$) is approximately **9.807 m/s²**.
- **Jupiter**: The gravitational acceleration ($$ g_{\text{Jupiter}} $$) is approximately **24.79 m/s²**.

### **Calculating the Difference**

1. **Determine Your Mass**

Let's denote your mass as $$ m $$. It's important to note that mass remains constant regardless of the planet you're on.

2. **Calculate Your Weight on Earth**

$$
   W_{\text{Earth}} = m \times g_{\text{Earth}} = m \times 9.807 \, \text{m/s}²
   $$

3. **Calculate Your Weight on Jupiter**

$$
   W_{\text{Jupiter}} = m \times g_{\text{Jupiter}} = m \times 24.79 \, \text{m/s}²
   $$

4. **Determine How Much More You'd Weigh on Jupiter**

To find out how much more you would weigh on Jupiter compared to Earth, divide your Jupiter weight by your Earth weight:

$$
   \frac{W_{\text{Jupiter}}}{W_{\text{Earth}}} = \frac{m \times 24.79}{m \times 9.807} = \frac{24.79}{9.807} \approx 2.53
   $$

This means you would weigh approximately **2.53 times** more on Jupiter than on Earth.

### **Example Calculation**

Suppose your mass is **70 kg**.

1. **Weight on Earth**:

$$
   W_{\text{Earth}} = 70 \, \text{kg} \times 9.807 \, \text{m/s}² \approx 686.5 \, \text{N} \quad (\text{Newtons})
   $$

2. **Weight on Jupiter**:

$$
   W_{\text{Jupiter}} = 70 \, \text{kg} \times 24.79 \, \text{m/s}² \approx 1,735.3 \, \text{N}
   $$

3. **Comparison**:

$$
   \frac{1,735.3 \, \text{N}}{686.5 \, \text{N}} \approx 2.53
   $$

So, a 70 kg person would weigh approximately **1,735.3 Newtons** on Jupiter compared to **686.5 Newtons** on Earth.

### **Conclusion**

You would weigh **about 2.53 times more on Jupiter** than you do on Earth due to Jupiter's stronger gravitational pull. This multiplier is derived from the ratio of Jupiter's gravitational acceleration to Earth's.
You would weigh about 2.53 times more on Jupiter than on Earth.

How much more would you weigh on Jupiter than Earth? Show your work.

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